And other fun topics!
My pre-TEDx talk interview on WITF public radio in Harrisburg is now up:
Tuesday, January 31, 2012
And other fun topics!
Sunday, January 29, 2012
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.
Saturday, January 28, 2012
Wednesday, January 25, 2012
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.
Monday, January 23, 2012
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.
Saturday, January 21, 2012
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.Cain cites several studies showing the various downsides to cooperation (vs. collaboration). First, there's creativity:
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.)
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.
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.
Thursday, January 19, 2012
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.
Tuesday, January 17, 2012
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.Such an incentive structure, Caplan argues, will result in grades that (like real-world raises and bonuses) reflect 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.
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."
Sunday, January 15, 2012
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?The reasoning behind such questions, explains reporter William Poundstone, is:
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.
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?"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.
"What color best represents your personality?"
"What animal are you?"
Friday, January 13, 2012
I. A 4th grade (TERC) Investigations homework assignment, assigned in early January:
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?
Wednesday, January 11, 2012
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.
Saturday, January 7, 2012
"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.
Friday, January 6, 2012
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!
Thursday, January 5, 2012
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.
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.
Wednesday, January 4, 2012
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?
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.
Amy P said...
Is there some sort of pre-written template available to the journalists who turn out these pieces? Ugh.
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.
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.
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.
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."
Tuesday, January 3, 2012
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.
"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.
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)?
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 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.
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).
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.
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).
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.
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.
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?
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.
Monday, January 2, 2012
"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.