Sunday, October 30, 2011

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

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?

Friday, October 28, 2011

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

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?

Wednesday, October 26, 2011

The pitfalls and plusses of multiple choice tests

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.

Monday, October 24, 2011

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

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.
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.

Saturday, October 22, 2011

Does autism really mean "visual thinking"?

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.

Thursday, October 20, 2011

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

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).

Tuesday, October 18, 2011

Why is anyone paying attention, II

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.

Sunday, October 16, 2011

Homeschooling update

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.

Wednesday, October 12, 2011

Front page articles on the edtech bandwagon

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.

Monday, October 10, 2011

Autism diaries, XXIV: Who is Christopher Columbus?

"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.

Saturday, October 8, 2011

Above and beyond empathy

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.

Thursday, October 6, 2011

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

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?

Tuesday, October 4, 2011

Narratives before expository writing: the problem with one size fits all

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.

Sunday, October 2, 2011

Reform Reading in Montgomery County MD

 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.