Out In Left Field

Math problems of the week: tasks for families in Investigations vs. Singapore Math

2012-02-02T08:38:00.000-05:00

I. The explanations and tasks that (TERC) Investigations explicitly gives to parents as part of its 3rd grade measurement unit [click to enlarge]:

II. The explanations and tasks that Singapore Math explicitly gives to parents as part of its 3rd grade measurement unit [no clicking necessary]:

III. Extra Credit:
Which curriculum shows more respect for parents: the one that explicitly involves them in teaching, or the one that doesn't.

Left-brainedness, working in groups, math education, No Child Left Behind

2012-01-31T08:24:00.003-05:00

And other fun topics!

My pre-TEDx talk interview on WITF public radio in Harrisburg is now up:

http://www.witf.org/smart-talk/the-brain-and-education

(Podcast here)

What we're missing at school

2012-01-29T08:31:00.003-05:00

Every once in a while I have doubts about homeschooling my daughter. Am I a good enough teacher? Is it wrong to keep her out of her neighborhood school (a school so coveted relative to its alternatives that parents line up outside all night to secure a spots)? Especially given that there are, theoretically, so many more opportunities for social interaction? No sooner do these doubts start emerging, however, than they are nipped in the bud by a casual conversation with a neighborhood parent.

One parent recently told me that her 5th grade daughter is so overwhelmed with homework that she's only able to do (non-academic) after-school activities on Fridays.

Another parent reminded me of how frustrated everyone is with the Investigations math curriculum, and of how intransigent the school leadership continues to be.

But most validating of homeschooling was what I've been hearing about the just-completed 5th grade Native American history unit. Students had no textbooks; the material was instead dispersed across various photocopied handouts. Some of the content, apparently, was only delivered orally in class, such that students were able to study it only if they'd taken decent notes.

Dominating the unit was the big project. The teachers assigned each student a tribe. The students then had to track down "5 different types of sources" on that tribe--i.e., they couldn't rely only on articles and books. Browsing the Internet, and somehow finding age-appropriate material there, was part of the task. From these 5 different types of sources they had to take notes and, ultimately, create a power point presentation that they presented to the rest of the class. The project was particularly daunting for a couple of students from broken homes, who had to transport materials between two separate homes, and whose parents had to keep track of what was happening at their ex-partners' houses.

The unit grade was based not just on the project, but on a test of the general material (those handouts and notes, which perhaps also amounted to "5 different types of sources"). Test questions ranged from factual ones about trade, to ones like "Discuss the different theories about how Native Americans got established in North America."

It stikes me that, for all the content in this unit--and there was quite a bit--the ultimate goal couldn't have been to teach content. Content, after all, is no longer fashionable in an age where you can look everything up on the Internet (except, say, when Wikipedia is protesting SOPA). If your ultimate goal was 5th graders learning content, why on earth would you not provide them with a good souce for it: a single source that organizes and integrates all the material they're supposed to learn and report on... at a 5th grade reading level?

The ultimate goal, I'm guessing, was instead to teach "higher-level" research skills.

How did students do without textbooks? One teacher announced to her class that the grades on the test ranged from 100 down to 20 (out of 100). One parent, whose bright, history-buff of a son got a B, suspects that those who got As were intensively grilled by their parents, and that the grades were generally quite low. Given the lack of a textbook and the teacher's reliance on the ability of 10 and 11-year-olds to take notes and keep track of multiple handouts, one can certainly see why.

In my world of graduate school teaching, if faced with such poor student test performance, we instructors would not be able to stop ourselves from worrying that we're doing something wrong. This, despite the fact that our students are much older and presumably more capable of taking responsibility for their own learning than 10 year olds are. What can I do differently next time, I would ask myself, either in terms of how I present the material, or in terms of what incentives I give students to keep on top of it, so that they learn it more thoroughly?

Perhaps I'm wrong, but it seems to me that not enough K12 teachers, at least at our local public school, engage in this sort of reflection. Admittedly, it may be only because they are never evaluated, as I am, by the students (or by the relevant adults: the students' parents)--in which case perhaps they should be.

What's much more likely to happen at our local public school is one of two things. If most of the class fails a test, the teacher sends an angry note home to parents. If only a few students perform poorly, the underperforming students, whose Executive Functioning, attention skills, and handwriting skills weren't up to the task, are red flagged as kids who may have learning disabilies and need Individualized Education Plans. Little changes in the regular classroom, but the Learning Support teacher (after the year-and-a-half-long wait list and evaluation process finally reach their conclusion) adds a few more students to his case load.

Letter in the today's Times

2012-01-28T10:38:00.001-05:00

...on what the narrowing of the definition of the definition of autism means in light of current trends in education: here.

Math problems of the week: traditional geometry vs. integrated mathematics

2012-01-27T08:04:00.003-05:00

Introducing proofs, II: expressing logical premises vs. "finding out" how logic is being used.

I. In Traditional Geometry, via Alison and Wonderland (Weeks & Atkins A Course in Geometry, pp. 38-9) [click to enlarge]:

II. In Integrated Math, via Edgar Allen Poe (Integrated Mathematics 2 (2002) p. 407) [click to enlarge]:

III. Extra Credit:
Which text invites greater literary appreciation?

Drawing the wrong conclusions from Race to Nowhere

2012-01-25T07:41:00.002-05:00

I finally had a chance to see Race to Nowhere, the movie everyone's been talking about (including yours truly) but few have had seen (seeing as it isn't playing in movie theaters).

Today's kids are stressed out--yes. Perhaps as never before. They seem to be spending less and less time playing than ever before. They may be getting more homework, and less sleep, than ever before. More and more of them are more stressed out than ever about getting into college and landing a decent job. The AP exams appear to be giving record numbers of students record levels of stress. All these things are true.

But many of the conclusions that the movies draws from all this are simply wrong, and serve merely to further entrench certain of our most problematic current practices. For example:

It's not the curriculum; it's the teacher. Sorry, it's both. The best teacher in the world can't teach decent math if all she has is TERC Investigations, especially if she's threatened with punishment for insubordination if she deviates from the curriculum.

Pressure to raise test scores prevents teachers from using methods that we know do work, like group activities and project-based learning. Sorry, but we don't know that these methods work better than their alternatives; in fact there's plenty of evidence that they don't. What the pressure to raise those No Child Left Behind test scores has instead done is cause schools to dumb down the curriculum and ignore the most capable students.

AP tests should be abolished. These do seem to be a growing source of stress, with record levels of failure, but as I noted earlier:

All those watered-down math and science classes and content-impoverished social studies classes disadvantage even our top students, such that by the time they reach high school it's hard--and extremely stressful--for them to make up for lost time, whether in math, biology, chemistry, or history.

The fact that record numbers of college students are having to take remedial classes shows that we are going about teaching them the wrong way. Yes, indeed. But the answer isn't to replace AP classes with even more group-centered, project-based learning. AP classes, in fact, are one of the few remaining ways in which we can hold high schools accountable for preparing students for non-remedial, college-level work.

The movie also overlooks or downplays some key issues. Much of the decline in free play, and much of the increase in childhood stress, has nothing to do with schools, but stems from excessive screen time at home, overly structured day care, restricted outdoor activities (our paranoia about pedophilia and playground accidents exceeding our paranoia about childhood obesity), and over-scheduling (all those sports; all that music, dance, and theater; later on, all those college resume-builders).

Much of the excess of today's homework takes the form of those time-consuming, high-ratio-of-effort-to-learning, and often organizationally-nightmarish and developmentally inappropriate busywork assignments favored by the Project Based Learning model that the movie, at least in places, implicitly endorses. Cut all that out, along with the summer projects, and pressure would decrease substantially, and open-ended play time could start making a comeback--the more so if schools would start reviving recess and parents would stop overscheduling.

Much of the stress of the college rat race comes from parents resorting to outside tutoring to make up for the deficiencies they perceive in their children's schooling, and from increasing competition from better-prepared overseas applicants whose schools haven't yet abandoned rigorous academics. The terrible employment situation only makes people crazier.

Finally, Race to Nowhere leaves out the possibility that intense academic challenges can be sources of joy, of flow. Set up properly. Yes, in that sense, it is the teacher (not just the curriculum). With a rigorous curriculum and a teacher who both understands it and knows how to teach it, kids can not only Run Somewhere, but perhaps even Run a Marathon.

The attack on science is bipartisan, II: The Enlightenment

2012-01-23T07:24:00.005-05:00

I'm a big fan of the Enlightenment. OK, not all of the individual philosophers that people have associated with it were truly enlightened (some were rather narrow-minded, even racist), but as for the Enlightenment's spirit and research program as a whole, I cherish it as a grand, left-brained entity, dominated by worthy stances like curiosity, skepticism, meticulous analysis, and humility before strict standards of truth.

As such, naturally, it is a thing that our right-brain world likes to marginalize or outright reject--to an extent that goes largely unappreciated.

Many political partisans, in particular, are in denial about just how bipartisan today's Enlightenment-bashing has become. Consider a recent New York Times book review of Randall J. Stephens and Karl W. Giberson's book The Annointed: Evangelical Truth in a Secular Age. Singling out "evangelical Americans" in particular, reviewer Molly Worthen writes:

The central question of the culture wars that have raged since the 1970s is not whether abortion is murder or gay marriage a civil right, but whether the Enlightenment was a good thing.

It's certainly true that many devoutly religious people, many them on the right, fault the Enlightenment for its scientific reductionism and insistence on scientific truth. But so do many postmodern/critical theorists (Foucault and his acolytes), education professionals, and New Age types, many of them on the left. The Enlightenment troubles these people not because it undermines religious truth, but because it undermines their religious-like beliefs in the instability and/or relativity of truth (as in "there's no one right answer"), and/or in certain types of magical thinking. For them, the Enlightenment's reductionism is unsettling not necessarily because it threatens to reduce human souls and religious spiritualism to neurology, but because it threatens to have a similar effect on our emotions, aesthetics, and secular spiritualism. Some also believe that the Enlightenment has led, among other things, to conquest, state-sponsored violence, economic exploitation, and environmental degradation (see, for example, The Debate About the Enlightenment.)

Most Enlightenment skeptics, of course, are far less extreme, whether they hail from the right or the left. As Worthen herself notes in connection with the evangelical right:

The “parallel culture” that “The Anointed” vividly describes... is not a bald rejection of Enlightenment reason, but a product of evangelicals’ complex struggle to reconcile faith with the life of the mind... Their promises to reconcile the Bible with modern thought do not conceal that this balancing act has forced evangelicals to live in a crisis of intellectual authority — a confusion so unabating that it has become the status quo.

The same might be said, mutatis mutandis, of many postmodern thinkers, "critical theorists," and secular spiritualists on the left.

Indeed, the bipartisan nature of our society's discomfort with the Enlightenment is seen also in its discomfort with Darwinian evolution (another "reductionist" theory that people have blamed for racism and other scourges). But here the crackpots on the right are so strongly, and so publicly associated with rejecting evolution that those on the left who also reject certain aspects of it aren't nearly so open and public about this.

Solitude is out of fashion, but maybe it's finally becoming fashionable to say so

2012-01-21T08:59:00.026-05:00

Finally, a prominent NY Times piece that breaks the Group Think mold: Susan Cain's opinion piece in this past weekend NYTimes' Week in Review on... Group Think.^*

Solitude is out of fashion. Our companies, our schools and our culture are in thrall to an idea I call the New Groupthink, which holds that creativity and achievement come from an oddly gregarious place. Most of us now work in teams, in offices without walls, for managers who prize people skills above all. Lone geniuses are out. Collaboration is in.

We see this, in particular, in society's reaction to Jobs' death (which I blogged about earlier):

In the wake of Steve Jobs’s death, we’ve seen a profusion of myths about the company’s success. Most focus on Mr. Jobs’s supernatural magnetism and tend to ignore the other crucial figure in Apple’s creation: a kindly, introverted engineering wizard, Steve Wozniak, who toiled alone on a beloved invention, the personal computer.

Although I remain skeptical that most of us spend most of our working hours interacting constantly in group offices, Cain writes:

Virtually all American workers now spend time on teams and some 70 percent inhabit open-plan offices, in which no one has “a room of one’s own.”

Her impression of elementary school classrooms, on the other hand, is something I and others have blogged about repeatedly--though try telling this to the many NYTimes (and other) reporters who think it's headline news whenever they see this:

Today, elementary school classrooms are commonly arranged in pods of desks, the better to foster group learning. Even subjects like math and creative writing are often taught as committee projects.

Acknowledging that:

Some teamwork is fine and offers a fun, stimulating, useful way to exchange ideas, manage information and build trust.

Cain draws the same distinction that I do between divvying-it-up collaboration and interacting-constantly cooperation:

But it’s one thing to associate with a group in which each member works autonomously on his piece of the puzzle; it’s another to be corralled into endless meetings or conference calls conducted in offices that afford no respite from the noise and gaze of co-workers.
...

Recent studies suggest that influential academic work is increasingly conducted by teams rather than by individuals. (Although teams whose members collaborate remotely, from separate universities, appear to be the most influential of all.)

Cain cites several studies showing the various downsides to cooperation (vs. collaboration). First, there's creativity:

Research strongly suggests that people are more creative when they enjoy privacy and freedom from interruption. And the most spectacularly creative people in many fields are often introverted.

Then there's physical and emotional health:

Studies show that open-plan offices make workers hostile, insecure and distracted. They’re also more likely to suffer from high blood pressure, stress, the flu and exhaustion.

Then there's productivity and quality of work:

People whose work is interrupted make 50 percent more mistakes and take twice as long to finish it.

Cain cites the Coding War Games, a study that compared the work of more than 600 computer programmers at 92 companies:

What distinguished programmers at the top-performing companies wasn’t greater experience or better pay. It was how much privacy, personal workspace and freedom from interruption they enjoyed. Sixty-two percent of the best performers said their workspace was sufficiently private compared with only 19 percent of the worst performers. Seventy-six percent of the worst programmers but only 38 percent of the best said that they were often interrupted needlessly.

Even one of the few elements of cooperative interactions I had thought was beneficial, it seems, isn't so:

Brainstorming sessions are one of the worst possible ways to stimulate creativity.. People in groups tend to sit back and let others do the work; they instinctively mimic others’ opinions and lose sight of their own; and, often succumb to peer pressure. The Emory University neuroscientist Gregory Berns found that when we take a stance different from the group’s, we activate the amygdala, a small organ in the brain associated with the fear of rejection. Professor Berns calls this “the pain of independence.”

Indeed, one has only to recall the Solomon Asch experiments to see how true that is.

Cain's recommendations?

Our offices should encourage casual, cafe-style interactions, but allow people to disappear into personalized, private spaces when they want to be alone. Our schools should teach children to work with others, but also to work on their own for sustained periods of time. And we must recognize that introverts like Steve Wozniak need extra quiet and privacy to do their best work.

This sounds reasonable, thought it's never been clear to me how qualified teachers (as opposed to psychologists and social workers) are to teach children how to work with others. To most children cooperation comes naturally, though some of them may need reminders and incentives. Less social children may need social skills groups run by trained therapists. Teachers should certainly encourage children to be kind and helpful, but I woiuldn't call that "teaching children to work with others."

More powerful than Cain's recommendations are the recommendations she cites from Apple's other Steve:

“Most inventors and engineers I’ve met are like me ... they live in their heads. They’re almost like artists. In fact, the very best of them are artists. And artists work best alone .... I’m going to give you some advice that might be hard to take. That advice is: Work alone... Not on a committee. Not on a team.”

------------------------------
^*It's worth noting, however, that three of the four responses published a few days later in the Times Letters were negative.

Math problems of the week: traditional geometry vs. Integrated Mathematics

2012-01-19T09:40:00.000-05:00

Introducing postulates and proofs: group games vs. whole-class discussion

I. From the beginning of the 1961 Weeks & Atkins A Course in Geometry "Proof" chapter (Chapter 3, p. 36):

II. From the middle of the 2002 Integrated Mathematics 2 (2002) "Logic and Proof" unit (Unit 7, p. 406):

III. Extra Credit:

Weeks & Atkins A Course in Geometry has two authors; Integrated Mathematics 2 has 35 authors (12 "senior authors," 8 "editorial advisers and reviewers," 8 "manuscript reviewers," and 7 "program consultants"). Write a theorem that relates the number of authors to:
1. the weight of the textbook.
2. the quality of the textbook.

Group projects in real life

2012-01-17T08:02:00.003-05:00

The media is almost as infatuated with the idea of large, hands-on, scientific collaborations as it is with the idea of cooperative, hands-on learning in the classroom. We see this most recently in a front-page article in a recent New York Times Science Section: a puff piece on the career of Eric Lander, who went from the "monastic" world of esoteric mathematics to the collaborative world of molecular biology, medicine, and genomics.^*

Of course, there's a connection between these two objects of media infatuation. One of the most commonly cited justifications for group projects in K12 classrooms is the increasingly collaborative world of STEM. And one of the most common critiques of my book is that it overlooks the purported fact that most of today's professionals work in groups.

I take pains in my book to lay out (twice) the key distinction between collaboration and cooperation--a distinction so essential that I also included it as an index entry ("collaboration vs. cooperation") and will once again excerpt some of the relevant passages here:

There's an important difference, people forget, between cooperation and collaboration. Yes, many modern mathematical and scientific puzzles are large enough that multiple scholars attack them simultaneously. But they do so not by divvying up the pieces, working independently, and only reconvening to present and tweak one another's solutions. They collaborate, but they mostly work separately, not cooperatively. (p. 42; italics as in the book).

...

In more cooperate settings, a single person is typically in charge, assigns specific tasks, and sends people back to their cubicles. Indeed, it's the cubicle, not the conference table, that predominates in most offices. (p. 194).

In the group activities that predominate in today's classrooms, in contrast, students are supposed to sit together, work together, and help each other out throughout the entire process--not just during periods of brainstorming or of combining their respective results.^**

There are other key differences between the K12 ideal and the professional reality. The former is a mixed-ability group assigned by the teacher in which all the students get the same grade. As blogger and economics professor Bryan Caplan points out in a recent post entitled How to Fix Group Projects:

If we really wanted to use group projects to prepare students for the world of work, then, we'd totally change the incentive structure. Away with equal status, equal rewards, and democracy! Instead:

1. The teacher would begin by selecting the best students to be team leaders.

2. Team leaders' grades would be based on their group's performance.
3. The team leader, not the teacher, would grade his own team members, using a budget of points based on his group's overall performance.

Such an incentive structure, Caplan argues, will result in grades that (like real-world raises and bonuses) reflect performance:

Since the team leader wants to maximize group performance, he has a strong incentive to reward performance and punish its absence.

Moreover:

To improve the system further, the teacher would demote underperforming leaders to the ranks, promote the best-performing non-leaders to leadership roles, and allow quits and firing.

Caplan acknowledges that not everyone will cotton to his scheme:

Many people will object that team leaders might "play favorites." Clearly some would. But at least they'd pay the price: Team leaders who reward incompetents will get lower grades themselves - and have trouble retaining talent (and their leadership positions!) if there's repeated play. In any case, if we're trying to teach people about the real world, isn't learning how to handle and cope with favoritism a vital skill?

Another objection might be that team leaders would be uncomfortable giving unequal grades to fellow students. Fair enough. But at least leaders would pay the price for their own squeamishness. And once again, they learn a vital skill: to put your feelings aside and judge people on their merits.

But, thinking again in terms of real-world incentives, Caplan acknowledges that teachers have "less than zero incentive" to teach these particular real-world skills via these particular real-world protocols.

-----------
^*A key exception to this trend is this past NYTimes Weekend Edition's front-page article on Groupthink, which I will be writing about later this week.
^**The Groupthink article suggests that, at least at certain companies, the collaborate-by-divvying-up model is shifting towards the cooperative-by-sitting-together one. While I'm guessing that the collaborative model still predominates (especially in academia, where people do still have rooms of their own and bosses can't force them to "inhabit open office plans"), were I rewriting my book in light of this article, I would acknowledge the trend and specify that the most effective of today's workplace collaborations involve "divvying up the pieces, working independently, and only reconvening to present and tweak one another's solutions."

"Creative" interview questions

2012-01-15T08:41:00.001-05:00

Next up in my end-of-2011 article catch-up is a Wall Street Journal piece on the growing trend by companies to ask off-beat questions in their interviews of prospective employees. Pioneered by Google, these include questions like:

You are shrunk to the height of a nickel and thrown into a blender. Your mass is reduced so that your density is the same as usual. The blades start moving in 60 seconds. What do you do?

Design an evacuation plan for San Francisco.

Use a programming language to describe a chicken.

What is the most beautiful equation you have ever seen? Explain.

The reasoning behind such questions, explains reporter William Poundstone, is:

that Google isn't looking for the smartest, or even the most technically capable, candidates. Google is looking for the candidates who will best fit Google.

Eerily reminiscent of the open-ended "creative" questions on the Aurora Battery, a giftedness-screening test that Robert Sternberg has proposed as a replacement for the traditional IQ test, and on the college entrance exam that Mr. Sternberg has designed as a replacement for the SATs, such questions presume that the best way to measure people's creativity is to gauge their spontaneous responses to off-beat, open-ended questions. As Poundstone notes:

By design, none of these questions has a right answer. This has led to intense speculation and even paranoia among Google job candidates. It's also led to other companies adopting Google-esque questions without having any idea what constitutes a good answer.

Copy-cat questions from AT&T, Johnson & Johnson and Bank of America (respectively) include:

"If you could be any superhero, who would it be?"

"What color best represents your personality?"

"What animal are you?"

Unfortunately, there's no more evidence that this kind of question actually does measure creativity--especially of the sort that's relevant to the given workplace--than there is evidence that the ability to write spontaneously from an off-beat prompt measures the kind of creativity it takes to be a good creative writer. The main effect of such questions may instead be to screen out the many left-brainers who clam up when asked for their spontaneous responses but who may be extraordinarily creative when it comes to search engine optimization, telecommunications, pharmaceuticals, and investment banking.

Math problems of the week: 4th grade Investigations vs. Singapore Math

2012-01-13T08:06:00.002-05:00

I. A 4th grade (TERC) Investigations homework assignment, assigned in early January:

II. An assignment from the very beginning of the 4th grade Singapore Math curriculum (Primary Mathematics 4B, pp. 40-41):

III. Extra Credit:
If you were a foreign power intent on undermining the technological future of the U.S., which math curriculum would you hire conspirators to sell to the U.S. education establishment?

Adding academic value now; improving quality of life later

2012-01-11T07:42:00.002-05:00

Time to catch up on some articles I missed over the last few weeks. First, there's the much-reported-upon NBER (National Bureau of Economic Research) working paper entitled "The Long-Term Impacts of Teachers: Teacher Value-Added and Student Outcomes in Adulthood". Here, researchers Raj Chetty (Harvard Economics Department), John N. Friedman (Harvard Public Policy Department), and Jonah E. Rockoff (Columbia Business School) find evidence that teachers who improve their student test scores the most in the short run also improve these students' more general life circumstances in the long term.

Defining a teacher's "value added" as:

The average test-score gain for his or her students, adjusted for differences across classrooms in student characteristics (such as their previous scores).

They note that:

When a high value-added (top 5%) teacher enters a school, end-of-school-year test scores in the grade he or she teaches rise immediately...

And that:

Students assigned to such high value-added teachers are more likely to go to college, earn higher incomes, and less likely to be teenage mothers. On average, having such a teacher for one year raises a child's total lifetime income by $9,000.

Significantly, none of the authors is a professor of education. What will the education establishment make of their results? Perhaps it will simply ignore them. Perhaps it will counter that test scores and salaries aren't meaningful measures of learning and well-being. Perhaps it will dismiss the article as an as-yet-un-peer-reviewed working paper. Or perhaps it will reverse the article's causal (short term -> long term) connections, fuzz-up the variables, and thereby concoct yet more reasons for refrains like "To Boost Learning, Start With Emotional Health".

What it won't do, I predict, is consider the possibilities that academic achievement can foster emotional well-being, that test scores might correlate with general success in life, and that schools should seek to fill as many teaching slots as possible with those who raise test scores the most.

Autism Diaries XXXII: But is he psychotic?

2012-01-09T07:55:00.003-05:00

So J takes pleasure in upsetting other people--a pleasure intense enough to drive much of his social interaction--and to have made me wonder whether, in addition to being deaf and autistic, my son might also be psychotic.

Especially since his mischievous perspective-taking may be unusual for autism. I suspect that most kids with autism checklist scores are as high as J's are neither as interested in other people's reactions, nor as capable of anticipating those reactions, as he is. And that it's more common for their various misbehaviors and social "mistakes" to fade rather than to intensify when people manage to convey to them the effect they're having on others.

But is J really a devious psychopath who derives pleasure whenever others feel pain? I had only to ask myself this question a couple of times before realizing something. It's not pain in general, but anger, frustration, and embarrassment, that J gets off on. And the pleasure he feels isn't general joy, but amusement in particular. In other words, he's not someone who feels happy when he sees (or imagines) people suffering; rather, he's a kid who thinks it's funny when he sees (or imagines) people getting angry, frustrated, or embarraassed--and what inspires his mirth is more people's overt reactions than their internal feelings.

In this respect, is he really that different from the rest of us? I'm thinking of all the times I've had to stifle a laugh when watching certain people lose their tempers; of all the amusement I get from shows and movies in which certain characters make fools of themselves or go apoplectic with rage (my first taste of this: the hapless, short-tempered Otto the Director from Electric Company). Indeed, aren't lost tempers, awkward moments, and public humiliations the basis for some of our most comical fictional scenes--even when the victims are characters for whom we also feel sympathy? Think Faulty Towers, The Office, or Curb Your Enthusiasm. What is it about watching someone lose his temper, or get stuck in an awkward, embarrassing situation, that people find so amusing?

For most of us, of course, such scenes are most entertaining when fictional. In real life, we tend to empathize, at least somewhat, with the victims, and this empathy tends to temper our mirth. What distinguishes J from the rest of us, perhaps, isn't so much that he finds anger and embarrassment so amusing, but that, lacking the gut-level empathy that typical people feel towards flesh and blood humans, he treats real life people as fictional characters.

Indeed, if J sees the social life around him as one big interactive sitcom whose interacting audience consists of just one person, that would explain quite a bit about the one-of-a-kind comedy with which he's been entertaining all those around him for going on 15 years.

Autism Diaries XXXI: Mischievous perspective-taking

2012-01-07T08:06:00.001-05:00

"Just tell him what your perspective is. Tell him how if he turns the lights off while you're trying to cook supper, you can't see what your doing."

This advice, given to us over a decade ago by the first psychiatrist to identify J as autistic, is as misguided now as it was back then.

Back then, it was misguided because J had neither the linguistic skills, nor the basic psychological reasoning skills, to even begin to understand things like "If you turn the lights off, Mommy can't see."

Now it's misguided because J has these skills and derives delight from frustrating others. In fact, one of his latest interests is, as he puts it, "to see people's reactions." "How did you react when you saw me filming fans in the restaurant?" he asks, hoping to hear that we felt embarrassed.

People who know little more about autism than that it involves difficulty with empathy can be forgiven for assuming that the way to address J's mischief is to tell him how much it upsets people. So again and again we hear well-meaning friends or relatives telling him, or telling us to tell him, how "it really hurts my feelings when you do that." But anyone who spends even a few hours trying to understand him, assuming that their empathy skills equal or exceed his, quickly realizes that this strategy is, as the behaviorist say, "reinforcing" rather than "aversive." In other words, it makes J more rather than less likely to repeat his behavior. And, in fact, those who have carried on the most with J about how upset he makes them feel are the most likely to be repeated targets of his mischief.

My advice to all who deal with J is to minimize all clues about their reactions (J already knows all he needs to know about these!), and instead to tell him in a quiet, deadpan voice about the kinds of consequences that actually upset him--especially the more intrinsic consequences, like the priviledges that get withheld when people no longer trust him, no longer want to help him or play with him, or (especially for those who own ceiling fans or Wiis) no longer want to invite him into their houses.

This concludes the Favorite Comments of 2011

2012-01-06T17:05:00.000-05:00

Thanks again for all your great comments. Now it's time for me to start writing my own posts again. I'll be back tomorrow with a new one.

TerriW on Artsy science

2012-01-06T08:07:00.000-05:00

(http://oilf.blogspot.com/2011/12/artsy-science-what-about-sciency-art-iv.html)

TerriW said...

You know, scientists often need to communicate with one another via written or oral methods (let's call it "Language Arts"), and it would be very powerful if schools could somehow incorporate this into their STEAM training. We could call it LASTEAM.

Wouldn't that be great? It would be an education with specific focus on Language Arts, Science, Technology, Art and Math!
Hmm. But you know, scientists often have to communicate with colleagues in other countries, it would be so powerful if we added a specific focus on foreign language, too. We could call it FLASTEAM!
But, wait! I have read that regular exercise allows people to think more clearly, perhaps if were to add some sort of fitness training -- let's call it Gym -- that would really intensify the synergy. Let us call it: FLAGSTEAM!

Jerrid Kruse, MagisterGreen, and Barry Garelick on Why open-ended projects aren’t so open after all

2012-01-05T07:58:00.000-05:00

http://oilf.blogspot.com/2011/12/why-open-ended-projects-arent-so-open.html)

Jerrid Kruse said...

You are setting up a strawman here. "open ended" does not me "without constraint". Furthermore, being told exactly what to do & structure are different ends of a spectrum. Most advocates of open ended assignments are working against the assignments that provide so much detail that all decisions are made for students. Constraints are important, but your argument gives teachers an excuse to do all the thinking for their students.

MagisterGreen said...

People mistakenly equate the words "creative" with "new and original". Providing students with guidelines and restrictions is not equivalent to making decisions for them or doing any, much less all, of the thinking for them. This inability, or unwillingness, to unyoke the idea behind "creative" from the idea of "new and original" is responsible for a great deal of the garbage foisted upon students as "projects".

“Art consists of limitation. The most beautiful part of every picture is the frame.” - G. K. Chesterton

Barry Garelick said...

"Constraints are important, but your argument gives teachers an excuse to do all the thinking for their students."

If the students have the tools with which to do the thinking, that's one thing. But often such assignments are given before students are proficient at organizing and analyzing information.

We definitely should give students problems for which they have not seen the “worked example”. But there is some amount of scaffolding and preparation to get students to that step. The ed school approach is to skip a lot of the scaffolding in the belief that students will learn the information, procedural, organizational and analytical tools they need in order to solve the problem in a “just in time” sort of way.

Mnemosyne’s Notebook and bky on Final algebra problems

2012-01-04T16:49:00.000-05:00

(http://oilf.blogspot.com/2011/12/math-problems-of-week-final-algebra.html)

Mnemosyne's Notebook said...

As an algebra teacher, I can tell you that textbooks (and teachers) go with this approach because students cannot calculate the values of the polynomials even with calculators. Some of my fellow teachers say, "Oh, they'll always have calculators with them on their cell phones." My thinking is, "Oh, they'll always have their brains with them - so let's stuff that with some math." One of my state's GLOs is that students should be informed and ethical users of technology. Nothing about helping them have the ability to create any technology.

And only a freak might consider the possibility that some nasty solar flairs could leave us with severely diminished electronics capabilities for several years. Why would we want to prepare for that? Somewhere, someone else will make calculators for our kids if that ever happens. Why prepare them for a world that might not be exponentially snazzier than today?

bky said...

A note about tables. I have a jr son who is taking what purports to be a high-school level algebra course (he can get 1 year of credit for alg I when he gets to high school). It is trivial junk. One thing that is weird is how often they are given a table of (x, y) values and have to figure out, over and over again, whether the points fall on a line or a hyperbola. In the meantime they don't do much of anything that I consider algebra. I think algebra is about manipulating formulas and doing calculations to solve problems. For them it's tables and graphs, tables and graphs, tables and graphs,....

Their curriculum is an unholy alliance of Connected Math and a giant book published by Holt. The Connected Math is full of what I call fake word problems. There will be wordiness establishing some (irrelevant) context and then they graph some "data" points that will fall on a line, or a y = kx curve for positive x. Bleh.
I mean y = k/x curve. Over and over.

AmyP, FedUpMom, kcab and Anonymous on More front page accolades for hands-on classrooms

2012-01-04T12:55:00.001-05:00

(http://oilf.blogspot.com/2011/12/more-front-page-accolades-hands-on.html)

Amy P said...

Is there some sort of pre-written template available to the journalists who turn out these pieces? Ugh.
FedUpMom said...

Something tells me that newspapers don't put their ace reporters on the education desk. I think this reporter is lazy more than anything else, and just repeating tired old phrases he's heard somewhere before. "No more desks in rows?" That might have been news in 1960.

Katharine Beals said...

Interestingly, the notion that students still mostly sit in rows is perpetuated by contemporary shows like South Park. Of course, it's easier to film (or depict) a class of kids if they're all sitting forward, but what makes things convenient for cinematographers and animators also contributes to the distorted views of classrooms by people in general and (sloppy) ed journalists in particular.

kcab said...

Just to offer a different view, maybe the tendency for desks to be arranged in rows varies a lot? I can't recall very many of my kids' elementary school classrooms having desks arranged in rows, but middle and high school have tended toward straightforward rows. Some classes never are (science, music) but most seem to be.

Anonymous said...

My sister is a teacher and she is really opposed to kids sitting around tables. Her son has Aspergers and she said it makes focusing even harder for him. She says that kids by nature are easily distracted and that the last thing you want to do is arrange desks in a way that makes it too easy for kids to focus on anything other than the teacher.
From what she has said, desks arranged in rows are pretty rare in the schools she has taught in. Her daughter attends a charter school and they do have rows. Her son attends a public school and they don't use rows.
My daughter takes homeschool classes through a charter school. They have rows in some classes but large tables in others. It would be interesting to see some statistics on rows versus other arrangement.

KimS on 4th grade Investigations vs. Singapore Math

2012-01-04T07:53:00.002-05:00

(http://oilf.blogspot.com/2011/11/math-problems-of-week-4th-grade.html)

KimS said...

In a true Investigations school, like the one my children regrettably attend, answering "How did you solve 8 x 8" with "I know my times tables" will earn them a 0. Even "8 x 8 = 64" will earn them a zero. Counting all of the squares on the array and putting the numbers in each square (1 ,2, 3, 4, 5, 6...), however, will earn them full points. And challenging the classroom teacher when she awards zero for "8 x 8 = 64" and " i know my times tables", will give you the response, "I know he solved it correctly, but I'll get fired if I give him full points for answering that way."

Barry Garelick, Lsquared, kcab, and kathyiggy on Edworld double speak

2012-01-03T17:14:00.001-05:00

(http://oilf.blogspot.com/2011/11/on-edworld-double-speak.html)

Barry Garelick said...
"Mere facts" and "mere procedures" are the diminutives that I've heard professors use when referring to math education and other subjects. I heard a teacher admonish her algebra class that "You have to learn how to apply your knowledge to new situations", as if this is something that one can consciously do without the necessary undergridding leading up to problem solving.

Lsquared said...

"For years now I've found myself increasingly nauseated by phrases like "higher level thinking"..."

Yeah, looking at "standards based curricula" will do that to you.

kcab said...

I've had a similar change in response to those catch phrases… After all, who in the world wants to be against conceptual understanding or creativity (as they are defined outside of the ed-world)?

kathyiggy said...

What about "taking ownership of your learning"? That one annoys me to no end. They are also using that ownership stuff in professional development courses at work too.

Deirdre Mundy on Why we can’t trust math (and STEM) professors

2012-01-03T12:00:00.002-05:00

(http://oilf.blogspot.com/2011/11/why-we-cant-trust-math-and-stem.html)

Deirdre Mundy said...

I just realized something about 21st century skills.
When I was in High School, I was at an STEM magnet. We had excellent Math and Science. We also had some "21st century skills" type projects. For instance, we spent a lot of time doing presentations in Hypercard, learning to use Dialogue, and using Lynx to search the web.

Three years later, Google was ubiquitous. I still use my math, science, and even history of science. Dialogue and Lynx? yeah, right.

We can't predict what technological changes are coming--- time spent blogging or creating power point slides is wasted. It's better to focus on content, since that DOESN'T change, and new methods are easy to learn.

ChemProf, TerriW, Anonymous, and GPC on Why do so many college students defect from STEM?

2012-01-03T07:56:00.003-05:00

(http://oilf.blogspot.com/2011/11/why-do-college-students-defect-from.html)

ChemProf said...

I wonder about any calculation that including incoming "premed" majors. In my experience, many of these students aren't actually interested in STEM fields, but were told by parents that being a doctor was a good goal. They tend to fall away more often than students who want to study science or math.
Also, for a contrary view, see http://www.scientificamerican.com/article.cfm?id=does-the-us-produce-too-m

Of course, some of this is an oversupply of bioish majors, where they do seem to have trouble working (and where some students are apparently paying for grad school, which is always a danger sign).

TerriW said...

My local district (which we don't attend, we homeschool) has as their big draw a huge STEM focus (Project Lead the Way, a Fab Lab) ... and they still use Everyday Mathematics.
So. You've got very hands-on-ish engineering lite stuff to make it all seem so fun to gin up interest in the non-hardcore math/science folks coupled with a leaves-something-to-be-desired math curriculum.
What is this supposed to *do* exactly? Say they get some kids to go down the engineering path in college who wouldn't otherwise do so. Can I suppose that they wouldn't otherwise do so because they, perhaps, aren't particularly strong in math? And EM sure isn't giving them the rock solid foundation they need to make it through the wash out courses.

I can't help but think it's a well-intentioned recipe for failure.

ChemProf said...

That fits with what I see a lot, TerriW. We get a lot of students who are excited about science, but when you talk to them about what they like, it is "docent science" like you'd see at the zoo or aquarium. Which is fine, and a great volunteer opportunity, not but a great career path. It seems to be a result of lots of science appreciation but not so much real science (which can be abstract a lot of the time).

Anonymous said...

I just read through the Scientific American article and I have read something along these lines before. What's often ignored is that the scientists and engineers we produce often aren't as good as those in other countries. They are simply far less qualified due to a poorer education at the K-12 level.

Most American companies have canceled projects or plans for new divisions due to an inability to find enough qualified people to fill required jobs. If you need 50 scientists with specific skills and you only can find 20, you will either not go ahead with a project or you will go overseas. So, even those 20 qualified people have lost out on a potential job.

We need to produce more highly qualified scientists and engineers precisely so companies can go ahead with new projects and new divisions that will create full employment for STEM graduates. But that isn't going to happen with the continual dumbing down of education.

GPC said...

A couple of problems jumped out at me from the Scientific American article. First the suggestion that American students don't do as badly on the PISA test as we think. There is no doubt that maybe the top 10-15% of American students are getting a world-class education. The point is that this isn't nearly enough. So, how the top 5% compare on PISA isn't really all that important. How the top 40% or 60% compare is what's important. The top 5% to 10% can't provide all of the qualified graduates that the largest economy in the world needs.

"On tests comparing the U.S., Japan and five Western European countries, for example, white Americans on average substantially outscored the Europeans in math and science and came second to the Japanese. American whites came first in reading by a wide margin."

There is far smaller disparity between the performance of privileged and underprivileged students in Western Europe than in America. We may be producing more elites at the very top but Western Europe is producing far larger numbers of educated people overall. This explains why there is less social mobility in America than in Western Europe. Again, this elite cannot provide all the qualified workers that our economy needs. Of course, there also have been studies done that compared higher performing American students to high performing students in other countries. American students did pretty badly. I would be curious to know more about this particular study because it seems to be at odds with many other comparisons.
American companies are panicking about where their future workforces will come from. They wouldn't be doing this if there was an oversupply of qualified candidates coming out of high school and college. I used to interview people for jobs. I met so many young, white, middle class college graduates who had terrible writing and math skills. They lacked the most basic knowledge of their field. I recently met a middle class white college student doing volunteer work at a library book sale. He had to use a calculator to figure out $3.50 from $10 to give me my change. He told me that he is terrible at math. Yes, there are highly educated Americans. But not nearly enough. This is why the company I worked for had such a hard time filling jobs with great pay and benefits (including 4 weeks of vacation because it was a European company).

Secondly, the article focused a lot on the competition for jobs in academia and research. Are these the absolute only places science graduates can work? There are thousands of middle and high schools in this country that badly need people with science degrees to teach. I have read that more than half of American students are taught science by teachers who don't have degrees in the Sciences. Sure, if science graduates are looking for jobs in a limited number of places, there will be an employment problem. Finance graduates would also have an employment problem if they limited their job options to Wall Street firms only.

Anonymous said...

The Global Report Card (GRC) is a project that uses PISA data to determine how individual school districts perform on an international level. The Pelham School District in Massachussetts ranks in the 95th percentile. So, if you do a comparison using Pelham students, they will obviously outperform the competition. The Beverly Hills School District ranks at the 53rd percentile. So, if you use those students as the basis of a comparison, they would underperform.
According to the GRC, of the 50 richest school districts with populations of 50,000 residents (not students), almost half perform at the 50th percentile or below. Newton, Mass comes in at number 1 at the 80th percentile. I suppose you can break PISA results down in different ways. But the GRC does indicate that we have a crisis even with our more privileged students.

I briefly scanned the SA article. It did seem to focus a lot of Ph.Ds. I assume most Science majors don't actually earn Ph.Ds. I remember an article from a few years back. If I am correct, it was the American Academy of Sciences issuing a warning that America will face a serious shortage of scientists when the baby boomers leave the workforce. According to the article, most of this loss would be in public health, like food safety, water safety, etc. Science majors also go into various healthcare fields. Maybe there is an oversupply of Ph.Ds but I think the point about a serious shortage of science teachers is a good one. If we were overproducing science graduates, you would think there would be no shortage of science teachers. But there is. I could be wrong, but doesn't this suggest that science graduates have many other options available to them?

ChemProf said...

I think some of the problem in any of these discussions is grouping everything under "STEM." And some of it is the peculiar world of academia. The best science/math undergrads are often encouraged to go to grad school whether it makes sense or not, and whether it meets their goals or not. I've encouraged some students to consider high school teaching (and there are some tremendous scholarships out there for science folks; google Noyes Scholarship) but I'm in the minority.

Once in grad school, there is a lot of pressure to only consider jobs as research institutions. I entered grad school wanting to teach at a liberal arts college, but I remember applying to a UC for a job and having my advisor write to me "oh good, I'm so pleased to see this application because I want to see you live up to your potential." Thanks, Dad. Jobs at national labs or in industry are seen as inferior.

And we are actually seeing signs of oversupply in some biology fields (and if you see the most plaintive complaints, you'll see they are from bio people). Saw a former student complaining about her tuition costs for her PhD in plant biology, which is just wrong. Never had a chem student pay for the PhD.

Dawn on Jobs vs. Gates

2012-01-02T23:14:00.002-05:00

(http://oilf.blogspot.com/2011/11/jobs-vs-gates-right-brained-assumptions.html)

Dawn said...

"That is the formula for true innovation, as Steve Jobs’s career showed."

Yeah (she says snarkily), Bill Gates has done nothing revolutionary and world changing, has he?
I am one of those intuitive thinkers like Jobs but frankly I'm getting tired of the way that kind of thinking is valued over other kinds of thinking. I don't think genius should equal "magical" thinking. It seems too much like people looking for short cuts from the hard work that people like Gates fearlessly engage in.

Anonymous and Chemprof on Yet another front in the war against math…entrepreneurs

2011-12-31T17:43:00.000-05:00

(http://oilf.blogspot.com/2011/10/yet-another-front-in-war-against-math.html)

Anonymous said...

I find it odd that he chose Geometry to eliminate when it has so many practical applications. Couldn't you use knowledge of geometry, history, a foreign language or a bunch of other things as the basis of a successful business?

I'm a small business owner. I never took a course in entrepreneurship but I figured out how to create a business plan pretty easily. Millions of entrepreneurs figured out how to fill unmet needs without ever taking a high school course in how to do it. High schools usually offer business and finance classes that pretty much cover the financial stuff. They offer writing classes which cover how to write. And colleges offer Marketing courses.
All you need to learn to become an entrepreneur is already being offered at the high school or college level. An entrepreneurship course is completely unnecessary.

ChemProf said...

I think part of this push is a (poor) response to college for all. High schools no longer offer business or finance courses, because those aren't college prep, so now there is a push to move those courses into the college prep curriculum.

C_T on the Pitfalls and plusses of multiple choice tests

2011-12-31T12:37:00.000-05:00

(http://oilf.blogspot.com/2011/10/pitfalls-and-plusses-of-multiple-choice.html)

C T said...

Sometimes in college, I was lucky enough to have courses with great multiple choice exams. Not only did I feel like they were fairly assessing me, but I learned while taking the tests and felt stretched intellectually. That some tests are written poorly is no reason to demonize them as some people do; just write better ones.

Anonymous, Amanda, and Deidre Mundy on Autism and visual thinking

2011-12-31T08:34:00.001-05:00

(http://oilf.blogspot.com/2011/10/does-autism-really-mean-visual-thinking.html)

Anonymous said...

This is a very astute observation. People on the autistic spectrum do need extra prompts to capture and focus their attention (as do ADHD and ADD people). Providing a visual prompt that they can access constantly or repeatedly and on their own is a great help, and would explain why nonverbal children with autism are rarely taught sign language, which is visual but evanescent.

Amanda said...

Another hypothesis: good diagrams and other visuals can make underlying structure and linkages much clearer than a page of text or a teacher explanation on their own: maybe what seems to work with autistic children would actually be good for all children.

Deirdre Mundy said...

With respect to lists, organization methods, visual schedules, etc---

In my experience, the difference isn't that these things DON'T help normal people as well--it's that the ADHD kids need more overt instruction, practice and time with the organizational tools that seem to be second nature to the "normal" kids. The same goes for phonics, I think-- the kids I've seen who are "natural readers" also use phonics, they just picked them up without overt instruction.....

Anonymous on Who is Christopher Columbus?

2011-12-30T17:31:00.000-05:00

(http://oilf.blogspot.com/2011/10/autism-diaries-xxiv-who-is-christopher.html)

Anonymous said...

In our fair city, Christopher Columbus Day is not even celebrated (school's in session), apparently because he is seen as part of the "history of oppression." My children never learned about him in school and they learned about the Mayflower from library books (outside of school time).
Back in 2007, a note was sent to teachers about Thanksgiving saying: Fact: For many Indian people, 'Thanksgiving' is a time of mourning ... a bitter reminder of 500 years of betrayal returned for friendship.

Deirdre Mundy, Laura, and momof4 on Differentiated instruction in the one room school house

2011-12-30T12:24:00.001-05:00

http://oilf.blogspot.com/2011/09/differentiated-instruction-in-one-room.html

Deirdre Mundy said...

The other plus of the one-room school house was that grade-acceleration was easy and subject-based. If a first grader was a math whiz, he could just work on the third grade lesson and recite math with them, even if he needed to stay with his age mates for reading.

On the other hand, discipline was probably LESS of a problem since the majority of families who bothered to send their kids to school would punish them if they were disobeying the teacher......

I think the closest modern equivalent to the one room school house may be home schooling-- which is more possible now, since in Laura's day simply providing food and clothing for the household was a full time job for BOTH pioneer parents and their kids!

Also, the pioneer school day was shorter and had a long recess... but the school wasn't expected to provide social services, just education....

And (to be negative here) pioneer one-room schools weren't the norm--- in the East, there was enough population density to support larger schools and individual grades. (Compare Laura's experience in Minnesota to Betsy and Tacy's, only about 80 miles down the road and 20 years later! )

And pioneers were a self-selecting bunch, in terms of hard work and discipline-- school was more likely to be a treat than a punishment, whereas for the city kids the alternative to school wasn't working the farm, but wandering around buying candy and playing with the hordes of other kids.......

So I'm not sure we really could recapture the ideal...

Laura said...

I've done some work on my family history - and many of my relatives attended one room schoolhouses, or small schools. A couple were even school teachers. It is simply amazing to read their letters and diaries. Their level of knowledge, even if they only attended school to 6th grade or 8th grade, was more than our High School graduates today! (Not counting current events of course!).

My great-grandmother spoke only Swedish until she went to school, and only went until 8th grade. However, she could easily hold her own in any Community College today.

On the other hand, my daughter suffered through current educational practices for a few years, when she attended a local parochial school. It wasn't as bad as the local public schools, but they used a lot of group work, journaling and other constructivist methods.

So to answer your question - Yes, I would join you going back to the "Good, Ol' Days" of Schooling. In a heart-beat!

momof4 said...

My DH attended a Catholic ES where all the teachers were nuns and had been trained by their order. It sounds like the Normal Schools some of my ES teachers attended. In both cases, teacher preparation was both explicit and practical; no fuzzy theories, just math, phonics, grammar and the disciplines. Today, the teachers at Catholic schools have attended the same ed schools as the public teachers, so it's not surprising to see the same stuff in the parochial classrooms.

I also have relatives who had less than a HS education and who were far better-educated than today's HS grads (or better). I also had relatives who attended one-room schools until HS, and acceleration was common.

Deirdre; I loved the Betsy-Tacy books - haven't heard anyone else even mention them!

Anonymous and Laura on Special Education and Everyday Math, revisited

2011-12-30T00:14:00.001-05:00

(http://oilf.blogspot.com/2011/09/special-education-and-everyday-math.html)

Anonymous said...

I don't think the ones that could do this, i.e. modify teaching methods, include good material, teach to the students, rather than to the book, are permitted to do so by administrators that buy into a curriculum and require "fidelity" of instruction in that curriculum. Only.

Laura said...

When my daughter's school changed its math curriculum from a traditional one to a more constructivist one (Not as bad as Everyday Math - but bad enough) - school became a real struggle. It became the straw that broke this Mama's back. I couldn't explain the math to her, because I didn't "Get it!" 4th grade math... *sigh*

We ended pulling her out and homeschooling her and using Saxon Math. So much better. Night and Day difference. This year we switched to Abeka Math for other reasons (It is still very traditional and straight-forward - but keeps on one subject longer than Saxon).
I just cannot understand how "they" expect any children (especially autistic children) to learn any kind of math, from this load of garbage they have heaped upon the educational system. Unbelievable.

Niels Henrik Abel on 1900s math vs. Interactive Math Program

2011-12-29T17:27:00.003-05:00

(http://oilf.blogspot.com/2011/09/math-problems-of-week-1900s-math-vs.html)

Niels Henrik Abel said...

"Homework 1: Past Experiences:
"Include this so you can look back later and compare your experiences before this year to your experiences with the Interactive Mathematics Program."
(Student response)

Well, let's see. Last year I had geometry with Mr. Smith. He was a tough teacher, but I'm really glad I had him, because we actually learned how to do some proofs, which he said we'd need to know, especially if we want to take calculus and physics and understand all that stuff. I was psyched, because I had read about Newton and Leibnitz and Kepler, and I really wanted to learn about this magical calculus that allowed them to understand some of the mysteries of nature. I was supposed to take intermediate algebra and trig this year, but they changed the math program and I got stuck with this stupid "Interactive Mathematics" thing. There's hardly any math at all, and what little there is is not going to help me at all when I finally do manage to get to calculus and physics. Give me back my math, please, instead of this crap.

Niels Henrik Abel and ChemProf on Please visit an actual classroom before you make recommendations, VII

2011-12-29T12:31:00.004-05:00

(http://oilf.blogspot.com/2011/08/please-visit-actual-classroom-before.html)

Niels Henrik Abel said...

I really don't get the inordinate fascination with "quantitative literacy." If you want to get a handle on finance, exponential growth/decay, and all the other "real world" crap that they stick in these types of textbooks, you still need to have a solid foundation of algebra, and the mathematical reasoning that goes along with it.
Can't get away from all those nasty, "irrelevant" Xs and Ys after all. And what Deirdre said is true: the "real world," "relevant" math is harder and more obtuse than the straightforward, "contrived" problems.

ChemProf said...

I teach freshman chemistry, and can tell you that students find algebra with lots of different symbols much more difficult than algebra with x. In kinetics, one of the most dreaded topics is finding a rate law from a mechanism, since it is pure symbolic manipulation.
It is also odd that they include "how computers are programs" when it is almost impossible to find a real programming class in high schools. I'm quite curious about what they think this would look like -- I'm betting it would be a lot of messing with the GUI and not much programming.

Deirdre Mundy on Accelerating within grade level with new new new Math

2011-12-29T08:29:00.000-05:00

(http://oilf.blogspot.com/2011/08/accelerating-within-grade-level-with.html)

Deirdre Mundy said...

The other thing is that while "going deeper" might be entertaining for geomerty or precal or calc when the kids get older and can have fun with proofs and whatnot, there's not much place to go with elementary math.
If the class is calculating areas and volumes, well, sure, you can give the brighter kids irregular shapes and have them try to figure out the areas---but once they've mastered the technique for that, where do they go?
If the class is working on multi-digit addition, and the kid's mastered it, what are you going to do? Just tack on more digits? In many cases, going "deeper" instead of accelerating just means soul-crushing busy work and more practice with the same algorithms the kids have already mastered.
On the other hand, it's easier for a teacher to just give MORE work than it is for her to give harder work, especially if she's not particularly math-inclined herself.

The funny thing is, at least when I was in school, the teachers claimed that making us help the slow kids helped teach us 'compassion.'
As a fifth grader, I didn't have the maturity to learn 'compassion' from that. I just resented them for their slowness and ended up doing the work FOR them so that I could get back to reading whatever decent book I'd hidden in my desk.

All that it taught me was snobbery. We would have been better off with a lecture on how different people are better at different things, and that sure, I could do school well, but Suzy Slowpoke could embroider and I couldn't even sew a button without impaling myself. And then the teachers could have HELPED SS THEMSELVES instead of having another little kid do it! (who admittedly, was sort of socially retarded, so maybe if I'd been a normal 10 year old I would have been better, but looking back, I was more like a 6 or 7 year old on the whole 'dealing with others' thing)

Anyway, the other problem is that for a lot of the smarter kids, they CAN'T help the slower kids, because they literally can't understand how someone could fail to grasp something so intuitive. I mean, how many pictures do you have to draw to get someone to realize that 1/2=2/4=3/6=7/14 etc. etc. As a ten year old, all you want to do is scream and impale your head on a spike so the stupidity of it all will stop making your brain hurt.

As an adult, dealing with the same sort of things, I realized that some people just take a LOT more time and repetition to grasp things than others do... but as a kid, you really do assume that everyone's brain works like yours and that if they can't remember something it's because they're deliberately forgetting it.
Maybe instead of "going deeper," they should just make all the advanced kids work on motor skills.... it would probably be more helpful in the long run.....

Deirdre Mundy on autism diaries XXVII: roundup of the latest experimentation and mischief

2011-12-28T17:26:00.000-05:00

(http://oilf.blogspot.com/2011/08/autism-diaries-xxvii-roundup-of-latest.html)

Deirdre Mundy said...

My dad apparently had great luck with "frogs and salamanders in the ice cubes" as a boy. But his pranks were aimed at making sisters scream, not parents groan.

…spring peepers are very small, so they fit in well. As are some salamanders. And for the others, if you, say, freeze them and put them in the container used for finished cubes, and your sister grabs a handfull and dumps them into her coke w/o looking, and then the salamanders thaw and wake up....
Well, apparently it's legendary. I have NOT let my kids do this, because I LIKE the frogs and salamanders and don't want them to get hurt or scared. :)

But more seriously, if your kid likes electronics, understands electronics and is GOOD at electronics, you should totally encourage him! Maybe you can redirect some of the 'prank' into "useful?" Like hit thrift stores, pick up non-functioning devices, and challenge him to fix them?

Brian Rude on Measuring higher-level scientific thinking

2011-12-28T12:25:00.000-05:00

(http://oilf.blogspot.com/2011/07/measuring-higher-level-scientific.html)

Brian Rude said...

Arguing against the scientific method is sort of like arguing against motherhood and apple pie. But I'm used to being the grinch, so here goes.
I would argue that in general the type of science appropriate for elementary and secondary education is primarily descriptive. To be scientifically literate students must build up a mass of information. That takes years to do. Without a solid foundation of information, much of which can be called descriptive information, there is nothing on which critical thinking can be applied.
We do not know about the world primarily through experimentation. We learn about the world primarily by making plausibility estimates. Contrived experimentation is important, but only key points in the development of a science. Contrived experimentation is a very ineffective and inefficient for learning science. Explanation and plausibility fitting are effective and efficient.

I have developed ideas along these lines in two articles on my website. "Rules and Methods of Science" is at http://www.brianrude.com/sci-mt.htm, and "The Rationale Of Laboratory Exercises In The Teaching Of Science" is at http://www.brianrude.com/ratlab.htm.

LexAequitas on Will geeks inherit the earth?

2011-12-28T08:23:00.002-05:00

(http://oilf.blogspot.com/2011/06/will-geeks-inherit-earth.html)
LexAequitas said...

I have 2 sons (actually 3, but for this explanation only the older two are needed).

Son one is bright, highly analytical, has a good grasp on logic and math, has a rock-solid memory, is tremendously interested in science and is straightforward and honest and opinionated. He has sometimes rocky relationships with peers due to his honesty and shyness. Similarly, in conferences his teachers dismiss his intelligence as almost an afterthought, and focus most of their attention on whether he's giving them the proper amount of respect/writing neatly/organizing his desk/doing things on their schedule. His grades tend to be highly uneven.

Son 2 (3 years younger) is of about average intellect, has a tenuous grasp of logic, and a poor memory -- but is also friendly, extremely outgoing, and usually cheerful. He makes friends easily, has enough sense not to go against the teacher, and even his rebelliousness/mischievousness is often viewed by teachers with a smile and wink. His great talent is to get everyone to love him.
I can't necessarily say that son 2 will do well in life and son 1 won't. But so far, son 2 is having a far easier time and enjoying his life a lot more.

Brian Rude, kcab and ChemProf on The virtues of explaining your answers

2011-12-27T17:19:00.002-05:00

(http://oilf.blogspot.com/2011/05/explaining-your-answers.html)

Brian Rude said...

I think it was in about fifth grade when one day the teacher told us, "If you can't say it, you don't know it." That always stayed with me, not because I believed it, but because I questioned it. I wondered if it were really true. It's totally understandable that a teacher would say that, but that doesn't mean it's really true. Over my lifetime I have given the idea some thought and concluded that it's not a simple matter. There are times when explicitly and precisely verbalizing what we are learning is very important. There are other times when verbalizing what we are learning is practically impossible and certainly not worth the time trying. Language is obviously a very powerful tool that we ought to develop as much as we can. But it is definitely not true that thought is only linguistic. With a little reflection one can come up with plenty of examples of nonverbal thought.

I have a few years experience teaching college math. Many times a student would come to my office for help. A common pattern was repeated many times. After getting oriented to the students difficulty (not always a quick or easy task) and selecting an appropriate problem to work on, I would be struggling to find just the right words to explain something, when the student would suddenly say, "Oh, I get it!". That would be my cue to shut up. Language is a wonderful tool, but a lot of thought consists of assembling ideas together in certain ways. When helping students I use language identify the mathematical ideas needed and assemble them in a way that will apply to the problem at hand. But the actual assembling of ideas itself is not linguistic so much as conceptual.
Most of us are quite adept at using a computer word processing program for writing. That involves a lot of learning. Were we forced to verbalize each step along the way when we learned? Can you verbalize everything you know about writing with a computer? Would it be beneficial to try to verbalize all that? What about driving. Have you ever tried to verbalize everything you know about driving? Would that be beneficial?
All this is not to say that language is not important. Obviously it is. But you can over do a good thing. I have been aware of the "explain your answer" fad in math education, but have always considered it just that, a fad. In a math class I think "explain your answer" should be translated into "show your work". And writing in a math class should simply mean "show your work".

kcab said...

I think the very best math students are able to explain their answers as well as work the problems. In reading a couple of books recently, "Count Down" and "Perfect Rigor", it seemed to me that the systems described for developing top math contest competitors had a lot of emphasis on teaching kids (not necessarily neurotypical) to explain their thought processes. My own mathy child is extremely good at explaining work, particularly aloud to others (the process of writing it seems tedious to him at times).

I think there is something to the idea that being able to explain one's work requires understanding a problem in a different way. I wonder though, whether anything is lost in the translation to words - is it necessary sometimes to hold off on the verbalization for a bit so that the problem can be completely seen? Wasn't there something about verbal descriptions of a memory altering and weakening the memory itself? I wonder if other non-verbal information is similarly affected.

ChemProf said...

In General Chemistry, I teach basic quantum mechanics. I occasionally get a very verbal student who wants me to explain why atoms act the way they do at a more fundamental level. But at that fundamental level, you are really talking about mathematics (or a description of mathematics -- saying "a superposition of basis sets" to a student who is in Calc I is not too meaningful). A few have been insistent that I must be able to explain in words, since "if you can't say it, you don't know it," and I've had to shut them down with a little bra-ket notation! So, there are a few things that aren't easily explained in words. And the people I know who really internalize quantum (I am not one of them) seem to do so in some non-verbal way.

Barry Garelick, Anonymous, and Amy P on The harmful effects of uttering “think” and “know”

2011-12-27T12:15:00.001-05:00

(http://oilf.blogspot.com/2011/06/harmful-effects-of-uttering-think-and.html)

Barry Garelick said...

I remember being puzzled by what "thinking" was and asked my mother "how do you think?" when I was in first grade. In first grade, we had a reading/writing activity book called "The Think and Do Book" so my conception of thinking was that it was different than "doing". But in time, I began to understand. I do not believe I suffered ill effects from exposure to such term.

Anonymous said...

Most people don't need to "think like a mathematician." That is a bizarre idea. Just as most children who are learning a sport (rules, skills, physical conditioning, and so forth) do not need to learn the physiological processes behind muscle function. Why would you postpone learning the sport until the kids are old enough to understand molecular biology? And, learning the sport by example and practice doesn't prevent the children from (later) learning why the muscles work the way they do. Now, it's true that children do need to think "big picutre" about the sport they are learning; and they need to bring an analytical approach to that learning. But that is not the same as understanding the "why" before attacking the "how."

Amy P said...

In language, there are a lot of forms that are pretty weird if you stop and think about them. For instance, if I say, "There is a cookie in the jar," what does "There" mean? Why not just say, "A cookie is in the jar." Likewise, when we say "It is cold today," what does "It" mean? Why not just say, "Is cold today." We use this stuff without thinking about it, without registering that it's peculiar.

Mnemosyne's Notebook on Honors classes for all

2011-12-27T08:14:00.002-05:00

(http://oilf.blogspot.com/2011/06/honors-classes-for-all.html)

Mnemosyne's Notebook said...

The Swiftian Solution would be to offer only AP Courses, since those would be richest in content.

Here in Hawaii, we teachers are taught that putting gifted students together with the less able is good for both. The research papers we were given to read during out teacher certification classes all showed that the less capable students did better on their projects when paired with more capable students(!). When I asked for results showing that the gifted students did better when paired with the less capable (as opposed to be paired with other gifted students) I was given anecdotes, but no data of real comparisons.

So, AP classes for all, with one gifted student per group - and only project work. That'll learn 'em all.

Kcab and ChemProf on Math problem of the week: 1900s algebra vs. Connected Mathematics

2011-12-26T17:12:00.001-05:00

(http://oilf.blogspot.com/2011/05/math-problem-of-week-1900s-algebra-vs.html)

kcab said...

I'm struck by how much more fun the problems in Wentworth are than those in Connected Math. Also, they remind me of math contest problems, which my kids find enjoyable.

ChemProf said...

I guarantee that some of my incoming students, who do reasonably well in calculus or pre-calc, would be stumped by these problems. One issue I see a lot in chemistry is the inability to take a word problem and figure out the math embedded within it. I'd love to see students spend more time on "inauthentic" problems like these in middle school and high school.

Happy Elf Mom, Deirdre Mundy and Niels Henrik Abel on Models for Autism: the math skills tradeoff

2011-12-26T12:45:00.000-05:00

(http://oilf.blogspot.com/2011/05/models-for-autism-math-skills-tradeoff.html)

Happy Elf Mom said...

Not sure. I know that Emperor is gifted in maths and NOT gifted in social skills. I keep him home to educate him because I'm pretty sure they're not going to teach my third grader algebra. :)

But when he goes to school someday, I'm afraid they will eat him alive. He just has no clue how to carry on a conversation and doesn't understand why people don't like him. I'm very sad for him in that aspect of his life.

Deirdre Mundy said...

The big problem I see is that schools have taken over 'socialization' as well as education. It used to be that kids were 'socialized' by family, the neighborhood, the church, the after school job.
Now school is responsible, and so everything has to become about academics AND socialization.
Teachers don't see the problem because ES teachers seem to be drawn from the segment of society who pick up social skills easily and naturally. So they see "more success!" because kids who would have struggle with academics are now excelling (because they're also graded on social skills.)

On the other hand, for the kids who struggle with social skills (Autism spectrum, ADHD, just plain quirky), passing as 'normal' takes a PHENOMENAL amount of effort. And even if they work really hard, they STILL come off as defective, just less defective than previously. (Speaking from personal experience here! ;) )

So, if they're forced to focus on appearing 'normal,' they STILL fail on social skills, but they also have no effort to spare to actually concentrate on the material!

I see this all the time with my ADHD daughter (runs in our family!! ;) )
If I make her sit still and display 'typical attentive student' body language, that's ALL she can do (until she melts down from exhaustion and stress and worry and failure.)
If I let her be....odd... she can master the material quickly, enjoys academics, and draws connections, thinks, and wonders.
Then we save the HARD stuff (personal space, ettiquitte, not crying, standing mostly still) for other times of day and other activities (CCD, art class, tai kwo do, speech therapy, church, playdates, grocery stores.)
But Math is math. Reading is reading. History is history.

But the schools insist on joining social skills with EVERYTHING, and then can't understand why the kids who stink at "social' get depressed and give up.
Even though a kid who dislikes MATH gets all sorts of sympathy and encouragement.
But, of course, social skills are easy and fun!....if you're normal and extroverted......like the ES teachers.....

Anonymous said...

I''m not remotely on the autistic spectrum, but I am someone who likes to choose when to be "social" and when not to. A classroom where I was expected to learn through interaction with other students, even if they were focused and on-task at all times, even if we were all at the same level, even if this were not an inefficient way to learn (usually), that classroom would have been a nightmare for me. I actually enjoyed being a baby boomer who never experienced a K-8 classroom with fewer than 35 kids in it; with those numbers, you do whole-class instruction and the students ask the teacher questions if they don't understand. Teachers facilitate whole-class discussions. The interactions I saw going on between the children working in groups in my own children's classrooms was not a model for good learning, and was painful to one of my (also not autistic) son, irritating to one daughter, and a matter of indifference to the other.

Niels Henrik Abel said...

Even though a kid who dislikes MATH gets all sorts of sympathy and encouragement.
But, of course, social skills are easy and fun!....if you're normal and extroverted......like the ES teachers.....
So true, so true!! Not being adept at math or science is considered acceptable (at least tacitly so), but those who are introverted and prefer to study or play alone (or with a buddy or two, as opposed to a larger group) are marked as defective and needing treatment to cure them of their "anti-social" (if anything, "asocial" is more accurate) behavior.
I was always turned off by that narrow-minded, petty view towards "loners." When will people realize that there is a difference between "being alone" and "being lonely"?

Jen on Blaming children for their ignorance, II

2011-12-26T08:42:00.000-05:00

(http://oilf.blogspot.com/2011/04/blaming-children-for-their-ignorance-ii.html)

Jen said...

Children aren't little adults.

The adults making curriculum seem to forget that a lot. They create things that would keep *their* attention about a subject they already understand.
I think this is why we get so much group thinking and "exploration" and the like before the students have just been taught. Directly. But direct teaching and practice seems boring for an adult who already understands it.

RMD on Blaming Children for their Ignorance

2011-12-25T17:40:00.002-05:00

RMD said...

I find it amazing that mankind has spent thousands of years trying to make sense of the world in a systematic way that helps us do really cool things, and modern pedagogy is willing to just let our kids experiment with the world assuming we don't have a 6000 year head start on our ancestors, rather than catching them up on the last 6000 years and then letting them experiment.

gasstationwithoutpumps and Deidre Mundy on Ideas that buzz: modern educators, clinicians, and writers

2011-12-25T12:37:00.002-05:00

(http://oilf.blogspot.com/2011/04/ideas-that-buzz-modern-educators.html)

gasstationwithoutpumps said...

"Buzz" and faddism have a lot to do with funding of science and are almost the sole determinant of who succeeds as an artist.
In both fields it is difficult sometimes to distinguish the brilliant from the cranks and so the mediocre rule.

Deirdre Mundy said...

I think you'll find that many home-schoolers are also buzz-less education reformers-- we can't change the system, or even find a listening ear.... but we can at least fix the system for OUR OWN KIDS.

In my fantasy education reform, we'd replace 'academic' pre-k and K with "montessori for all."

It's not that montessori doesn't TEACH academics.. it just teaches them in an age appropriate manner. It also teaches habits of concentration and calm that many kids today seem to lack.

The thing that I find odd is that, in the US today, Montessori is basically the preserve of wealthy elites, even though it was originally developed for poor tenement children in Italy.

Anyway--homeschoolers actually, as a group, devote a fair amount of time to education and curriculum research. But, as parents, they mostly care about what works.
But when you're a stay-at-home, crunchy-granola-religious-pseudo-hippy, you don't generate buzz---it's more like ANTI-buzz.

Jerrid Kruse, Hainish, FedupMom, Barry Garelick, and LynnG on Between the basic elements and the fuzzy abstractions

2011-12-25T08:23:00.000-05:00

(http://oilf.blogspot.com/2011/04/between-basic-elements-and-fuzzy.html)

Jerrid Kruse said...

My first reaction was that you haven't defined structure well enough so it ends up being this abstract concept - like the ones you lament. Then, I figured out what you mean by structure and your post makes much sense. (Examples are great, but are not a definition, sometimes the abstract is a very very good thing).
However, this structure you long for is most often reduced to a set of rules to be memorized rather than a set of understandings. Because the structure is interpreted this way, it rarely leads to the big ideas you are talking about. But hey, I was just glad to see you care about the big ideas.

Hainish said...

I don't think it's that teachers forget or want to forget structure, I think that it's below the radar for them. It doesn't even register. Instead of seeing the structure, they see the "lower-level" things--the names and dates and individual words--so they write it off as being too trivial to care about.

But, maybe I'm being uncharitable.

FedUpMom said...

At my younger daughter's school, they use Trailblazers math.

They've had a lot of complaints, of course, so in response they make the kids do a lot of very low level stuff -- computerized drill of adding and subtracting whole numbers, stuff like that.
The problem is that there's a whole layer of conceptual stuff that they still don't cover.
So they've got the airy-fairy "what's your favorite number?" level covered, and the bog-level drills covered, but none of the necessary concepts in between.

Barry Garelick said...

However, this structure you long for is most often reduced to a set of rules to be memorized rather than a set of understandings.
You don't teach a "set of understandings". The understandings are first about the procedures--presented in proper context, the understandings will follow. Sometimes the conceptual underpinnings will occur in a later grade/course. It wasn't until I took algebra, for example, that I understood why the invert and multiply rule for fractional division worked. In the meantime, however, I certainly knew when to apply fractional division to solve problems.

The hang-up over "big picture" is a continual confusion between epistemology and pedagogy. Novices don't learn to become experts by being given problems that only experts can solve.

Sweller talks about this in his article "Why Minimal Guidance During Instruction Doesn't Work":
According to Kyle (1980), scientific inquiry is a systematic and investigative performance ability incorporating unrestrained thinking capabilities after a person has acquired a broad, critical knowledge of the particular subject matter through formal teaching processes. It may not be equated with investigative methods of science teaching, self-instructional teaching techniques, or open-ended teaching techniques. Educators who confuse the two are guilty of the improper use of inquiry as a paradigm on which to base an instructional strategy.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.169.8810&rep=rep1&type=pdf

LynnG said...

The cumulative building of knowledge in the various disciplines (and they are called "disciplines" for a reason) is under-appreciated in k-12 education.

In an effort to make everything relevant right now, the structure of knowledge has been lost.

I asked a couple 9th graders "which came first, the Vietnam War or the Civil War?" they had no idea. But they could all reflect at length about the evils of slavery and discrimination, without reference to any of the major events in the history of civil rights.
Our children have been taught that their feelings about big issues is far more important than knowledge of the these things.

FedupMom, GasstationWithoutPumps, Anonymous on The Race to Remediation

2011-12-24T17:12:00.001-05:00

(http://oilf.blogspot.com/2011/03/race-to-remediation.html)

FedUpMom said...

Katharine, I often hear people ask, "which is it -- are kids overworked or underprepared?"
I think it's a false dichotomy. It is absolutely possible for kids to be both overworked and underprepared, and I think it's extremely common.

How can this be? It's because the mountains of homework and test prep that our kids labor under are in fact meaningless crap.

Anonymous said...

Katherine, the high rejection rates of the top colleges (and many that are not top) is a direct result of the fact that today's students are likely to apply to 10 colleges rather than 3 (or even 1, which was common when I was in high school).

gasstationwithoutpumps said...

The pools have gotten bigger, but not better at the top schools. In fact, the increasing size of the application pools has resulted in dilution of the pools with more less-prepared students. As a result, criteria that worked well enough in the past at getting a decent entering class may fail on the weaker pool. (At one time random selection from the pool would have gotten a decent entering class, but not so much any more.)

Also, in most schools faculty don't select the entering class—admissions officers do. The admissions officers and the faculty may have very different ideas about what the ideal entering class is like. Admissions officers are much more interested in demographics (race, gender, geographic origin, … ) than in individual readiness, which may compromise their ability to select students who will do well in college.

Anonymous said...

At the same time, and in many of the same schools, some kids are underprepared and some kids are overachievers - both academically and in extracurriculars. A couple of years ago, a graduate wrote a book about the tremendous pressure on kids from her old HS; I'm very familiar with that school and there are plenty of relaxed kids (probably most) and some drifters. The overachievers do apply to many schools,often a mix of Ivies, the Duke type, UVA and UNC (as out-of-staters) and perhaps their state flagship school or a smaller private as their safe school. The issue of admissions people and academics having different priorities is also valid. I've often thought I'd like to see academic departments select their students with as much diligence and care as the coaches select their players. I'm sure it would be a different mix; the physics and math departments aren't likely to worry about one B in English from a math genius, but I know one kid that was rejected from MIT while they admitted a weaker math but better all-around kid from his school (same sex and race).

Deirdre Mundy on Models for Autism

2011-12-24T12:10:00.001-05:00

(http://oilf.blogspot.com/2011/03/models-for-autism.html)

Deirdre Mundy said...

Have you seen the trailers for Wretches and Jabberers? The men featured in that movie seem to be type 1.
Also, in terms of gluten and dairy avoidance 'curing' autism -- severe food allergies can cause autism-like symptoms in a child, BUT if avoiding the allergen 'cures' her, then it wasn't AUTISM. It was a food allergy. I think this is where a lot of the 'diet cure' advocates run into issues.

The doctor tells them that diet doesn't cure autism. They see a cure for their child. So look! Doctors are wrong! Actually, the Dr. is just commenting that the cure means it WASN'T autism in the first place....
The biggest issue I see with "the spectrum" is that it seems like we're taking a bunch of symptoms and saying "everyone with these symptoms must have the same underlying disorder!" When really, if I have a runny nose, it could be allergies, it could be a cold, it could be flu, it could be that I ate a bowl of curry, it could be that I stuck a foreign object up there.

Treating all runny noses as if they had the same cause would be insane.... but it seems like that's where we are with autism right now....

Lsquared, Deirdre Mundy, and Chemprof on More fallacies in the media about cooperative groups

2011-12-24T09:06:00.001-05:00

(http://oilf.blogspot.com/2011/02/more-fallacies-in-media-about.html)

Lsquared said...

I agree. My reference points are mostly math. Andrew Wiles proved Fermat's Last Theorem. He couldn't have done it if Ken Ribet hadn't proved that if the Taniyama-Shimura conjecture was proved, then it would also prove Fermat's last theorem, so it wasn't a result that was done without knowing other people's work, but when he was working on it, he worked completely alone, and didn't talk to anyone about what he was doing until he believed he had the solution. Science needs both the sharing of knowledge, and the persistence of the individual working alone. Collaborators aren't rare, but they aren't the only way to go, either.

Deirdre Mundy said...

Also, it seems to me that the most productive TRULY cooperative efforts in science have come from a partnership, or perhaps a trio. And these fruitful collaborations usually grow organically, out of a mutual interest, rather tahn being imposed from above.
So we get the Curies, and Watson,Crick and Franklin (and notice Franklin always gets left out.) and Miller-Urey, etc. etc....
So partnerships, not groups. And freely chosen ones. Totally UNLIKE what happens in a classroom environt when a teacher decides that "Groupwork is necessary for learning!!!"
Also, as an aside, in an elementary classroom, brainstorming is usually an exercise in stupid. Coming up with 20 lame ideas is NOT a good substitute for one or two GOOD ones.....
ChemProf said...

Since grad school, I've published many collaborative papers. Never did we sit and brainstorm. Sometimes we'd talk and argue a point, but often it was more iterative -- one person would write a draft, and the other person would read and comment on it, pointing out questions or problems with interpretation. It never resembled elementary-school "group work." In fact, I've found in general that the least productive meetings are the ones without some kind of first pass on paper or an agenda. Without that focus, even educated adults tend to just talk around the issue and waste time. Anyone who has ever sat through a faculty meeting without an agenda should be familiar with this phenomena.

Deirdre Mundy on eliminating busy work

2011-12-23T17:14:00.001-05:00

(http://oilf.blogspot.com/2011/01/defanging-evil-machine.html)

Deirdre Mundy said...

But if you eliminated all the busy work, the school day would only be about an hour and a half long! And then people would have to PAY for babysitters!

Seriously -- My daughter's homeschooled day is about 1.5 hours long. But I don't count the time she spends coloring, drawing, making up stories, learning myths, doing wordfinds or watching documentaries as "school." School is the part of the day where she is doing the work that I've determined is necessary for her academic growth. (At this point, mostly reading and math). The other stuff is what she chooses to do for fun. I'm not going to give her 'credit' for drawing a diorama of African animals. BUT if she was in school, it would be a 'project.' And, honestly, it would probably have had all the joy sucked out of it.

Schools need busy work, because there is no way that a 6 year old can do PRODUCTIVE work for nearly 7 hours a day. And babysitting 25 kids at once means trying to keep them as quiet and sedentary as possible.

In my ideal world, the school day would stay under 3 hours long until 4th or 5th grade. But it would never fly. Somehow, we've grown to equate "time in a classroom" with "instruction time" and believe that "more" is the same as "More efficient."

Linda on the Pennsylvania State Assessment Anchors (PSSA)

2011-12-23T12:11:00.001-05:00

(http://oilf.blogspot.com/2011/01/math-problems-of-week-4th-grade.html)

Linda said...

Yes, the PSSA is taken in the spring of fourth grade. I teach at a school in PA that does Singapore and the PSSAs are the bane of my existence. There is practically no computation on the PSSAs and the kids are allowed to use calculators on most of it. Our students can do some really fantastic math, on which they are not tested. Basically, the month before the PSSAs we have to put the real math away and drill the kids in things like symmetry (there are a million questions on symmetry) and other random bits of unimportant stuff that they love to focus on. The higher up the kids get the farther back in Singapore I have to dig for test review. The PSSA fourth grade picture graphs are in the Singapore book 2B.

Barry Garelick, FMA, and JC on The Stereotype of Rote Learning in East Asian Classrooms:

2011-12-23T09:01:00.001-05:00

(http://oilf.blogspot.com/2011/01/stereotype-of-rote-learning-in-east.html)

Barry Garelick said...

The argument posited by the Times and others is compelling for reform math apologists of all stripes and colors. By saying that the Chinese system is test oriented, then getting high marks on a test is evidence of lower order thinking, and that getting low marks on a test is evidence of higher order thinking. Sort of like the excuse I used to use when a beagle I had wouldn't obey any of my commands. I told people it was because she was so smart she knew exactly what the command was but she just was choosing not to follow it.

FMA said...

Saying that Asians are less creative or that tests like PISA aren't a good indicator of competence are self-comforting mechanisms. We see that they are ahead of us but we want to comfort ourselves by saying it doesn't mean anthing because (enter excuse here).
America really needs another Sputnik Moment. Obviously PISA results aren't waking us up to reality. Maybe China trouncing us on clean energy will wake us up. They're already ahead of us. Hopefully we will wake up before it's too late to catch up.
Bob Compton, producer of 2 Million Minutes and the upcoming film The Finland Phenomenon put it well:

"If your kid has graduated three years behind the rest of the world in every subject, how do they catch up? It’s very serious."

http://news.medill.northwestern.edu/chicago/news.aspx?id=151583

JC said...

Why so much opposition to drilling in American education? Neuroscientists say that something has been learned when a connection for it has been created in the brain. Building these connections requires repetition (drilling). You simply can't learn without repetition. The brain simply doesn't build connections without it.

Creativity won't be much use to our students if they don't know anything. Knowledge and creativity have to go hand-in-hand to be useful.

FMA said...

"Why so much opposition to drilling in American education? Neuroscientists say that something has been learned when a connection for it has been created in the brain. Building these connections requires repetition (drilling)."

There is a big disconnect between how we actually learn and how too many educators think we should learn. It is a problem of ideology over evidence.

Favorite comments of 2011!

2011-12-23T08:49:00.001-05:00

You taught me; you moved me; you made me laugh--it was such a pleasure, and an education, to reread your comments of 2011. I've collected my favorite ones of many, and there are so many of them that I'll be posting 3 sets a day for approximately the next ten days. Enjoy!

Might suspending your preconceptions and biases be something to strive for?

2011-12-21T07:27:00.005-05:00

This week's Education Week is promoting not just "creativity," but "personal connections" and "relevance." In "Can Readers Really Stay Within the Standards Lines?", authors Maja Wilson, a former high school English teacher and current teacher of literacy instruction at the University of Maine, and Thomas Newkirk, a professor of English at the University of New Hampshire, express concern about the common core standards for K12 English.

What specifically concerns them is what the common core standards (CCS) say that K12 readers should be focusing on--namely "the text itself," or "the text on its own terms." They find this an old- fashioned ("early and mid-1900s") notion, and also disagree with CCS's idea that "while the personal connections and judgments of the reader may enter in later, they should do so only after students demonstrate 'a clear understanding of what they read.'" Nor do they like CCS's proposal that publishers should pose "text-dependent questions [that] can only be answered by careful scrutiny of the text" and that "80 to 90 percent of the Reading Standards in each grade require text-dependent analysis; accordingly, aligned curriculum materials should have a similar percentage of text-dependent questions." Finally, they question CCS's conception of what close readings are all about: "Student knowledge drawn from the text is demonstrated when the student uses evidence from the text to support a claim about the text."

All this, they write, both represses the reader, and shows "distrust of reader response." Second, "this readerly repression is unnatural, and probably impossible":

Since you are obviously still reading this Commentary, you be the judge. Have you stayed within "the text itself"? Have you cordoned off preconceptions, biases, prior reading, and associations until you finish and comprehend this text?

Third, if you don't make things relevant to students' lives, how can they possibly find them interesting:

All the instruction in the world won't help a reader who has already decided that a text is distant and irrelevant. But helping students understand the text itself means helping students find themselves in it. We worry that if textbooks, curriculum, and assessments align themselves to the view of reading in the common-core guidelines, students will become alienated from the very complex texts with which they will be required to grapple.

Wilson and Newkirk then contrast two ways one would teach, say, Nicholas Carr's 2008 essay from The Atlantic, "Is Google Making Us Stupid?" Their way:

Before assigning the essay, we would have students log their media use for a day (texts, emails, video games, TV, reading, surfing the Internet) and share this 24-hour profile with classmates. We might ask students to free-write and perhaps debate the question: "What advantages or disadvantages do you see in this pattern of media use?" This "gateway" activity would prepare students to think about Carr's argument. As they read, they'd be mentally comparing their own position with Carr's. Surely, we want them to understand Carr's argument, but we'd help them do that by making use of their experiences and opinions.

Versus:

In the classroom envisioned by the standards guidelines, these personal connections and opinions might be allowed later, after students have encountered and come to know Carr's text "on its own terms." Some preteaching would be allowed in the common-core classroom—as long as it didn't distract from the text. So students might be presented with a list of vocabulary words in the article or maybe be given information about the genre being read. But as they read, their attention would be focused almost exclusively on Carr's argument.

I agree with Wilson and Newkirk that it's difficult for readers to "cordon off preconceptions and biases." But does that make it desirable to encourage the opposite? I realize I'm about to suggest something as old-fashioned as the common core standards, but here goes: Might preconceptions and biases be things that potentially interfere with accurate text comprehension; things, in other words, that we might want K12 schools to discourage? Maybe my impressions are distorted by my own preconceptions and biases, but it seems to me that, when my students write analyses of the week's reading, the main way in which they go wrong (when they go wrong) is by focusing insufficiently on the text, and one of the main reasons why their focus is insufficient is because they are... distracted by their preconceptions and biases.

In fact, you see this everywhere--particularly in areas where conflicting, strongly-held beliefs come into play. How often have you posted a careful, meticulously qualified comment on the Internet, only to have someone who disagrees with you mischaracterize your "some" as "all," your "not all" as "none," your "sometimes" as "always," or your "not always" as "never;" exaggerate your evaluative phrases; erase your qualifications and delineations; or otherwise obliterate all the subtlety you've tried so hard to communicate, distorting your position into a straw man to be zealously ripped apart? While this tactic may simply indicate that your adversary doesn't have any good arguments against your actual views, it's often also a case in point of preconceptions and biases interfering with reading comprehension.

I suspect that that's what's going in a recent Amazon customer review of my book. Here Jennifer Bardsley, who has also appeared on this blog and who describes herself as holding views on educational theory that are "the polar opposite" of mine, writes:

Despite what Dr. Beals claims, STEM careers require communication and collaboration. Do engineers create digital cameras in isolation? Do cancer researches conduct private experiments and then keep mum about their findings? In my opinion, gently encouraging students to become better about sharing their ideas and thinking can only help them in the long run.^*

But here's a passage straight from the book (Raising a Left-Brain Child in a Right Brain World):

There's an important difference, people forget, between cooperation and collaboration. Yes, many modern mathematical and scientific puzzles are large enough that multiple scholars attack them simultaneously. But they do so not by divvying up the pieces, working independently, and only reconvening to present and tweak one another's solutions. They collaborate, but they mostly work separately, not cooperatively. (p. 42; italics as in the book).

(There's also an entire section devoted to "Teaching Rules for Conversations," which includes strategies for encouraging unsocial children to share their thoughts more effectively with others.)

Perhaps if we did more to encourage people to begin by suspending their biases and immersing themselves in other people's arguments--or worlds, or whatever else their words create--we'd have a society that is not only more literate, but also more open-mined and tolerant. For this, the common core standards for K12 English may be a start--so long as they don't end up being distorted by people's preconceptions and biases.
___
^*Ms Bardsley also faults Left Brain Child for lacking footnotes and a bibliography, not noting that references are repeatedly embedded in the text (publishers' preferred format for trade books), or that some of the world's most heavily footnoted texts are complete nonsense.

Online learning revisited: death knell for the lecture

2011-12-19T07:28:00.002-05:00

Perhaps the best reason for claiming that the lectures are dead, or inappropriate for 21st century classrooms, is that online learning modes offer better alternatives. This is the case made by Daphne Koller, a professor in the Stanford Artificial Intelligence Laboratory who teaches one of Stanford's three online computer science classes, and who is also the author of a recent Science Times article entitled Death Knell for the Lecture: Technology as a Passport to Personalized Education.

Since I recently wrote a blog post critiquing online learning environments, I was particularly interested in what Koller had to say. One of her best arguments is about the flexibility of videotaped presentations, which can be much shorter than lectures:

Presenting content in short, bite-size chunks, rather than monolithic hourlong lectures, is better suited to students’ attention spans, and provides the flexibility to tailor instruction to individual students. Those with less preparation can dwell longer on background material without feeling uncomfortable about how they might be perceived by classmates or the instructor.

Conversely, students with an aptitude for the topic can move ahead rapidly, avoiding boredom and disengagement. In short, everyone has access to a personalized experience that resembles individual tutoring.

The only concern I have about this is that it leaves it up to the students to decide when they're ready to skip things or move on. They--particularly the weaker, less motivated among them--may not always be the best judges of this, and may be tempted to skip over content that they don't find interesting (which may specifically include stuff they don't understand).

While software programs can't ensure that students are devoting sufficient attention to the video presentations, they can control their access to the specific assignments, providing additional tasks when students show weaknesses and advancing them to the next level if and only if they've mastered the current one. Ideally these two features--student control over which presentations to which, and ability-based advancement--allow, as Koller points out, a kind of individualized tutoring that may optimize learning. In this connection, Koller notes that:

In 1984, Benjamin Bloom showed that individual tutoring had a huge advantage over standard lecture environments: The average tutored student performed better than 98 percent of the students in the standard class.

Third, as Koller points out, while online curricula may not be able to address all areas of difficulty or confusion, the broader online environment allows efficient ways to pool student questions and to connect those with questions to those with answers:

Our Stanford courses provide a forum in which students can vote on questions and answers, allowing the most important questions to be answered quickly — often by another student. In the future, we can adapt Web technology to support even more interactive formats, like real-time group discussions, affordably and at large scale.

Furthermore, as others have noted as well, putting teaching presentations online allows for:

the flipped classroom, [where] teachers have time to interact with students, motivate them and challenge them.

Fourth, online environments are a better laboratory than brick and mortar schools are for identifying what works in education:

More broadly, the online format gives us the ability to identify what works. Until now, many education studies have been based on populations of a few dozen students. Online technology can capture every click: what students watched more than once, where they paused, what mistakes they made. This mass of data is an invaluable resource for understanding the learning process and figuring out which strategies really serve students best.

All these things, indeed, are the big advantages of online learning. Beyond this, the more instruction you automate, the more money you save and the more you can circumvent shortages of qualified teachers. But there's one big limitation to automated instruction. As I know from evaluating language teaching software programs and creating such programs myself, it's quite easy to automate a passive, multiple choice, right-or-wrong answer learning protocol. But a truly active learning environment--one in which students receive helpful feedback about where they went wrong and what to do about it--is both more more pedagogically effective, and much more difficult to automate. Here, Koller may be overly optimistic

For many types of questions, we now have methods to automatically assess students’ work, allowing them to practice while receiving instant feedback about their performance. With some effort in technology development, our ability to check answers for many types of questions will get closer and closer to that of human graders.

It's telling that the online subject with which Koller is most familiar is computer science. As I note in my earlier post:

The only truly active learning environment that I've ever seen in any software program for any academic subject is that which a computer programming language platform provides for--what else?--computer programming. Only here does the feedback--the error messages or the unexpected outputs--precisely reflect what you've done wrong.

We're a long way from achieving that in any other subject (with the exception of English morphsyntax for English language learners).

More distorting openers from Edweek

2011-12-17T09:01:00.004-05:00

First we have, from last week's issue, the headline: "To Boost Learning, Start With Emotional Health." The implication: that dealing with emotional health takes precedence over academics.

By the middle of the article, however, this position has mutated into something more moderate:

But evidence has shown that when it comes to the success of our children, both [health and education] are equally important.

As for specific proposals, quoting author Jane Isaacs Lowe, a senior program officer at the Robert Wood Johnson Foundation, these are:

Playworks, which supports a full-time, trained staff person—often an AmeriCorps member—to facilitate recess in schools in low-income communities... [to] help kids play new and classic games, teach them to resolve conflicts safely, and encourage healthy physical activity at recess and throughout the school day.

and:

Achool-based health centers [in partnership with] the Center for Health and Health Care in Schools, or CHHCS, another nonprofit organization, to address both physical- and mental-health issues.

Both of these sound eminently reasonable; why embed them in standard-issue right-brained propaganda?

Then, in this week's issue, we have "Studies Explore How to Nurture Students' Creativity" and its opening paragraph:

In the continuing debate about American competitiveness in the global economy, politicians and educators alike have pointed not to students' test scores, but to their creativity and ingenuity, as models for the rest of the world.

And, a couple of paragraphs later:

Howard E. Gardner, a professor of cognition and education at Harvard University, considers creativity one of five "minds," or ways of thinking—along with discipline, synthesis, respect, and ethics—that will be essential for young people to succeed in the future.
...

"While cognitive capacities are obviously valuable for creating," he said, "only those of a robust, risk-taking personality and temperament are likely to pursue a creative path."

As in Edweek's earlier STEAM article, the assumption here is that the arts are the best way to inspire creativity. Only if you proceed beyond the first section of the article do you discover that (in what could have been the article's title) Studies Show We Don't Know How to Use the Arts to Inspire Creativity:

Ellen Winner, the psychology chair and the director of the Arts and Mind Lab at Boston College, told participants at the Learning and the Brain conference that in a continuing series of studies on arts education and creativity, she had found "very little evidence that studying the arts improves grades or test scores, or that studying the arts improves creativity.

"These transfer claims have been posited without any particular mechanism; there's a lot of magical thinking going on," said Ms. Winner.

And only if you continue reading do you learn how problematic it is when teachers attempt to assess creativity:

Even educators hoping to improve students' creativity can inadvertently quash their willingness to take creative risks, according to Robert J. Sternberg, an expert in intelligence-testing research, who is provost and senior vice president of Oklahoma State University in Stillwater.

"Risk is essential to creativity, … but if you want to get into the good college and the good graduate school and the good job, you don't want to take too big a risk," Mr. Sternberg said at the National Academy of Education meeting. "Schools often encourage you to do the opposite of what you'd need to be creative."

In one study, for example, Mr. Sternberg found that university students in New Haven who took more risks got higher marks for creativity in a drawing contest, but for a writing contest, "when the kids in essays took controversial stands, the raters often rated them down," he said.

For all this, the article concludes on an optimistic note. First, cites unnamed "experts" as claiming that:

Schools can help students become more generally creative, going beyond simply mastering content knowledge or how to perform specific skills to using their imagination to solve problems.

Then, with paragraph on Ellen Winner that contradicts the earlier one, it reasserta s the notion that arts classes can inspire creativity:

In her most recent research, Ms. Winner and her colleagues spent a year interviewing teachers and videotaping five arts classes at Boston Arts Academy and the Walnut Hill School for the Arts in Natick, Mass. From that material, the researchers identified eight "habits of mind" taught as part of art class that transfer to other subjects.

Among those habits was one called "stretching and exploration"—the equivalent of creativity in the context of the study.

The "stretch and explore" habit in art class looks similar to experimentation in science classes. Rather than simply telling a student how to perform a task, Ms. Winner said, the teacher might ask students "to try new things, take risks, and not be afraid of mistakes, but instead to capitalize on their mistakes."

Only if you scrutinize the next paragraph does it become clear that this approach, like so many other fashionable approaches in education today, is as yet unsupported by evidence:

Now, Ms. Winner and her colleagues are involved in a two-year longitudinal study to develop measures to gauge whether the "stretching and exploring" that students learn to do in art class transfers to more creative thinking and problem-solving in math or science class.

Think we'll hear back from Edweek when the definitive results come in? If so, how exactly will Edweek sandwich them, and can we predict the headline ahead of time?

Math problems of the week: 4th grade Investigations vs. Singapore Math

2011-12-15T10:19:00.000-05:00

I. A 4th grade (TERC) Investigations homework assignment, assigned in late November:

II. From a similar point in the 4th grade Singapore Math Curriculum (Primary Mathematics 4A):

III. Extra Credit:

Neither traditional math, nor Singapore Math, spell out shortcuts as explicitly Investigations does ("Can you use the first problem to help you solve the second problem?"). Instead, students of traditional math and Singapore Math discover these tricks on their own. Which is better, child-centered discovery of ad hoc shortcuts, or more explicit hints via teachers, worksheets, and other authoritative entities?

Artsy science: what about sciency art, IV

2011-12-13T15:07:00.000-05:00

An article in this week's Education Week entitled "Building STEAM: Blending the Arts With STEM Subjects couldn't help but grab my attention. Here's the opener:

The acronym STEM—shorthand for science, technology, engineering, and mathematics—has quickly taken hold in education policy circles, but some experts in the arts community and beyond suggest it may be missing another initial to make the combination more powerful. The idea? Move from STEM to STEAM, with an A for the arts.

The actual term "STEAM," author Erik Robelin admits, may not catch on; but there are buzzwords aplenty to buttress it:

...momentum appears to be mounting to explore ways that the intersection of the arts with the STEM fields can enhance student engagement and learning, and even help unlock creative thinking and innovation.
...

One core idea ...STEAM advocates emphasize is that the arts hold great potential to foster creativity and new ways of thinking that can help unleash STEM innovation.

“There is creativity in STEM itself, super genius in it, ... but in arts education, it really is the raison d’etre to be out of the box, to accept the chaos,” said John Maeda, the president of the Rhode Island School of Design, in Providence.

Artists and designers, he said, are “risk takers, they can think around corners.”

...

Carrie Fitzsimmons, the executive director of ArtScience Labs, the Cambridge, Mass.-based organization that manages the ArtScience Prize. “It’s all fun, experiential learning, but we’re teaching them to be critical thinkers and problem-solvers.”

Naturally, Robelin doesn't interview any actual scientists on whether boosting scientific creativity and student engagement in science depends on the arts. He does reference, however:

a 2008 study led by Robert Root-Bernstein of Michigan State University, which found that Nobel laureates in the sciences were 22 times more likely than scientists in general to be involved in the performing arts.

And, he adds:

Albert Einstein was an accomplished violinist. And then there’s the Renaissance figure who some view as the personification of STEAM: Leonardo da Vinci, the Italian painter and sculptor who also made a name for himself as a scientist, engineer, and inventor.

Specific examples of STEAM include the following:

Through art-making projects, students at one [Philadelphia] school manipulated the abstract concepts underlying fractions for a more concrete understanding of how they work. The students even created a “fraction mural” displayed at the school.

...performing artists in theater, music, dance, and puppetry working alongside classroom teachers in preschool and kindergarten settings.

[A team of students] creating public art installations that communicate how people around the world struggle to gain access to fresh water.

...watercolor paintings of cells...."beautiful artistic renderings, and students could pick out the structures that they had been studying."

A number of highly enthusiastic non-scientists are quoted, including Karen Childress-Evans, the San Diego school district’s director of visual and performing arts; Jenny Montgomery, an art teacher at the Dayton Regional STEM School (quoted above in reference to the watercolors); Harvey Seifter, an expert in arts-based learning; and U.S. Rep. James Langevin (D. Rhode Island), who:

introduced a House resolution to highlight how “the innovative practices of art and design play an essential role in improving STEM education and advancing STEM research.”

Less enthusiastic are the scientists, whose comments are buried in the dead center of the article: Alan J. Friedman, a former head of the New York Hall of Science, who holds a doctorate in physics, and Susan Singer, a Carleton College biology professor. Says Friedman:

"They [art and science] also have some very essential differences that are at the core of what they are, which is why I have trouble with STEAM.”

The scientists may also be more troubled than the non-scientists are by the lack of STEAM-supporting data:

“There is no question, to me, the critical missing piece is the data,” said Mr. Seifter. He adds that even as he’s witnessed the power of the intersection, he sees a critical need for a “solid body of empirical knowledge about what the arts bring to the STEM equation.”

Indeed, research examining the effect of arts integration on student achievement across disciplines appears to show mixed results.

But there are plenty of funds for the fishing expeditions that will secure for the Powers that Be the data they know must be out there:

The NSF has provided research grants and underwritten a number of conferences and workshops around the nation this year.

...

One advocate of the STEM to STEAM push is Harvey Seifter, the director of the Art of Science Learning, a project financed by an NSF grant that organized three conferences last spring in Washington, Chicago, and San Diego that brought together scientists, artists, and researchers, as well as educators, business leaders, and policymakers to explore how the arts can be engaged to strengthen STEM learning and skills and produce a more creative American workforce.

...

The Philadelphia Arts in Education Partnership, with support from a $1.1 million Education Department grant, is working with city schools to help elementary students better understand abstract concepts in science and mathematics, such as fractions and geometric shapes, through art-making projects.

...

In California, a $1.1 million grant last year by the state’s Postsecondary Education Commission, using federal teacher-quality aid, is supporting the 134,000-student San Diego school district’s work linking the arts with science in grades 3-5.

The data is surely just around the corner, even if it's mostly not about academic achievement. For example, the Philadelphia Arts in Education Partnership has a four-year grant from the Education Department’s Arts in Education Model Development and Dissemination program which includes:

an “intense research component” and will look at a variety of effects, including student test scores, suspensions, and unexcused absences, as well as parent engagement in homework and changes in teaching practices.

Even some of the non-scientists, however, have their reservations about STEAM. Here, again, is Karen Childress-Evans:

“It’s not just teaching science through the arts, but teaching science and the arts together, and what comes from that is more than either of them standing alone.”

And here, again, is Jenny Montgomery:

At the same time, Ms. Montgomery said, even in a STEM school, it’s important for art not simply to be valued for its application to other disciplines.

“I also uphold the value of making art for art’s sake,” she said, “that students have an opportunity just to engage in art for the sheer joy of it.”

And science for science's sake? Or using science in art class? None of these folks seem to notice, or care, that the latter is nonexistent, and that the former has been receding from our classrooms for years now. Perhaps if the Erik Robelen had interviewed a few more scientists, and not buried their words in the dead center of his article, this issue would have surfaced. But if you once again follow the money, taking a look at the article's acknowledgements, you see why it doesn't:

Coverage of leadership, expanded learning time, and arts education is supported in part by a grant from The Wallace Foundation.

Is there no Power that Be out there interested funding coverage of, and research on science for science's sake?

Why open-ended projects aren't so open-ended after all

2011-12-11T08:21:00.000-05:00

The other day, as my daughter and I biked home from her violin lesson, we found a large truck blocking our usual way. So we tried continuing straight instead of turning right, which led us to the far end of the park, which we then realized we could cut through on one of its diagonal paths. This turned out to be a much nicer, and even slightly faster, way home. Without the obstacle, we might never have deviated from our routine to discover it.

Jonah Lehrer makes a similar point in his Head Case column in a recent weekend edition of the Wall Street Journal. He proposes that the reason why most artistic genres are highly constrained is that they force artists to come up with new ideas. Rhyming constraints, for example, can force poets to find words they might otherwise never have thought of using in the context at hand. Unexpected word choices transport poetry from the trite and well trodden, bringing us fresh associations and imagery.

Lehrer's piece references a couple of recent experiments. Unfortunately, as far as I can tell, these don't really bolster his case: they seem to be more about distractions than about obstacles. I predict, however, that experiments that do measure the effects of obstacles on creativity will eventually prove him right.

If he is, then we have one more argument against open-ended assignments. Not only do they not provide enough structure to help autistic spectrum children and other left-brainers get started; they also may not sufficiently jostle students in general out of their habits and inspire them to seek out roads less traveled by.

Math problems of the week: final algebra problems from the 1900s vs. the 21st century

2011-12-09T13:29:00.001-05:00

I. The final problem in Wentworth's New School Algebra, published in 1898:

Find by a graph the number of real roots of:
x⁸ - 8 = 0
x³ - 5x² + 8x + 14 = 0

II. The final problem in The University of Chicago Math Progject Algebra, published in 2002:

Use the table to plot the graph of the polynomial function
P(x) = 2x³ - x²- 6x

Why can you be sure that all the x-intercepts are listed in the table?

x__|__Value
-3_ |_-45__
-2_ |__-8__
-1.5 |__ 0_
-1_ |___3_
_-.5 |__2.5
_0_ |__0__
_.5_ |__-3_
_1_ |__-5_
_1.5|__-4.5
_2_ |__0_
_3_ |__27_

III. Extra Credit
Chicago Math students regularly use graphing calculators; 1900's math students didn't. So why do Chicago Math students get to rely on a table for their final algebra problem?

Autism Diaries XXXI: Where on earth are you going to send him to high school?

2011-12-07T08:00:00.001-05:00

"Where on earth are you going to send him to high school?" The title of this latest installment is a quote from a speech therapist who, after evaluating J several years ago, noted that she'd never before seen such a discrepancy, even in autism, between language comprehension and general intelligence.

Well, it's now three months into J's first year of high school, and I think it's finally safe to say that we actually did find an appropriate high school for him: the best one out there, in fact; a science and engineering magnet with a single, excellent special ed teacher. His first report card came back last week and I met with all his teachers and he's doing... just fine. His teachers seem, without exception, to respect his intelligence, his quirks, and his talents. I do not take this for granted. Indeed, this is the first school that hasn't had one or more teachers freaking out at having J in his or her classroom.

There's a catch, of course. While this school, not surprisingly, has other autistic spectrum students, never before has it had anyone with J's degree of comprehension deficits. His comprehension is good enough for Geometry, Biology, Engineering, and Computer Science, and I believe he'll do fine in World History next year. It's when language is socially embedded, aesthetically oriented, or presupposes a basic level of socio-cultural background knowledge that everything falls apart. In particular, the poetry and novels he's been reading for English class have gone totally over his head.

Wouldn't it be nice if J could work independently in this class, sticking with straight-up nonfiction? Sure, I'd be thrilled if this child of mine could lead a full, neurotypical life that includes digesting great literature and deconstructing poetry. But this is a kid who didn't even begin to understand the concept of narrative until he started playing Harry Potter computer games at the age of 6 or 7; who to this day is baffled by some of the simplest of dialogs, character interactions, and introspective ruminations; and who, except for Captain Underpants, has never in his life shown any interest in reading a book.

Not that he's not quite literary, in his own, idiosyncratic way. He can write from a prompt without a moment of writer's block. He can produce decent poetry on demand. And he delights on metaphorical word play. In fact, I'll use this post as an opportunity to share some recent gems:

"It looks like the train is sweeping up the passengers." (Said after watching a train obscure the commuter-lined platform opposite us, fill up, and then continue on, leaving an emptied-out platform in its wake.)

"High notes are light and low notes are dark." (It would seem that this kind of synesthesia exists even in congenitally deaf cochlear implant users like J.)

And, my favorite, said in reference to our crowded, weedy blackberry plot, where, by the end of the summer, the plants were all over one another: "It looks like the plants are fighting."

More front-page accolades hands-on classrooms, III

2011-12-05T12:48:00.004-05:00

From yesterday's Philadelphia Inquirer:

High school feels different in the big white mansion at the edge of the Navy Yard - no desks in rows. No 47-minute class periods. No warnings to remove the hat, put the cellphone away, take the exam seriously.

Instead, small groups of students are designing their own workshop space. They're drawing up more efficient bus routes for the Philadelphia School District. Their teachers act as mentors, sounding boards, not lecturers.

The premise? American high schools are broken.

The curriculum?

...a challenging curriculum built on student interests through hands-on projects. It means fostering strong relationships that form the underpinnings of everything.

There may be no Algebra 2 or English 4 at the workshop, but students learn the essential skills they need from those courses - solving simultaneous equations, interpreting complicated texts.

"No desks in rows"; teachers who are "mentors, not lecturers"; "hands-on projects"--why does "innovative" classroom boilerplate, ubiquitous in our "model" schools, continue to be front page news?
The current school of the week is the Sustainability Workshop, an alternative senior-year program inspired by a West Philadelphia after-school program whose students "have been building hybrid cars and winning important competitions for more than a decade" and whose members "want to turn the workshop into a full-fledged school... by 2013." Currently, 28 students attend, selected based on their attendance and behavior records. Their academic skills, one teacher says, "are all over the map."

Naturally, the school has attracted all sorts of premature attention--well before any efficacy results could possibly surface:

Three months in, the school has garnered national buzz and attracted more than $500,000 in private funding from the Barra Foundation, the Greater Philadelphia Innovation Cluster, and others.

Deep thinkers are already gushing over the workshop.

Says Andrew Zwicker of the Princeton Physics Plasma Laboratory and "associate director of education and workforce development for the innovation cluster": "It is so clearly the future of education. Or at least it should be."

Yikes.

Before jumping to these apparently foregone conclusions, the founders and the funders should first seek out reliable data on whether it's more effective to replace the seqential math pedagogy that is still in use by the many countries whose high schoolers outperform ours with an ad hoc "just in time" approach to advanced topics like simultaneous equations. And by reliable, I mean data that takes into account selection biases--of the sort you might find when 28 self-selected and behaviorally screened applicants opt against their typically terrible local high schools in favor of a brand new, well-funded program with a much higher (and more highly qualified) teacher to student ratio. The persistence of traditional math taught badly, as Barry Garelick has pointed out, doesn't mean we should give up on trying to teach it properly.

How--and how not--to resuscitate the magic of childhood

2011-12-03T10:31:00.008-05:00

One of the most common edworld justifications for spending less time on the structured teaching of core academic subjects, particularly in the early grades, is that children no longer have enough time in their lives for unstructured, imaginative play.

On this point, I'm in total agreement. For several generations now children have spent less time in yards, streets, and parks, and more time in front of screens; less time unsupervised in basements and attics and more time in scheduled, structured day cares, camps, and extra-curricular classes; less time playing games and more time doing homework (even during summer vacations); less time running around freely in open spaces and more time in adult-directed sports. And the toys that adults provide them with--from prefab minikitchens with plastic food, to verisimilitudinous costumes, to lego "kits" complete with instructions--leave hardly any room for their imaginations. Even today's playgrounds, with their uniform, space-hogging climbing structures (that more or less tell you how to play on them) and their dearth of unstructured spaces are less inspiring than they used to be. And everywhere, in our safety-obsessed, bully-vigilant society that imagines pedophiles lurking around every corner, parents are hovering in the background, ready at the drop of a hat (or the raising of a stick) to jump in and defend, moderate, or turn even basic block playing into teachable moments.

One can only wonder what this means for the happiness--and stress levels--of today's children, not to mention the memories they will take away from childhood. What about their capacity for imagination and creativity; their ability to socialize in unstructured, unscripted situations? What about their symbolic reasoning skills? If all their "imaginative" toys resemble the real things, what will inspire them to imagine an oblong block as a telephone or a cardboard box as a cave?

But does the remedy lie in altering what happens in our elementary school classrooms--specifically, in having children spend less time in structured, teacher-directed math and reading activities? Much of the problem, after all, is in what's happening--or not happening--after school, and (reluctant though people are, especially those in the business, to realize this) there's a limit to what schools can do about broader societal problems. Indeed, in their drive to be all things to "the whole child," schools have already seriously compromised our children's academic and vocational futures.

But there are ways in which schools can help a great deal. Preschools and kindergartens should toss out the minikitchens and costumes, replacing them with more plain wooden blocks and nonspecific dressups. They should also increase the time allotted for unstructured activities, and, along with all of the rest of the elementary school grades, increase recess by 300% (and stop, stop, stop using recess deprivation as a punishment). And--I've said this before--our K8 classes should almost as drastically decrease the homework assignments, eliminating all those high-ratio-of-effort-to-learning projects and Reform Math problems, and assigning no homework at all to children in grades K-3, and no summer vacation homework to anyone. Finally, they should eliminate the computers (and all other video playing devices, and all the movies and "educational videos" that go with them) entirely from our classrooms--except as tools for teaching kids how to program computers. But that's a whole nother story.

Math problems of the week: 6th grade Everyday Math vs. Singapore Math

2011-12-01T08:15:00.002-05:00

1. The final arithmetic problem set in the 6th grade Everyday Mathematics Student Math Journal 1, p. 161:

II. The final arithmetic problem set in 6th grade Singapore Math Primary Mathematics Workbook 6B, pp. 14-18:

The Day of Reckoning, brought to us from India

2011-11-29T08:00:00.000-05:00

Together, the rise of Reform Math, the reduction in ability-based grouping and AP classes, the demise of the close reading and the analytical essay (see also this), and the growing rarity of instruction in the finer points of English grammar and sentence construction, have caused current and future American high school graduates to be decreasingly prepared for college. As more and more American college students display skills in math, writing, and reading comprehension that are way below expectations (ending up, even in some of the more selective colleges, in remedial math and writing classes), college admissions committees are increasingly looking abroad.

While much of the news about overseas applicants centers on China, with its thousands of Ivy League-aspiring applicants and their glossy, high-production value applications (and the growing suspicion that a fair amount of cheating is involved), it's India, I predict, that will bring to the American K12 education system the day of reckoning that we so desperately need it to have. First, unlike their Chinese counterparts, college applicants from India face no linguistic barriers; many speak and write a much more eloquent English than American (and even British) students do. Second, there are apparently tons of extremely well-qualified Indian applicants pinning their hopes on America's top colleges.

Indeed, as an October New York Times article inadvertently suggests, the Day of Reckoning may be close at hand:

Moulshri Mohan was an excellent student at one of the top private high schools in New Delhi. When she applied to colleges, she received scholarship offers of $20,000 from Dartmouth and $15,000 from Smith. Her pile of acceptance letters would have made any ambitious teenager smile: Cornell, Bryn Mawr, Duke, Wesleyan, Barnard and the University of Virginia.

But because of her 93.5 percent cumulative score on her final high school examinations, which are the sole criteria for admission to most colleges here, Ms. Mohan was rejected by the top colleges at Delhi University, better known as D.U., her family’s first choice and one of India’s top schools.
...

Ms. Mohan, 18, is now one of a surging number of Indian students attending American colleges and universities, as competition in India has grown formidable, even for the best students. With about half of India’s 1.2 billion people under the age of 25, and with the ranks of the middle class swelling, the country’s handful of highly selective universities are overwhelmed.

True, another reason--indeed, the only reason mentioned in the Times article--why American recruiters are seizing on this opportunity is because so many of the crème de la crème of overseas students are wealthy enough to pay full tuition, unlike many of their American counterparts. But it also helps that the K12 schools they attend aren't using Reform Math, aren't renouncing ability-based grouping, and aren't failing to provide college prep classes that are truly college preparatory. Indeed, if it were primarily her parents' pocket books that make Moulshri Mohan so attractive to Dartmouth and Smith, why are they offering her so many thousands of dollars of scholarship money?

So here are my dire predictions. In the next ten years, as the effects of Reform Math continue to percolate up the American school system, and as the number of highly qualified Indian students continues to outpace the numbers of spots at the best Indian universities, there will be a the growing displacement of American students by Indian students. Only then will a large enough proportion of the Powers that Be start realizing how urgent it is to enact actual education reform--reform, that is, that reverses the century's-long tide that has pushed our K12 schools further and further away from what's happening in the most successful school systems overseas.

How about a college for high school "underachievers"

2011-11-27T08:27:00.030-05:00

There are, perhaps now more than ever, a certain number of bright students who decide at some crucial point in the middle of high school to stop caring about their grades. Such students, of course, have always existed. Perhaps mostly male, some of them develop a taste for laziness as the workload increases; others decide that spending their time productively is more valuable than doing what they perceive, sometimes rightly, as busy work, even if this means tarnishing their academic records at the worst possible time. Not all of these guys end up with terrible GPAs; some, coasting on their natural abilities, and/or finding a large enough portion of their school work sufficiently gratifying, earn grades that are merely mediocre.

But even merely mediocre burns many more higher-educational bridges than it used to. At the same time, at the more high-powered high schools, a few new factors have surfaced that make the bright but bored/cynical high school student even more likely to check out. He (or she) looks around him and sees a seemingly senseless rat race populated by academically successful classmates whose parents are nonetheless micromanaging homework, hiring private tutors, and enrolling them in Kaplan Test Prep; classmates with long lists of resume-builders, ghost-written college application essays, and extra time allowances on standardized tests that savvy parents secure as accommodations for what the kids themselves say are baseless attentional and/or processing speed diagnoses.

Among the unaccommodated (or accommodated for good reasons), untutored, and unmicromanaged high school "underachievers" are some of the most interesting, solid, creative kids out there. Indeed, the reason why some of these kids have remained untutored, unmicromanaged and un-unnecessarily-accommodated isn't that the parents didn't do their level best to manage things otherwise, but that the kids refused as a matter of principle to go along with it. Sure, some of them, particularly the lazier ones, may have some significant maturing to do, but a lot can happen in the many months between the college application deadline and the first day of classes. The college admissions process catches these kids at a particularly vulnerable time in their academic lives; nine months on they may be perfectly college-ready.

Wouldn't it be nice if some college would make these high school "underachievers" its niche, basing its admissions decisions (almost) entirely on test scores (problematic though these are, they are less problematic than grades); probing, intellectually challenging interviews conducted by perceptive interviewers; and extensive, proctored essays on unexpected but accessible topics? In this topsy turvy world in which admissions committees can no longer tell which applicants can really read, write, and think on their own (the SAT essay not being available to them, and its scoring being quite problematic), this may, in fact, be the best way to identify those who really are capable of college-level work.

Math problems of the week: 4th grade Investigation vs. Singapore Math

2011-11-25T18:11:00.000-05:00

Early 4th grade multiplication problems

I. A (TERC) Investigations homework sheet, assigned in late November [click to enlarge]:

II. The first 4th grade Singapore Math multiplications problems (Primary Mathematics, 4B workbook):

III. Extra Credit

How many points should a child get for answering "I memorized my multiplication tables" as his or her explanation for his or her answers to the Investigations problems?

Should Singapore Math teachers be concerned if a student attempts to solve the Singapore Math multiplication problems using Investigations-type "Array Cards"?

Autism diaries XXX: "You need to think about the future"

2011-11-23T08:13:00.034-05:00

The temptations of short-term pleasure still often prevail. So, when J's tutor accidentally leaves her gmail account open, he can't stop himself from seizing the moment, "impersonating" her, emailing several of her relatives to tell them that "my house burned down," and elaborating the fictional details with her brother over g-chat.

But, miracle of miracles, he's also becoming aware of the virtues of delayed gratification. Lately, for example, he's been suspending his urge to charge through bottlenecks of trolley and train commuters to land the best seat available on the earliest train possible, and calling his good behavior to my attention, all because he wants me to start letting him travel to school on his own, with all the perks that that will bring him (a cell phone and not having to read The Story of the World with Mommy on the way to school).

Just this weekend, having read about the Battle of Marathon two days earlier (in The Story of the World with Mommy on the way to school), he observes, while walking by the Philadelphia Marathon on his way with me to Chinatown, that the winners of these races, running as fast as they can bear to, are "thinking about the future," and that if he ever wants to win a race he needs to do the same. I point out that this also applies to chess tournaments, where, even though he's doing better and better (earning enough points for a bronze metal in the city-wide public school tournament the day before), he's still tempted to open with the checkmate-in-four-moves gambit that no one at chess tournaments falls for and that ends up compromising his game.

At a shopping gallery a few blocks closer to Chinatown, after filming some of the ceiling fans he doesn't yet have on tape, he checks out the latest price of Wiis and discovers that he now can afford one. All those years of pining after, and jokingly pleading for a Wii ("Buy me a Wii or I'll call 911") and saving up money from yard work and snow shoveling (last year was particularly lucrative) have finally reached their happy conclusion.

He's got his Wii, his Mii, and his printout of "WII RULES!" ("Before you play: Wash your hands, Make sure you have no drink, Make sure you have permission; When you play: Do not eat, Make sure the control is away from everything, Wear the strap on the control, Share with other people; After you play: Make sure the CD is where I can find, Make sure the remote is where I can find, Make sure the console is off"), in which he wants all of us to think about the future--and, of course, his future in particular.

(We've reminded him, however, that Mii is not master of the Wii-universe: we still own the TV screen and control its power supply).

On edworld double speak

2011-11-21T08:58:00.001-05:00

For years now I've found myself increasingly nauseated by phrases like "higher level thinking", "be creative," "conceptual understanding," "critical thinking," "reflection," "multi-culturalism," "discovery learning," "open-ended problems," "community of learners," and "life-long learning." My now-automatic (and, admittedly, hyperbolic) mental translations include:

high-level -> fact-free
discovery-based -> instruction-free
reflection -> navel gazing
open-ended -> anything goes
creativity -> color & glitter
multicultural -> bromides plus "non-Western" trivia

Before I knew anything about current trends in education, I associated these phrases with many of the things I valued most; with what my ultimate goals were for myself as both a student and a teacher. Things like rote calculations and memorization of facts and procedures were things I valued far less, dismissing them as mere tools, rungs, or building blocks for helping you attain what really matters--and dismissing certain classmates of mine as excelling in regurgitation and rapid computing (things I myself have never excelled in), but not in conceptual understanding or creative synthesis (which I hoped were my relative strengths).

But now that I've seen how many of these tools, rungs, and builing blocks are missing from today's classrooms, I find myself appreciating them as never before, and harping on them as I never in a million years would have imagined myself doing.

Equally baffling to my ealier self, when I hear "higher-level" thinking and "conceptual understanding" I no longer think of a substantive synthesis or analysis of a richly interconnected body of (internalized) knowledge, but of a lack--of substance, of teaching, and of learning; and, ultimately, of all the good these words used to connote.

Why we can't trust math (and STEM) professors, II

2011-11-19T09:13:00.011-05:00

In an earlier post, I list various reasons why we can't trust the math professors on Reform Math. I'm now realizing that I omitted one. Math (and science) professors, as rigorous and analytical as they are within their chosen fields, are perhaps no less credulous than the rest of the public about claims made by "education experts." Two recent articles show two mathematicians and one quantum physicist who have eagerly drunk the edworld Kool-Aid now parotting the usual arguments and buzzwords.

First, a November 11th article in Slate entitled "How to Fix Math Education in High School and College" cites self-styled “mathemagician” Arthur T. Benjamin, who teaches at Harvey Mudd College, on daily life relevance and 21st century skills:

One of the primary problems with math education today, according to Benjamin, is that the sequence of courses leads students in the wrong direction. “For the last 200 years, the mathematics that we’ve learned starts with arithmetic and algebra, and everything we do after that is taking us toward one subject, calculus. I think that is the wrong mathematical goal for 90 percent of our students,” he says. “We’re now living in an age of information and data, and the mathematics that will be most relevant to our daily lives is probability and statistics.”

and on computation undermining rather than supporting conceptual understanding:

Benjamin... hopes that mathematical education will be less about computation—we’ve got calculators for that!—and more conceptual, like “understanding when you need to do integrals, when you need to do a square root.”

Then we have an article in a community newspaper on a public hearing regarding Haverford High School's switch to College Preparatory Mathematics (CPM), a Reform Math algebra and geometry curriculm. Here we have the views of Michelle Francl, a Ph.D. and professor of quantum mechanics at Bryn Mawr College, on what research has shown about cooperative learning:

Michelle Francl... said research has shown that "cooperative learning approaches are significantly more effective than traditional lecture and individual work in student mastery of mathematics, as measured by standardized tests."

And we have Villanova math professor Robert Styer's views on creativity:

[He] noted that industry wants people who can "think creatively and outside the box," and CPM is good for teaching that.

Mathematicians buying into the belief systems of ordinary humans isn't particularly noteworthy... except when those in power use this phenomenon as further justification for those beliefs. For example, Haverford school director Phil Hopkins:

He noted that people supporting CPM were academics, educators and mathematicians, while "those who are objecting are not...I haven't heard anything that would make me say we made a bad choice and need to change."

To be fair, there are plenty of mathematicians (especially those who have kids in Reform Math classrooms and/or who have closely examined Reform Math textbooks) who oppose Reform Math. And, naturally, when these mathematicians speak out against it, they're treated as out-of-touch mathematicians rather than as in-touch, math-aware educators.

Math problem of the week: 6th grade 1920's math vs. Connected Math

2011-11-17T13:09:00.000-05:00

The first fractions-to-decimals conversion problems in 6th grade 1920's math vs. 6th grade Connected Math.

I. From Hamilton's Essentials of Arithmetic, Second Book (published in 1919), chapter I, "Decimals" section [click to enlarge]:

II. From Connected Mathematics' Bits and Pieces I, Investigation 3, "Moving Between Fractions and Decimals" [click to enlarge]:

III. Extra Credit:

If you divide the mathematical challenges of each problem set by its verbal challenges (i.e., the challenge of figuring out what each problem is asking you to do), which problem set has the larger quotient?

Should 6th graders by encouraged to conceive of fractions as shadings on a hundredths grid, or as a division of the numerator by the denominator?

Why is our home schooling program so Western? Part IV

2011-11-15T09:43:00.000-05:00

(Final installment!)

What about English-language texts that incorporate elements of the non-Western cannon, or expose children to non-Western cultures? Shouldn't I be including more of these in our homeschooling curriculum?

Unfortunately, the more recent introduction of writing systems into many languages, and the dearth of good translations of non-Indoeuropean, non-Semitic texts into English, mean that there simply isn't that much high-quality literature from the non-Western canon that is accessible to English-speaking students--especially the younger ones.

Meanwhile, too much of what passes for instances of non-Western cultural heritage turn out to be unmemorable settings of "traditional" folk tales vapidly retold by North American outsiders, and books of multicultural trivia that reduce languages to alphabets and simple phrases, and cultures to highly formulaic, summary accounts of food, dress, and ceremonies--all of it flowing seemlessly into one ear and out the other.

Why is our home schooling program so Western? Part III

2011-11-13T08:22:00.003-05:00

Beyond the issue of availability of good materials, there are some other reasons why we ultimately switched gears and chose French over Chinese.

First, there's the issue of cognitive retention. In comparison with French and other Indoeuropean languages, Chinese presents two disadvantages. One is its writing system. Mastering the thousands of Chinese characters required for basic literacy demands hours of daily practice. I've seen first hand how a short hiatus can result in massive forgetting. One simply cannot learn to read anything of substance in Chinese without a long-term commitement to significant daily practice. Another is its vocabulary. Chinese words are especially challenging for English speakers to remember because they bear no resemblance to English words.

So if your (or your child's) goal is to learn a language spoken by billions that may someday become a job-opportunity-expanding lingua franca, or a language whose pronunciation, vocabulary, and written form (though not so much its morpho-syntax) differs greatly from English, and you can commit to the hours, days, and years of instruction (or don't care about learning the written form of the language), Chinese is just the ticket. But if your goal is fast mastery and easy retention of a spoken and written language, you're better of with one that uses an alphabet and whose words bear some resemblance to English words.

Which brings us to French--the original lingua franca. Like other Indoeuropean languages, it shares not only our basic writing system, but also tons of cognates (glace-glacier; sympathique-sympathetic; regarder-regard; to name just a few my daughter has recently observed). This means that English-speaking French learners are immersed in mnemonic devises. The effect of these cognates goes in the other direction as well: learning a Romance language like French enhances one's acquisition of many of the more sophisticated elements of English vocabulary. Cognates aside, French difers from English along the more linguistically interesting dimension of morpho-syntax, arguably at least as much as Chinese does. It therefore presents a nice combination of (1) mutual reinforcement with English vocabulary and an easily-mastered writing system, and (2) morpho-syntactic challenge and a window into some of the morpho-syntactic variability of the world's languages.

The mutual reinforcement of retention and enrichment also argues (in the Western world) for the Western cannon. The myths, fables, and histories that a native English speaker is most likely to remember are the ones that are alluded to or depicted throughout English-language literature and in much of the art that one encounters in our major art museums. As core knowledge avocate E. D. Hirsch has argued, knowing these classic tales and histories also enriches one's understanding of English-language texts, even at the level of basic comprehension. Just a few days ago a New York Times Op-Ed piece referenced an ancient Babylonian king in an allusion that would resonate with any child who has read Story of the World, Volume I. Familiarity with the best-known ancient civilizations--from China to Mesopotamia to Rome--is also both enriched by, an enriching of, one's visits to the many ancient civilization wings at museums around the country.

Math problems of the week: 3rd grade Investigations vs. Singapore Math

2011-11-11T08:11:00.003-05:00

The culminations of first semester 3rd grade multiplication and division units:

I. The entirety of the 3rd grade (TERC) Investigations End-of-Unit Asssessment for the "Multiplication Towers and Division Stories" unit [click to enlarge]:

II. The two most comparable pages of the 7-page Review that follows the 3rd grade Singapore Math "Multiplication and Division" unit [click to enlarge]:

III. Extra Credit
Investigations features short, easy, unit-specific assessments; Singapore Math features more challenging, lengthy, culumlative reviews. What does this indicate about the priorities of each curriculum?

Why is our home schooling so Western? Part II

2011-11-09T08:05:00.001-05:00

Why, in particular, is our history (The Story of the World), language curriculum (French), and musical curriculum (mostly Northern European classical) so Western?

One reason relates to what's been written down. Written historical records of ancient times are unevenly distributed around the globe, favoring the parts of the world traditionally covered in ancient history classes--and in The Story of the World (which include Egypt, the Middle East, China, India, North Africa, and Turkey).

Another has to do with available resources and my familiarity with what's out there. French happens to be my strongest foreign language, and I've long known about French in Action, which is the best available, child-accessible, audio-visual language curriculum I'm aware of for any language. In particular, I haven't found anything comparable for young English speakers learning Mandarin Chinese (the first foreign language my daughter studied--in a once-a-week after-school program--and a language with which I am only somewhat familiar). There are a number of software programs out there that purport to teach all sorts of languages, but these, imho, are so highly deficient they they aren't worth bothering with--even if they didn't cost hundreds of dollars.

Non-Western music scores, non-Western musical instruments, and non-Western music teachers are also hard to come by in this corner of the world.

But there are some other, more cognitive/academic reasons for some of our homeschooling choices. Stay tuned for Part III.

Why do college students defect from STEM

2011-11-07T11:26:00.002-05:00

In this weekend's New York Times Education Supplement, author Christopher Drew asks "why science majors change their mind," and why "roughly 40 percent of students planning engineering and science majors end up switching to other subjects or failing to get any degree." His short answer, "it's just so darn hard," rings true. So does his observation about "the proliferation of grade inflation in the humanities and social sciences, which provides another incentive for students to leave STEM majors."

It's in his investigation of why science is "just so hard," and what to do about it, that Drew falls short. His focus is a single data point, Notre Dame student Matthew Moniz:

He had been the kind of recruit most engineering departments dream about. He had scored an 800 in math on the SAT and in the 700s in both reading and writing. He also had taken Calculus BC and five other Advanced Placement courses at a prep school in Washington, D.C., and had long planned to major in engineering.

But as Mr. Moniz sat in his mechanics class in 2009, he realized he had already had enough. “I was trying to memorize equations, and engineering’s all about the application, which they really didn’t teach too well,” he says. “It was just like, ‘Do these practice problems, then you’re on your own.’ ” And as he looked ahead at the curriculum, he did not see much relief on the horizon.

So Mr. Moniz, a 21-year-old who likes poetry and had enjoyed introductory psychology, switched to a double major in psychology and English, where the classes are “a lot more discussion based.” He will graduate in May and plans to be a clinical psychologist. Of his four freshman buddies at Notre Dame, one switched to business, another to music. One of the two who is still in engineering plans to work in finance after graduation.

Mr. Moniz’s experience illustrates how some of the best-prepared students find engineering education too narrow and lacking the passion of other fields. They also see easier ways to make money.

From this one data point, the solution emerges naturally. It is-- you guessed it--a greater emphasis on relevance, aspiration, leadership, and student-centered project-based learning. At Notre Dame, for example,

Dr. Kilpatrick [the Dean] has revamped and expanded a freshman design course that had gotten “a little bit stale.” The students now do four projects. They build Lego robots and design bridges capable of carrying heavy loads at minimal cost. They also create electronic circuit boards and dream up a project of their own.

“They learn how to work with their hands, how to program the robot and how to work with design constraints,” he says. But he also says it’s inevitable that students will be lost. Some new students do not have a good feel for how deeply technical engineering is. Other bright students may have breezed through high school without developing disciplined habits. By contrast, students in China and India focus relentlessly on math and science from an early age.

Drew also cites Worcester, which

ripped up its traditional curriculum in the 1970s to make room for extensive research, design and social-service projects by juniors and seniors, including many conducted on trips with professors overseas. In 2007, it added optional first-year projects — which a quarter of its freshmen do — focused on world problems like hunger or disease.

Some of this sounds quite reasonable. There's perhaps no subject where project-based-learning is more appropriate than engineering. But how much sense does it make to dilute the course requirements for, say, biology and chemistry with overseas field trips and social service projects when there's so much hard material to cover to prepare students to compete for research & development jobs in STEM?

Besides field trips and social service projects, and also not to be confused with research and development, there's leadership. The University of Illinois, for example:

began this fall to require freshmen engineering students to take a course on aspirations for the profession and encourages them to do a design project or take a leadership seminar.

The underlying assumption is that the problem isn't so much that STEM majors are difficult, but that students find the classes boring and irrelevant to daily life, and that they lack confidence. Says Arthur C. Heinricher, the dean of undergraduate studies at Worcester Polytechnique, in reference to its student-centered projects:

"That kind of early engagement, and letting them see they can work on something that is interesting and important, is a big deal. That hooks students.”

More generally:

...The main goals [at Worcester] are to enable students to work closely with faculty members, build confidence and promote teamwork. Studies have shown that women, in particular, want to see their schoolwork is connected to helping people, and the projects help them feel more comfortable in STEM fields, where men far outnumber women everywhere except in biology.

It doesn't seem to occur to Drew, or to any of his interviewees, to consider a more obvious reason why STEM courses are "so darn hard" for students these days, and why they lack confidence: the decreasingly poor preparation that they are receiving in high school math and science classes. There are many reasons for this, ranging from the No Child Left Behind-inspired dumbing down of the curriculum, to the decline in AP course offerings and ability-based grouping, to the ravages of Reform Math (which begin in elementary school). But among these reasons is precisely the kind of child-centered, project-based learning that Drew and his interviewees are advocating (one need look no further than Philaelphia's project-based Science and Leadership Academy, and its dismal test scores in science). While it often sounds great in theory, project-based learning is an inefficient and disorganized way of learning the core curriculum necessary for college-level science courses and STEM r&d jobs.

Furthermore, if you're ill prepared for college-level math and science classes, and therefore don't understand what's going on in class unless it's hands-on and student-centered,of course non-hands-on courses will seem dry, narrow, borring, and irrelevant to your aspirations.

And of course you will end up dropping out, especially if you face competition from classmates who got their K12 science training overseas, where rigorous math and science classes still abound. Indeed, this explains why, as the article notes, "the attrition rate can be higher at the most selective schools, where...the competition overwhelms even well-qualified students." The most selective schools, after all, attract the highest numbers of better-trained STEM students from overseas.

Ironically, Drew begins his article by alluding to "test scores showing American students falling behind their counterparts in Slovenia and Singapore." Isn't the first step, then, to look inside Slovenian and Singaporean classrooms and see what sorts of curricula and pedagogy these countries are using? I could be wrong, but I'm guessing that one would find many more hours of rigorous study of core content, and many fewer hours of leadership, inspiration, and project-based learning.

Why is our home schooling program so Western? Part I

2011-11-05T08:30:00.002-04:00

Currently, my daughter is reading Greco-Roman history, Greek myths, Bible stories, Lives of Saints, Aesop's fables, and American and British children's novels; she's learning French; she's playing and listening to Western European classical music on Western European classical instruments.

With home schooling you have the lattitude to include anything you want, and, in particular, to fill any gaps that your child would otherwise experience in the public education system. So why have we chosen such a Western, Eurocentric curriculum when we could be drawing from all over the world?

On closer inspection, our curriculum isn't as Eurocentric as it first appears. Our history source, for example, is The Story of the World. Before we got to the Greeks and Romans we spent time with the ancient civilizations of Egypt, the Middle East, China, India, and the Phoenicians. Later we encountered the Persians and the Carthaginians and, later still, Byzantium. I myself have learned more about early South America and early sub-Saharan Africa from The Story of the World than I have from any public school textbook. As for our classic tales, we'll soon be moving Eastwards to the Arabian Nights.

My daughter has moved eastwards in music as well. In addition to Bach and Beethoven, she is also playing Kabalevsky. The math she does is decidedly Singaporean. The animals she's learned about (our 4th and 5th grade home school science has been largly zoology) hail from all over the globe.

To be fair, though, most of the humanities topics we cover do fall into that much-maligned Western canon. So I'd better have good reasons for choosing this route. Stay tuned for Part II...

Math problems of the week: 21st century geometry vs. 1960s geometry

2011-11-03T08:38:00.002-04:00

I. The first and last pages of the Discovery Geometry (2003) Chapter Review of the "Reasoning in Geometry" chapter , pp. 138 and 140 [click to enlarge]:

II. The Weeks & Adkins A Course in Geometry (1961) Chapter Review of the "Proof" chapter, p. 55 [click to enlarge]:

III. Extra Credit
If you had to ditch a geometry course in order to make room for an entrepreneurship course, would you be more likely to ditch the Weeks & Atkins course, or the Discovering Geometry course?

Jobs vs. Gates: right-brained assumptions about genius and creativity

2011-11-01T09:26:00.006-04:00

When we Americans think of genius and creativity, as opposed to mere smarts, most of us think of so-called "right-brain" rather than "left-brain" skills. A recent case in point is Steve Jobs' biographer Walter Isaacson. In his opinion piece in this past week's Week in Review, Isaacson's contrast between genius Jobs and super-smart Gates falls exactly along the right-brain, left-brain fault line, with predictable results. Presented with a logic puzzle:

Mr. Jobs tossed out a few intuitive guesses but showed no interest in grappling with the problem rigorously.

This causes Isaacon to

think about how Bill Gates would have gone click-click-click and logically nailed the answer in 15 seconds, and also how Mr. Gates devoured science books as a vacation pleasure...

The impatient intuitor vs. the mechanically logical Aspie. Guess which one is the creative genius:

So was Mr. Jobs smart? Not conventionally. Instead, he was a genius. That may seem like a silly word game, but in fact his success dramatizes an interesting distinction between intelligence and genius. His imaginative leaps were instinctive, unexpected, and at times magical. They were sparked by intuition, not analytic rigor. Trained in Zen Buddhism, Mr. Jobs came to value experiential wisdom over empirical analysis. He didn’t study data or crunch numbers but like a pathfinder, he could sniff the winds and sense what lay ahead.

Intuition vs. analysis and genius vs. smarts leads, almost inevitably, to East vs. West:

He told me he began to appreciate the power of intuition, in contrast to what he called “Western rational thought,” when he wandered around India after dropping out of college. “The people in the Indian countryside don’t use their intellect like we do,” he said. “They use their intuition instead ... Intuition is a very powerful thing, more powerful than intellect, in my opinion. That’s had a big impact on my work.”

Then there's experiential wisdom vs. conventional learning and imagination vs. knowledge:

Mr. Jobs’s intuition was based not on conventional learning but on experiential wisdom. He also had a lot of imagination and knew how to apply it. As Einstein said, “Imagination is more important than knowledge.”

Genius also involves "the ability to apply creativity and aesthetic sensibilities to a challenge," specifically, an interdisciplinary one:

In the world of invention and innovation, that means combining an appreciation of the humanities with an understanding of science — connecting artistry to technology, poetry to processors. This was Mr. Jobs’s specialty. “I always thought of myself as a humanities person as a kid, but I liked electronics,” he said. “Then I read something that one of my heroes, Edwin Land of Polaroid, said about the importance of people who could stand at the intersection of humanities and sciences, and I decided that’s what I wanted to do.”

Dealing the death blow to Gates (vs. Jobs), there's empathy and social skills:

The ability to merge creativity with technology depends on one’s ability to be emotionally attuned to others. Mr. Jobs could be petulant and unkind in dealing with other people, which caused some to think he lacked basic emotional awareness. In fact, it was the opposite. He could size people up, understand their inner thoughts, cajole them, intimidate them, target their deepest vulnerabilities, and delight them at will. He knew, intuitively, how to create products that pleased, interfaces that were friendly, and marketing messages that were enticing.

It's eerie how closely the traits Isaacson praises in Jobs dovetail with the educational priorities of today's education world: imagination and creativity; intuition in place of analysis; experiential learning in place of "conventional" learning; interdisciplinary breadth; an emphasis on empathy and social skills; and a rejection of "white," "Western" modes of thought.

In his East vs. West, Isaacson also mirrors the education world's simulltaneous caricature of Western thought as excessively left-brained, and of the more Eastern parts of Asia--even Steve Jobs' intuition-driven India--as even more excessively left-brained:

China and India are likely to produce many rigorous analytical thinkers and knowledgeable technologists. But smart and educated people don’t always spawn innovation. America’s advantage, if it continues to have one, will be that it can produce people who are also more creative and imaginative, those who know how to stand at the intersection of the humanities and the sciences. That is the formula for true innovation, as Steve Jobs’s career showed.

In characterizing genius and creativity as being specific to the intuition-driven, empathy-driven, experientially-taught, interdisciplinary thinking side of humanity, and as being the comparative advantage of the U.S. over its competitors, the many pieces like Isaacson's are furthering well-established trends in education that have already become ridiculous parodies of what people like Isaacson are advocating.

For one recent example of some of this, take a look the following science project rubric I came across yesterday [click to enlarge]:

This is only one of many variations on the sort of rubric that is proliferating around our k12 schools and turning science into a superficial exercise in, and parody of, the creative and user-friendly design skills that Steve Jobs had in earnest--skills that constitute only a fraction of the many forms that genius can take.

Yet another front in the war against math... entrepreneurs

2011-10-30T09:19:00.001-04:00

Or, rather, people with PhDs in "the evaluation of innovation."

Here's some wisdom from one such Innovation Doctor, Marty Nemko (Ph.D, Berkeley), as broadcast this past weekend in the Washington Post:

People on both sides of the aisle agree that the best way to create new, permanent jobs is to create more (and ethical) entrepreneurs. Here’s one way to create them: Replace one high school course with a course in entrepreneurship.

Which course? You guessed it: high school geometry. After all, the Common Core Standards (the ultimate authority on what geometry really is), has included the following abstrusity in its discussion of high school geometry:

“Transformations (rigid motions followed by dilations) define similarity in the same way that rigid motions define congruence.”

Nemko notes that:

The most commonly offered defense of requiring a year of geometry in high school is that it teaches thinking skills. No less than Plato believed that so strongly that he had “Let no one ignorant of geometry enter” engraved over the entrance to the The Academy.

It takes an Innovation Doctor like Nemko to explode this millennia-old rationale with the following rehetorical bombshell:

I have yet to be presented with evidence that teaching thinking skills in an abstract context such as geometry yields better real-world thinking skills than if taught in a real-world context, such as in a course in entrepreneurship, personal finance, or conflict resolution.

Ah, yes, real world math. Where have we heard that before? But is entrepreneurship the only real-world application that matters for our ailing economy? What about STEM (Science, Technology, Engineering and Math)? At the risk of evincing similar hubris, I humbly offer the following response to Nemko:

I have yet to be presented with evidence that teaching thinking skills in a real-world context, such as in a course in entrepreneurship, personal finance, or conflict resolution, yields a better foundation for STEM development than if taught in an academic context, such as in a course in geometry.

So there.

We're left with one question. Which of kind of "thinking skills"--thinking skills for entrepreneurship, or thinking skills for STEM r&D-- is better taught in the classroom, and which is better learned out in the real world?

Math problems of the week: Connected Math vs. 1900's algebra

2011-10-28T08:33:00.000-04:00

I. The first solving equations problem set in Connected Mathematics 2, Moving Straight Ahead: Linear Relationships (published in 2006):

II. The first solving equations problem set in Wentworth's New School Algebra (published in 1898):

III. Extra Credit
Is it dangerous to have high schoolers dive right into algebraic solutions to equations without having them use tables first?

The pitfalls and plusses of multiple choice tests

2011-10-26T09:38:00.006-04:00

Perhaps no test is regarded with greater suspicion than the multiple choice test. It measures trivial, disembodied facts and passive knowledge in a format that never arises in real life; it can be gamed; it's riddled with trick questions. These criticisms are justified, but not because multiple choice tests are inherently flawed. It's just that so many of the ones one comes across are bad.

They're bad because it's really hard to design good ones. Their format--passive selection of one of several short answers--makes it easy for test designers to fall one of into several traps. Most tempting is the "match the definition to the label" question, which often confuses labels with concepts and ends up testing trivial knowledge. Nearly as tempting is the "gotcha" question--often the easiest way to make a test difficult enough that scores fall into a convenient bell curve. Gotcha questions fall into one of two subtypes. The trick question is phrased in such a way that, unless you read it really carefully, it lures you towards a wrong answer; the "did you do the reading" question asks a highly specific, often trivial question that you'll only be able to answer if you did all the reading carefully and remember it in detail. Balancing out the gotcha questions are ones that make the test easier than it should be: testers often accidentally include questions whose answers are obvious even to outsiders, or sets of choices that collectively signal, to those skilled at gaming tests, which one is correct.

Consider the following questions I've culled from two different online introductory psychology quizzes. First we have two in the "match the definition to the label" category, both of which also tap common knowledge of common terminology:

The debate among psychologists regarding the relative contributions of environment and heredity to the developmental process is called
A) the critical period
B) the nature-nurture controversy
C) the stage controversy
D) behaviorism

The "two-way street" concept in childrearing suggests that
A) both mothers and fathers need to accept responsibility for childrearing
B) parents need to be consistent in their childrearing approaches with all their children
C) children act as important influences on their siblings
D) children's behavior affects their parents' behavior just as parents' behavior affects their children's behavior

This next one is similar. Its answer doesn't involve a common term like "nature-nurture" or "two-way street," but is still inferrable from the standard definitions of the various words that follow "self-":

A teacher asks students to keep a record of how much time they spend doing homework daily, and they find that their study time increases. What is this procedure called?
a) Self-assessment
b) Self-monitoring
c) Self-enhancement
d) Self-reinforcement

Yet another "match the definition to the label" question, rather than being obvious, is out to trick you:

The use of technology to present material that progresses in small steps toward a well-defined final goal and is sequenced so that students can answer correctly the majority of the time is called
a) applied behavior analysis.
b) computer-tailored instruction.
c) drill and practice.
d) programmed instruction.

If you didn't memorize the course terminology, the word "technology" might lead you to "computer-tailored instruction;" alternatively, "small steps" and "well-defined goal" might lead you to "applied behavior analysis."

Then we have a did-you-do-the-reading question which simultaneously manages to be gameable. Did you ever notice how often the "all of the above," "none of the above," and "some of the above" answers are the correct ones?

With regard to variation in development, the text asserts that
A) different children develop at different rates
B) children vary in their own rate of development from one period to the next
C) little variation exists between children beyond the age of seven
D) a and b above

Here are some other examples of this (I found no counterexamples in these tests):

In which of the following areas do adolescents have more challenges when compared with younger and older individuals?
A) parent-child conflicts
B) mood changes
C) risky behavior
D) all of the above

According to research comparing children in day-care centers versus children raised by mothers in their own homes, the biggest differences were found in the children's
A) physical health
B) intellectual development
C) attachment
D) none of the above

Returning to trick questions, another one uses "identical twins" to lure you towards "genetics." While even an outsider can rule out "imprinting," only if you remember the particular study on toilet training alluded to here will you know the correct answer:

Research on toilet training conducted with identical twins illustrates the importance of which developmental factor?
A) maturation
B) imprinting
C) nurture
D) genetics

Perhaps the biggest problem with multiple choice questions is that they so often tap superficial knowledge of labels rather than deep understanding of concepts. We've already seen four examples of this; here are two more:

The recognition that the volume of water remains the same whether it is in a short, wide beaker, or a long, narrow beaker is called
A) reversibility
B) conservation
C) decentering
D) formal operations

According to Kohlberg, at what level of moral development would a child most likely be concerned about pleasing his parents and teachers?
A) the preconventional level
B) the premoral level
C) the conventional level
D) the principled level

My reaction to these questions is who cares what the recognition about water volume is called, and who cares what Kollbeg called the parent-pleasing level of moral development? Aren't there more interesting, understanding-tapping questions that one could ask about these issues? For example, couldn't one ask which developmental milestone co-occurs with, or might account for, the recognition about water volume?

In fact, there are good multiple choice questions, even within the two psychology tests I'm discussing here:

Which of the following is not developed during the infancy period?
A) object permanence
B) telegraphic speech
C) separation anxiety
D) transductive reasoning

Which of the following describes the correct developmental sequence of play?
A) parallel play, solitary play, cooperative play
B) solitary play, cooperative play, parallel play
C) solitary play, parallel play, cooperative play
D) cooperative play, solitary play, parallel play

Which of the following cognitive abilities improves throughout adulthood?
A) reasoning about everyday problems
B) knowledge of facts and word meanings
C) abstract problem solving and divergent thinking
D) general recall

Compared to individuals in their 20s, individuals in their 70s showed declines in
A) knowledge of word meanings
B) understanding mathematical concepts
C) solving life problems
D) fluid intelligence

Adult personalities are likely to change in each of the following areas except
A) enjoyment of being with other people
B) becoming more dependable
C) becoming more candid
D) becoming more accepting of life's hardships

It's just that--as I know from personal experience--it can take tremendous time and effort to ensure that a multiple choice question requires no more and no less than an accurate comprehension of meaningful, course-specific concepts.

Why exert the effort? Because if one has hundreds of students, multiple choice tests save much more time than they take to devise, freeing up precious hours for things other than assessment. And because there are times when the objectivity and standardizability of multiple choice tests makes them far preferable to the more subjective (if more "authentic") alternatives (c.f. the recent discussion on kitchentablemath on the essay section of the SAT Writing test.)

Designed well, multiple choice tests can measure exactly what they're suppose to. If they didn't, few people would take the PSAT, SAT, AP seriously, let alone treat them--as so many people and institutions so often do--as meaningful measures of aptitude or achievement.

Is the Pope Jewish, II: classroom technology and the children of technocrats

2011-10-24T10:30:00.009-04:00

In a post I wrote just two weeks ago, I discussed two New York Times articles about the failure of technology in the classroom to raise test scores in Arizona, and the failure of one of the most acclaimed educational technologies, Cognitive Tutor, to raise test scores in general. I concluded by asking:

Will these recent exposés about the limitations of educational technology for subjects other than computer science have any effect whatsoever on the edtech bandwagon?...We might as well ask whether the Pope is Jewish.

Sure enough, just one week later (last Wednesday), yet another NY Times article on online education appears, this one discussing how the Munster Indiana school district has jumped on the bandwagon:

Laura Norman used to ask her seventh-grade scientists to take out their textbooks and flip to Page Such-and-Such. Now, she tells them to take out their laptops.

The day all have seen coming — traditional textbooks being replaced by interactive computer programs — arrived this year in this traditional, well-regarded school district.

Munster's technological revolution was particularly sudden:

Unlike the tentative, incremental steps of digital initiatives at many schools nationwide, Munster made an all-in leap in a few frenetic months — removing all math and science textbooks for its 2,600 students in grades 5 to 12, and providing a window into the hurdles and hiccups of such an overhaul.

But Munster isn't the first to go digital:

Schools in Mooresville, N.C., for example, started moving away from printed textbooks four years ago, and now 90 percent of their curriculum is online.

and:

Munster’s is part of a new wave of digital overhauls in the two dozen states that have historically required schools to choose textbooks from government-approved lists. Florida, Louisiana, Utah and West Virginia approved multimedia textbooks for the first time for the 2011-12 school year, and Indiana went so far as to scrap its textbook-approval process altogether, partly because, officials said, the definition of a textbook will only continue to fracture.

The cost? Munster has paid $1.1 million for infrastructure while parents pay an annual $150 rental fee for laptops, Schools in general: are "spending an estimated $2.2 billion on educational software."

The benefits? No efficacy data is cited, of course. Students, to some extent, get to work at their own rates. And then there's this:

Angela Bartolomeo’s sixth graders spent a recent Wednesday rearranging terms of equations on an interactive Smart Board and dragging-and-dropping answers in ways that chalkboards never could. (In between, a cartoon character exclaimed that “Multiplying by 1 does not change the value of a number!” in his best superhero baritone.)

And this:

Ms. Norman, the seventh-grade science teacher, is using material from Discovery Education, which on that Wednesday included videos from Discovery’s “Mythbuster” series (commercial-free), an interactive glossary and other eye candy to help students investigate whether cellphones cause cancer. When Ms. Norman told the students to take out their ear buds to watch a video, two in the back yelped, “Cool!”

And this:

“With a textbook, you can only read what’s on the pages — here you can click on things and watch videos,” said Patrick Wu, a seventh grader. “It’s more fun to use a keyboard than a pencil. And my grades are better because I’m focusing more.”

Whether students are focusing on the right things is another matter. And wouldn't it be nice if there were explanations, rather than exclamations, regarding what happens when you multiply a number by 1? The basic problem with computerized instruction, as I noted earlier, is that it almost never provides perspicuous feedback. Answers are either right, or wrong, and that's it.

Perhaps no one knows the limitations of computer software better than computer software experts. Where are these people sending their kids to school? An article in this weekend's New York Times provides a glimpse. Focusing on Silicon valley, it describes how the chief technology officer of eBay, along with "employees of Silicon Valley giants like Google, Apple, Yahoo and Hewlett-Packard," are sending their children to the area's Waldorf school:

The school’s chief teaching tools are anything but high-tech: pens and paper, knitting needles and, occasionally, mud. Not a computer to be found. No screens at all. They are not allowed in the classroom, and the school even frowns on their use at home.

Noting that "three-quarters of the students here have parents with a strong high-tech connection," the Times observes:

Schools nationwide have rushed to supply their classrooms with computers, and many policy makers say it is foolish to do otherwise. But the contrarian point of view can be found at the epicenter of the tech economy, where some parents and educators have a message: computers and schools don’t mix.

The article quotes Waldorf parent Alan Eagle, who "holds a computer science degree from Dartmouth and works in executive communications at Google, where he has written speeches for the chairman," and who "uses an iPad and a smartphone:"

“I fundamentally reject the notion you need technology aids in grammar school... The idea that an app on an iPad can better teach my kids to read or do arithmetic, that’s ridiculous.”

Of course, there is one particular way in which computers could be highly effective teaching tools: for instruction in computer programming. But has there has been a rise, or a decline, in computer programming instruction in the decades since schools began jumping on the edtech bandwagon?

We might as well ask whether the pope is Jewish.

Does autism really mean "visual thinking"?

2011-10-22T08:15:00.002-04:00

Many people have claimed, my students included, that people with autism are "visual thinkers." But try as I have to find empirical support for this, I've mostly come up dry. All of my Google Scholar searches lead ultimately to Temple Grandin and to her anecdotal accounts of her own visual thinking. What about autistic individuals in general?

The notion that autistic people are "visual thinkers" seems to stem primarily, not from experimental data, but from the sorts of therapeutic and teaching strategies that appear to work best. Pictures, flowcharts, visual schedules, written prompts and directions: these are the common denominators of a whole range of autism remediations.

But why are they so effective? Is it necessarily because autistic children are deeply visual in their thinking? Or might it have more to do with their difficulties in paying attention to the things we want them to attend to? Perhaps it all boils down to the fact that aural information is fleeting while visual information tends to linger. If a child tunes out to your oral directions, the written directions are still there waiting. Similarly "visual," by this token, are kids with ADD/ADHD.

Language delays also play a role: where words fail, as they so often do in autism, a picture speaks a thousand words.

Finally, there's that special appeal of text--of letters and numbers--not just for the hyperlexic subpopulation, but for AS children in general, drawn as they are towards shapes and symbols. J, for example, follows a movie much better with the captions on--and not just because he's deaf or "visual", but because he's much more interested in printed words than in the ones that come out of people's mouths.

Math problems of the week: 4th grade Investigations vs.Singapore Math

2011-10-20T13:25:00.000-04:00

Finding out how many people counted vs. finding common multiples

I. A 4th grade Investigations homework assignment, assigned in early November [click to enlarge]:

II. The 9th assignment in the 4th grade Singapore Math Primary Mathematics 4A workbook [click to enlarge]:

III. Extra Credit
Why does the Investigations assignment, but not the Singapore Math assigment, have to spell out its purpose? (See NOTE in the upper right corner of the former).

Why is anyone paying attention, II

2011-10-18T13:10:00.004-04:00

A few weeks ago, I marveled at how a book with "a flawed premise, flawed data; and no results" could garner any attention at all. In this case, the book was David Sloan Wilson's The Neighborhood Project: Using Evolution to Improve My City, One Block at a Time, and it received one of the most devastating NYTimes book reviews I've ever seen.

Another tome whose attention and popularity I've wondered about is Now You See It, a book about cognitive science by English professor Cathy N. Davidson. It, too, has received a devastating review in the New York Times. What's particularly damning is that the reviewer is Christopher Chabris, a psychology professor who co-conducted the experiment around which Davidson centers her book. This is the experiment that also stars, much more appropriately, in Chabris' own book, The Invisible Gorilla, and Other Ways Our Intuitions Deceive Us: the experiment in which subjects told to count the passes in a basketball game failed to notice a man in a gorilla suit walking through the court and thumping his chest. Here is Chabris on Davidson:

Davidson’s book is subtitled “How the Brain Science of Attention Will Transform the Way We Live, Work, and Learn,” but there is almost no brain science in the book at all, and attention is invoked mainly as a metaphor.

Metaphors can work well in English class, but Davidson is more ambitious, extending what she calls the "attention blindness" of the Gorilla Experiment into the human brain:

Davidson is so taken with the phenomenon that she proclaims it “the fundamental structuring principle of the brain.” Inattentional blindness (as it is properly called) is an important and counterintuitive fact about how perception works, but even I don’t think it can carry half as much weight as Davidson loads upon it. And she provides little but anecdotal support for a central argument of the book: that since every individual is bound to miss something, by working together people can cover one another’s blind spots and collectively see the big picture.

While Chabris calls this "neurobabble," it, plus a smattering of anecdotal evidence, are all you need when it comes to convincing people how to reform schools:

"We currently have a national education policy based on a style of learning — the standardized, machine-readable multiple-choice test — that reinforces a type of thinking and form of attention well suited to the industrial worker — a role that increasingly fewer of our kids will ever fill,” she writes. Thanks mainly to the Internet, “their world is different from the one into which we were born, therefore they start shearing and shaping different neural pathways from the outset. We may not even be able to see their unique gifts and efficiencies.”

Davidson can also be seen, in the earlier Wall Street Journal Review, noting that "Our schoolmaster-led classrooms and grading customs look pretty much as they did not just in the last century but in the 19th century." But it's in Chabris' review that we learn what our "grading customs" should be replaced with. As Chabris puts it:

Anything that comes from the Internet must ipso facto be worth incorporating into education — hence her proposal that grading be “crowdsourced” to the very students under evaluation. Davidson seems to interpret the harsh criticism she received when she first floated this idea a few years ago as a sign that she must be on to something.

If criticism means you're on to something, Davidson should be especially thrilled with this:

Like many authors who embrace new ideas rather than build on what has come before, Davidson sets out to destroy the old beliefs, as if burning down a forest in order to plant new crops. Take intelligence testing: Davidson starts with the mistaken assertion that I.Q. refers to a purely innate cognitive ability, and then says that the “inherited component to I.Q.” is not genetic but “inherited cultural privilege.” Both claims are contradicted by virtually every relevant study ever conducted.

What makes her book so popular, of course, is precisely how it embraces new ideas and attempts to destroy old ones--and in a way that resonates so harmoniously with today's right-brained values:

Switching rapidly from one task to another actually helps us see connections between ideas and be more creative than we would if we held ourselves to a regimen of completing one task before we start another, she suggests. Mind-wandering,” she writes, “might turn out to be exactly what we need to encourage more of in order to accomplish the best work in a global, multimedia digital age.”...

It takes a neuroscientist, rather than an English professor, to point out the hard, cold, left-brained facts:

...But this speculation is up against facts Davidson omits: the results of experiments showing that for all but perhaps an elite 2 to 3 percent of subjects, doing things in sequence leads to better performance than trying to do them simultaneously.

Yes, let's remember this: not just for my "left-brainers", but for 97-98 percent of the population, doing things in sequence leads to better performance than trying to do them simultaneously. If only Davidson herself had followed this advice.

Homeschooling update

2011-10-16T08:47:00.001-04:00

My daughter is now in 5th grade, and, having turned in our portfolio and a new Affidavi this summer, I'm once again authorized to homeschool her.

We've made a couple of organizational changes. Initially I had thought she needed the structure of a schedule, but after observing how frustrated she would sometimes get, I now give her a checklist instead. As a result, she is less stressed out and more efficient. She also likes the freedom of deciding what order to do things in. Her music teachers have caught on to our flexible schedule, and she now has her piano, violin, and (new instrument!) organ lessons early in the day. Come winter, it'll be nice not to be biking around in the dark.

She completed the 5th grade regular Singapore Math curriculum over the summer (when we lightened up, but kept up the math, reading, and French), and is working on the 5th grade Challenging Word Problems. The problems get quite complex, with upwards of 4 distinct steps, and so I'm requiring her to spell out each one in her math notebook and label everything. She's becoming less resistant to this as she finds herself getting a lot less lost and performing the wrong calculations less and less often. Note that this requirement is completely different from the "explain your answer in words, numbers, and pictures" of so much school math (e.g., TERC/Investigations). Instead of "meta-cognitively reflecting" (which has no proven cognitive benefits, frustrates her, and detracts from the actual math), she's unburdening her working memory, helping herself keep track, and developing good habits for algebra and beyond.

She's begun diagramming sentences, which she seems to enjoy. I see this as a scaffolding for learning, later on, the finer points of style, and as a practice for making sense sense of complicated sentences and foreign language grammar.

On that note, to the French in Action videos we've added a French workbook and a new cable channel: TVMonde5. She's picking up more and more, sometimes making connections to English vocabulary (just yesterday connecting French glace to English glacier).

Most of the rest is reading and writing. She's continuing to read (and summarize) classic myths and fables, and poetry; current novels include Island of the Blue Dolphins, volume 9 of Series of Unfortunate Events, and the Phantom Tollboth. She's finished North American Wildlife and now reading and writing about bugs. She continues to watch (and take notes on) one or two David Atttenborough nature videos per week. She's continuing to work her way through the Story of the World series, with daily summaries in her history notebook.

As for social studies, we've added Friday night Girl Scouts and Saturday morning Theater School to the weekly mix. As I write, she is doing her only homework assignment all week: making a cat toy for Girl Scouts.

Math problems of the week: 5th grade 1920s math vs. Trailblazers

2011-10-14T08:37:00.001-04:00

I. The first mixed fractions addition section in the second 5th grade fractions unit in Hamilton's Essentials of Arithmetic (published in 1919), p. 323 [click to enlarge]:

II. The first mixed fractions additions section in the second 5th grade fractions unit in the Trailblazer's Student Guide (published in 1998), p. 389:

III. Extra Credit
Should Trailblazers 5th graders lose points if they don't solve the first four problems using pattern blocks?

Front page articles on the edtech bandwagon

2011-10-12T08:02:00.001-04:00

Fast on the heels of a front page New York Times exposé on how education technology has failed to raise test scores comes a front page Education Week article on the virtues of replacing teacher-centered lessons at school with technology-centered lessons at home. The technology in question is that of the Khan Academy, whose library of lectures and problem sets is impressive in its vastness but not in its instructional feedback. If you input a wrong answer to a math problem you are told that your answer is wrong, but not why, nor how to fix it. Despite this, the Khan Academy has empowered teachers like 10th grade biology teacher Susan Kramer to skip over direct, structured instruction, and instead to watch her students "weave through rows of desks, pretending to be proteins and picking up plastic-bead 'carbohydrates' and goofy 'phosphate' hats as they navigate their 'cell.'"

To be fair, the Khan Academy (1) hasn't been around that long and (2) is the creation of a former hedge fund manager with degrees in math, computer science, and engineering but not in, say, cognitive science and child development. As such, the Khan Academy hasn't profited from the "over 20 years of research into how students think and learn" that underpins more established educational software programs like Carnegie Mellon's Cognitive Tutor.

So it was a bit disconcerting to find, fast on the heels of the Edweek's Khan Academy article, a front page article in Sunday's New York Times on Cognitive Tutor, and how it, too, has turned out to have no statistically significant impact on test scores. While I'd never had a chance to try it out (unlike the Khan Academy, Cognitive Tutor gates access to demos and charges big bucks instead of nothing at all), I'd heard only good things about it, and J enjoyed soaring through its algebra lessons during middle school. But as soon as I read the Times' description of its pedagogy, its limitations became crystal clear:

When the screen says: “You are saving to buy a bicycle. You have $10, and each day you are able to save $2,” the student must convert the word problem into an algebraic expression. If he is stumped, he can click on the “Hint” button.

“Define a variable for the time from now,” the software advises. Still stumped? Click “Next Hint.”

“Use x to represent the time from now.” Aha. The student types “2x+10.”

A math buff would soar right through this; for anyone else, the hints seem way too much of a crutch. There's no mechanism here for ensuring that you're working things out to the best of your ability before resorting to "hint"---i.e., nothing to stop you from clicking "hint" the moment you're not sure what to do. And what if your answer is almost right: say you forgot to include the initial $10, or let x stand for hours rather than days? As far as I can tell (I've now tried it out a bit), you're either right or wrong, and that's it. The program simply isn't sophisticated enough to highlight exactly what needs adjustment. And there's a very simple reason for this. As I discovered in creating a software program that highlights grammatical errors in English phrases and sentences, this kind of perspicuous feedback takes a huge amount of coding (of the sort that you don't find in any other language teaching software program, thank you very much). Programming in the analogous feedback for mathematical expressions and equations strikes me as even more prohibitive.

On closer inspection, therefore, Cognitive Tutor seems inevitably to foster--in all but the brightest, most motivated students (the ones most able to basically teach themselves)--far too passive of a learning environment for lasting learning. Indeed, the only truly active learning environment that I've ever seen in any software program for any academic subject is that which a computer programming language platform provides for--what else?--computer programming. Only here does the feedback--the error messages or the unexpected outputs--precisely reflect what you've done wrong.

Will these recent exposés about the limitations of educational technology for subjects other than computer science have any effect whatsoever on the edtech bandwagon?

We might as well ask whether recent cognitive science findings have had any effect on how schools teach "higher level thinking." Or whether mainstreaming kids on the autistic spectrum has had any effect on mandatory group work and personal reflections. Or whether parental concerns have had any effect on schools choosing Reform Math. Or whether, for that matter, the Pope is Jewish.

Autism diaries, XXIV: Who is Christopher Columbus?

2011-10-10T07:45:00.004-04:00

"I don't know."

The revelation in question happened in late August, but I share it today in honor of someone who appears to be fading from America's k12 classrooms.

I actually wasn't that surprised when, while reading with J about the Age of Exploration in The Story of the World, Volume 2, it emerged that he didn't know who Christopher Columbus was. After all, one of the main reasons I've been working my way through this four-volume series with him is that I know he's picked up very little world history in the course of his 15 1/2 years. But, while he's still mostly oblivious to the incidental factoids that float all around him, he's increasingly attending to school, and increasingly sitting in the same classes, doing the same assignments, and taking the same tests, as everyone else.

So while I'm guessing that most (all?) of his schoolmates not only have heard of Christopher Columbus, but also know something about what he's famous for, I'm also guesssing that none of them learned these things from a social studies class or reading assignment that made them their focus.

Indeed, in this age where it's anyone's guess which facts our schools are making it their responsibility to teach, it occurs to me that students like J--with their narrow interests and their tendency to tune out most of the ambient information that others soak up without deliberate instruction--are a valuable resource. Next time you wonder whether your school is actually teaching (rather than merely mentioning in passing) the Bill of Rights (say), or the Cold War, or the Silk Road, ask an Aspie. That is, look for a spaced-out, narowly focused child on the autistic spectrum who hasn't made the topic their personal specialty, and see what he or she can tell you about it.

Above and beyond empathy

2011-10-08T08:36:00.004-04:00

In a recent NY Times column entitled "The Limits of Empathy," David Brooks writes about how gut-level empathy falls short of guaranteeing moral behavior, and, worse, can even lead us astray:

Empathy makes you more aware of other people’s suffering, but it’s not clear it actually motivates you to take moral action or prevents you from taking immoral action.

...

Empathy orients you toward moral action, but it doesn’t seem to help much when that action comes at a personal cost. You may feel a pang for the homeless guy on the other side of the street, but the odds are that you are not going to cross the street to give him a dollar.

Brooks cites a recent paper by philosopher Jesse Prinz (a graduate school classmate of mine) on studies investigating the link between empathy and moral action:

“These studies suggest that empathy is not a major player when it comes to moral motivation. Its contribution is negligible in children, modest in adults, and nonexistent when costs are significant.”

Prinz also observes, in Brooks' words, that:

[Empathy] influences people to care more about cute victims than ugly victims. It leads to nepotism. It subverts justice; juries give lighter sentences to defendants that show sadness. It leads us to react to shocking incidents, like a hurricane, but not longstanding conditions, like global hunger or preventable diseases.

...or my personal obsession: preventable educational catastrophes. On that note, substitute "empathy" with "appreciation," "moral" with "academic," and "moral judgment" with "rigorous analysis," and some of Brooks' observations sound a lot like Reform Math and its various cousins:

These days empathy has become a shortcut. It has become a way to experience delicious moral emotions without confronting the weaknesses in our nature that prevent us from actually acting upon them. It has become a way to experience the illusion of moral progress without having to do the nasty work of making moral judgments.

Indeed, speaking of schools:

In a culture that is inarticulate about moral categories and touchy about giving offense, teaching empathy is a safe way for schools and other institutions to seem virtuous without risking controversy or hurting anybody’s feelings.

Just as math and science appreciation must be channeled into structure, analysis, and hard work, so, too with empathy:

People who actually perform pro-social action don’t only feel for those who are suffering, they feel compelled to act by a sense of duty. Their lives are structured by sacred codes.

Reforming society entails a similarly left-brained approach:

If you want to make the world a better place, help people debate, understand, reform, revere and enact their codes. Accept that codes conflict.

Accept that codes conflict. This is key, especially when Brooks uses words like "sacred." And maybe I'm biased, but I suspect that left-brainers are a lot better at this than right-brainers are.

Math problems of the week: 1900's algebra vs. Chicago Math algebra

2011-10-06T11:33:00.000-04:00

Final problem sets on graphing

I. From the end of Wentworth's New School Algebra (1898), p. 423 [click to enlarge]:

II. From the end of The University of Chicago School Mathematics Project Algebra: Integrated Mathematics (2002), p. 815:

III. Extra Credit:

How do you think 21st century Chicago Math students, equipped with graphing calculators, would do on the 1900's graphing problems?

Narratives before expository writing: the problem with one size fits all

2011-10-04T08:05:00.000-04:00

In preparation for a class I'll be teaching soon, I've been reading up on reading disabilities. The various articles and chapters I've reviewed tackle a number of disabilities--from dyslexia to Specific Language Impairment to ADD/ADHD to autistic spectrum disorders. And they suggest a number of disability-specific remediations. Many of these, unfortunately but not so surprisingly, haven't been tested for efficacy, but most sound eminently reasonable.

It's when it comes to which sorts of texts are most challenging that the reading disability literature starts to falter. For this is where the peculiar stengths and weaknesses of students on the autistic spectrum--the strengths and weaknesses that distinguish these students from all their other reading-disabled peers--most come into play.

It is the underlying assumption of the literature on reading disabilities that, everything else being equal, narrative texts (i.e., chronological, character-centered stories) are easier than expository texts (logically or thematically organized explications). As far as remediation goes, this implies that that academic subjects that might typically be taught in a more expository way are best introduced--at least to struggling readers--in narrative form.

Here, for example, are recommendations from Carol Westby in "Assessing and Remediating Text Comprehension Problems":

Narratives can provide students with some of the schema knowledge that they will need to comprehend expository texts in social studies and science lessons.
...
For example, when beginning a unit on weather for third-grade students, a teacher read the book The Storm in the Night, in which a grandfather and grandson sit out a storm while the grandfather tells about his fear of storms as a child. Following the story, children can be encouraged to share their experiences with storms.

However well this might work for students with dyslexia, ADHD, and/or Specific Language Impairment, I'm guessing that many children with autism would be bored out of their minds. Most would find it much less taxing--and much more engaging--to read an expository piece on different types of storms than to listen first to their teacher reading about a grandfather's childhood fear of storms and then to their classmates talking about their personal experiences.

Indeed, as I've argued elsewhere, if we want to maximize the academic progress and minimize the boredom and frustration of children with autism, it might be best to skip over the more socially and emotionally-driven narratives and go straight to the most technical, logical, fact-rich (and linguistically accessible) expository pieces that we can find.

Reform Reading in Montgomery County MD

2011-10-02T08:42:00.006-04:00

Parents in Montgomery County, MD are already worried about the apparent demise of appropriately challenging elementary school math classes. A new article in the Montgomery County Gazette presents reasons for similar concerns about reading classes:

Engrossed in the picture book “Grandpa Comes to Stay,” second-grader Jake Barreto hardly acted like a student with specific marching orders.

A picture book for 2nd graders?

Perhaps instruction is "differentiated," with different students reading different books. But it sure doesn't look that way. Illustrating the article is a picture of a teacher standing up in front of an electronic Pomethean Board facing what looks like an entire class. The caption describes the teacher as "conduct[ing] a reading lesson under the new curriculum."

The new curriculum, "one of the largest academic initiatives in the Montgomery County Public Schools," is ominously entitled Curriculum 2.0:

Curriculum 2.0 is billed by the school system as a way to teach critical thinking and problem-solving skills. It stresses the mastery of material over the quantity studied, and integrates more subjects, like science and social studies, into lesson plans for math and English.
...
Curriculum 2.0 functions like an inverted pyramid, with the broadest concepts at the top and daily and weekly objectives and tasks on the bottom. At the top are the critical thinking, creative thinking, and academic skills the school system has adapted from the Common Core standards.

As an example of first grade "critical thinking" skills, the article cites "identifying attributes of an object." As for academic skills, it cites "Collaboration." Collaboration? Here are both goals in action:

Using an electronic Promethean board, Stroud quizzed pupils on the three key details that helped describe lions in the book, and asked them to identify a topic sentence. They also had to work in groups to identify the big paws and teeth that made the lions leonine.

The article doesn't give examples of "creative thinking," so one can only imagine what these look like.

Lower down on Curriculum 2.0's pyramid are "unifying questions," for example, "How can asking questions or solving problems in different ways help you make sense of ideas?"

Specific "reading objectives" help students answer this question. In the case of 2nd grade Jake and his picture book, the reading objective was "to identify with a character’s perspective." (Jake's answer to this one was "I think they had a good time.") The math objective was "to compare 3-digit numbers using '<'"

The article notes that Curriculum 2.0 "is based on the national academic standards, which have been adopted by 44 states and the District of Columbia called the Common Core State Standards." It's also completely at odds not only with what makes reading interesting, but also with what recent cognitive science has shown about the domain-specificity of "critical thinking" skills. What all this amounts to, then, is very bad news for our latest elementary school students, and yet another cautionary tale about the Common Core Standards.

Math problems of the week: 4th grade Investigations vs. Singapore Math

2011-09-30T08:28:00.000-04:00

I. A 4th grade (TERC) Investigations homework sheet, handed out in mid-November (Unit 3, Section 4.1, p. 52) [click on picture to enlarge]:

II. From an earlier point in the 4th grade Singapore Math curriculum (Primary Mathematics 4A, p. 54) [click on picture to enlarge]:

III. Extra Credit

1. Compare the mathematical and logical demands of the two problem sets.

2. How do the different roles of logical reasoning vs. visual representation parallel what we see in Reform vs. traditional geometry?

Autism Diaries XXVIII: Deep thoughts

2011-09-28T08:12:00.003-04:00

Answers to the week one survey questions at his new high school:

What is a big question that you wonder about a lot?
What is your password.

What do you know deep in your heart to be true?
It pumps blood.

What is something that you notice that other people don't?
Ceiling fans.

How do you feel about life's uncertainties and opportunities?
I feel fine.

What is your most favorite activity?
Making lots of money.

What is your least favorite activity?
Getting killed.

The mystery of high functioning autism

2011-09-26T08:59:00.001-04:00

I used to think of Temple Grandin as someone who'd been severely autistic as a child but made extraordinary progress during adolescence and early adulthood. My impressions came largely from Grandin's Thinking in Pictures, in which she notes that at two and a half she had "no speech and no interest in people," and then mostly discusses her adolescent and adult years. It was only in the last month, when I finally got around to reading Grandin's earlier memoir, Emergence, that I realized how much of her extraordinary progress must have occurred in early childhood.

Here she is, for example, as a fourth grader:

One time when I was visiting my friend, Sue Hart, we were playing in her hayloft. From the loft we looked down on the garden of Mrs. McDonnell, our fourth grade teacher. Sue said, "Bet you can't throw the red jack ball into Mrs. McDonell's bird bath."

So I threw the ball from the loft and bounced it out off the bird bath. For some reason, I don't know why, there were about a hundred big brown empty whiskey bottles up in that hayloft. Sue said, "Why don't you throw a whiskey bottle out?"

So I threw the bottle and it smashed the bird bath... We proceeded to throw everyone one of those whiskey bottles out of the hayloft against the fourth grade teacher's chimney, her sidewalk, her porch, her rose bushes. There was broken glass all over her garden.

The next day in school Mrs. McDonnell told the class about the terrible damage that had been done to her garden. I wasn't about to get caught so at lunch time I sat down next to Mrs. McDonnell in the cafeteria. "Mrs. McDonnell, what a terrible thing to happen to your lovely garden," I said.

"Thank you, Temple, for caring." Mrs McDonnell smiled warmly at me.
For once, I looked her straight in the eye and told her that I had no idea who had ruined her garden. "But I was at my friend Sue's house," I said, "and we saw Robert Lewis and Burt Jenkins near your house yesterday."

"Thank you for telling me this, Temple. You're a nice little girl to care."
...
I didn't feel bad about getting [Robert and Burt] in trouble. They might have done it if they'd thought of it.

A few paragraphs later we find her proposing to her cousin that they did up his neighbor's yard after he complains that they are tattletales and says he'd "sure like to fix them." When Peter worries that he'll get blamed, Temple giggles "Who's to blame? The dogs did it."

A number of things are remarkable here:

So I threw the ball from the loft and bounced it out off the bird bath: understanding linguistic idioms and social gambits ("Bet you can't...")

What a terrible thing to happen to your lovely garden: complex language, conversationally appropriate remarks, and sophisticated deception.

Mrs McDonnell smiled warmly at me: facial expression reading.

They might have done it if they'd thought of it: complex perspective taking.

Who's to blame? The dogs did it: sophisticated, non-literal subtext.

By Junior High her deception (and interest in others) becomes even more (self-sacrificingly) sophisticated:

When I think about it now, I realize that part of my mischief... was the thrill of wondering what would happen--the reaction of my peers--and if I'd get caught. A good example of this was gym class, where I'd wait until the other girls had gone into the gym and then hide their classroom clothes. When gym was over, I laughed and laughed to myself as I watched them run around trying to find their clothes... I always hid mine, too, so I wouldn't be a suspect.

If you watch and listen to Temple Grandin today, and if you know what to look for, you see immediately that she's the real thing. Her face, her gaze, her gestures, her tone of voice, her responses to spontaneous questions: all of these cry out Asperger's. But the social and linguistic skills of her early childhood--so seldom the focus of today's discussions and publications about her--cast all of this in a new light. Now the big mystery isn't how Grandin became such a high functioning adult, but how she went from "no speech and no interest in people" at two and a half to the level of social sophistication we see at nine or ten, and how, despite all this early sophistication, she still remains, after all these decades, so squarely on the spectrum.

Autism diaries XXVIII: adventures to and from high school

2011-09-24T11:34:00.006-04:00

As a special ed student, J qualifies for special transportation to and from his new high school. I'd like him to be able, eventually, to take public transportation just like his classmates, and so every morning I ride in with him, taking the green trolley to the orange train.

J has the logistics down pat and knows exactly where to get on and off. But every morning I see him do something that shows just how unready he is to travel on his own. He sneezes without covering his mouth; he lets go of his backpack; he can't keep his balance while standing while the trolley's in motion, leaning into nearby passengers; he pushes the turnstyle too hard. Most alarmingly, he can't resist the urge to charge past people, especially when there's one seat left on the trolley (as there so often is, way in the back, past all the standing passengers), or he sees a train a flight of stairs below him sitting on the tracks, its doors about to close.

So we have our morning transit riding tutorial, and then I let special transportation take over in the afternoon. But because apparently no other special ed kids are commuting between our part of town and where J attends school, this special transportation comes in the form of a taxicab.

J loves it. Especially because the driver readily follows his directions and drops him off wherever he asks.

So, if you have lunch money left over, why not get dropped at the Hoops Deli around the corner. You walk home from there grinning and brandishing a bottle of lemonade, and then, if your mother fails to catch on, tell her that "I stole a basketball and threw it through the hoop." Make sure she knows you are "speaking metaphorically."

Math problems of the week: 1960's vs. 21st Century geometry

2011-09-22T08:18:00.001-04:00

Second set of introductory problems:

I. From Weeks Adkins A Course in Geometry (1961), pp. 11-12 [click to enlarge]:

II. From Discovering Geometry: An Investigative Approach (2003), pp. 8-9 [click to enlarge]:

III. Extra Credit:

1. Which is more important in the 21st century: precise definitions or artistic designs?

2. Estimate the volume and mass of the Discovery and Akins texts. Hint: one of these texts has twice the volume and three times the mass of the other.

Grandiose theories about group selection

2011-09-20T08:05:00.006-04:00

The book is out; the buzz is out. Here's National Public Radio, The New York Times, and Nature, all fawning over David Sloan Wilson and his The Neighborhood Project: Using Evolution to Improve My City, One Block at a Time.

Only a few weeks after all this do we get the critical review--and it is one of the most devastating New York Times Book Reviews I've seen, especially given the reviewer's credentials. He is Jerry Coyne, a professor of ecology and evolution at the University of Chicago.

First, Coyne argues, Wilson's basic premise is flawed:

Wilson is well known for his controversial work on evolution via “group selection.” While modern evolutionary theory emphasizes natural selection acting on genes and individuals, Wilson sees an important role for selection acting on entire social groups, particularly in the evolution of “prosociality”: that complex of behaviors, including altruism and compassion, that underlies human cooperation.

...

Group selection isn’t widely accepted by evolutionists for several reasons. First, it’s not an efficient way to select for traits, like altruistic behavior, that are supposed to be detrimental to the individual but good for the group. Groups divide to form other groups much less often than organisms reproduce to form other organisms, so group selection for altruism would be unlikely to override the tendency of each group to quickly lose its altruists through natural selection favoring cheaters. Further, we simply have little evidence that selection on groups has promoted the evolution of any trait. Finally, other, more plausible evolutionary forces, like direct selection on individuals for reciprocal support, could have made us prosocial.

Second, Wilson's data is flawed. It consists of surveys of children in different neighborhoods that are supposed to measure (a) how "prosocial" they are and (b) how "supportive" their neighborhoods are:

Prosociality is determined by the level of agreement with statements like “I am trying to help solve social problems.” At the same time, support from their environment is measured by students’ agreement with questions like “I have a family that gives love and support” or “I have good neighbors that help me succeed.”

As Coyne points out, "both statistics derive... from self-report, so there is no independent evaluation of students’ environments." Nonetheless:

Wilson makes much of the correlation between prosociality and a supportive environment, arguing that prosocial nature comes from prosocial nurture.

This flawed conclusion then leads to a half-baked strategy that thus far has yielded no results:

After using the survey to identify neighborhoods with higher or lower degrees of prosociality, Wilson’s strategy is to improve the city by having them compete. This involves neighborhood contests to design city parks, studies of churches to determine why some are better able to recruit and retain members...

..

Five years into the Neighborhood Project, it has apparently yielded only one published paper, which gives the results of the prosociality survey. The Binghamton parks contest went belly-up, as people weren’t interested in competing according to Wilson’s schedule.

A flawed premise, flawed data; and no results: why, then, is anyone paying attention? Perhaps it's the way Wilson carries on about how many other areas his theory extends into, from economics to education, and because we love grandiose theories more than data and analysis. Or perhaps it's what Wilson has to say about schools in particular, and how this resonates with right-brained educational Romanticism:

Education, for instance, will be transformed by going back to the ways of our distant ancestors, who gave their children no formal instruction but let them learn from unstructured play and interaction with older kids.

Or perhaps what recent research has concluded about narcissistic leaders applies to narcisstic public figures in general:

Wilson’s enthusiasm has a way of shading into hubris, as when he proclaims: “Now that my intellectual life and my everyday life have been thrown together, I can almost feel the connections taking place inside my head. Like a Shakespearean play, the length and breadth of human nature are being enacted in front of me on a local stage.”

As an aside, I've often wondered how truly cooperative humans really are. As far as I can tell, the supposed mystery of our supposed cooperativity has been one of the main reasons why some evolutionary biologists (however much in the minority they are) have invoked group-level selection in the first place. But are we really as cooperative (and as altruistic) as we'd like to think? Sure, we're great at pretending we are; after all, we all depend on reciprocal support, and we zealously keep tabs on, and zealously gossip about, one another's behavior. But what about gossip's greatest thrill: revelations of all the backstabbing and cheating and pettiness that occur whenever people (especially those who try hardest to seem noble and cooperative and above it all) think they can get away with it.