Reverse mainstreaming: taking the lead from transit museums

In an age where increasing numbers of kids with autism are being mainstreamed into regular classrooms that, in turn, are decreasingly hospitable to their learning needs (cf the rise of Reform Math, group-centered learning, personal reflections, and large, open-ended projects), it's refreshing to read of a different sort of institution that is moving in the opposite direction: namely, the transit museum.

These museums, with their trains and time tables, attract large numbers of children on the autistic spectrum. With Britain taking the lead (as it so often has in appreciating the strengths and interests of children with autism), these museums are now hosting programs specifically for this population. As reported in a recent New York Times article:

In Britain, home to Thomas the Tank Engine and the site of Thomas fund-raiser walks organized by the National Autistic Society, the movement to tailor transit museum programs to children with autism is more established. The London Transport Museum recently hosted an event for high school students to spend time with the timetabling department. The National Railway Museum in York, England, set up a disability forum to start catering to visitors with autism.

Observes one British mother, who started a train club in Cheshire, England:

“When we go to train museums, they’re absolutely filled with children with autism... They’ve all been really well attended. It’s partly for the kids and partly for the parents. It’s nice to meet other people trailing around train museums.”

The New York Transit Museum is following suit:

The museum created a “Subway Sleuths” after-school program for 9- and 10-year-olds with autism that focuses on the history of New York City trains but seeks to make the children more at ease socially.

Parents are thrilled:

The response to the program been so positive that the museum is planning to expand it in the fall. 

They appear to value, in particular, the importance of their children "being around others with similar interests."

Perhaps our public schools could try something similar. How about offering magnet programs specifically focused on the academic subjects of greatest interest to those on the autistic spectrum--e.g., math, engineering and computer science--and tailoring the instruction and the assignments specifically to AS children? This, of course, would require schools to reverse their relentless drive to mainstream all children into one-size-fits-all classrooms and, for math in particular, to toss out Reform Math.

But I'd bet a lot of AS parents (and perhaps others as well) would be thrilled to have this option.

Please visit an actual classroom before you make recommendations, VII

If our most outspoken math and science professors (Jordan Ellenberg, Brian Greene), self-styled education experts (Alfie Kohn, Susan Engel), education reporters, and even literature professors (Cathy Davidson) are to be believed, our k12 schools are still mired in the 19th century, led by drill masters who force meaningless facts and meaninglessly abstract math and science concepts down students' throats, totally oblivious to the 21st century world all around them.

Our eager diagnosticians propose the same basic cures for this supposed illness: make classrooms more student centered (preferably student group-centered), and make the curriculum more concrete and relevant to students' lives. And our major newspapers--especially The New York Times--are equally eager to give them a forum.

In the latest collusion between armchair academia and the Fourth Estate, we hear from Sol Garfunkel, executive director of the Consortium for Mathematics and Its Applications, and David Mumford, an emeritus professor of mathematics at Brown. Writing in past Thursday's New York Time OP-Ed pages on How to Fix Our Math Education, they begin by diagnosing the illness. Our current math curriculum, they write, is "highly abstract," "'pure' math with no context," with its "mysterious variable x" and its emphasis on solving quadratic equations, understanding transformations and complex numbers. This, they write, is "simply not the best way to prepare a vast majority of high school students for life":

Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.

In its place:  "a math curriculum that focused on real-life problems" and that "will lead students to appreciate how a mathematical formula models and clarifies real-world situations--what they call a "contextual approach, in the style of all working scientists,"  where instead of x and y, you have, for example, E, m and c, as in Einstein's E=mc².

Presumably Garfunkel and Mumford have never actually looked at the latest high school math texts, which contain such problems as this and this. While arguably not good examples of real world math, this stuff is hardly abstract and "pure." For truly real-world algebra you have to go back in time to the 1960's or before.

But Garfunkel and Mumford want to do more than just tinker with the curriculum; they want to stop teaching algebra, geometry and calculus, at least to most students: 

Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers.

In short:

What we need is “quantitative literacy,” the ability to make quantitative connections whenever life requires (as when we are confronted with conflicting medical test results but need to decide whether to undergo a further procedure) and “mathematical modeling,” the ability to move practically between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car).

We've been here before: back in 1920, when the Committee on the Problem of Mathematics, headed by William Heard Kilpatrick, argued that algebra and geometry should be eliminated from most courses of study. As Diane Ravitch describes it in Left Back:

The Kilpatrick committee recommended that mathematics be tailored for four different groups: first, the "general readers," who needed only ordinary arithmetic in their everyday lives; second, students preparing for certain trades (e.g., plumbers or machinists), who needed a modest amount of mathematics, but certainly not algebra and geometry; third, the few students who wanted to become engineers who needed certain mathematical skills and knowledge for their jobs; and last, the "group of specializers," including students "who 'like' mathematics," for whom the existing program seemed about right, although the committee proposed "even for this group a far-reaching reorganization of practically all of secondary mathematics."

This sounds an awful like the European system of vocational tracking which so many Americans rightly bemoan. Is this really what Garfunkel and Mumford want? Do they really want it determined in high school who is going to pursue physics and mathematics, or major in one of the many subjects for which college-level math is the prerequisite? 

Equally questionable are Garfunkel and Mumford's closing assertions. First:

We believe that the best way for the United States to compete globally is to strive for universal quantitative literacy: teaching topics that make sense to all students and can be used by them throughout their lives.

Perhaps Garfunkel and Mumford no longer see mathematics and science as worthwhile areas for American competition. Second:

It is through real-life applications that mathematics emerged in the past, has flourished for centuries and connects to our culture now.

Here Garfunkel and Mumford aren't repeating history, but rewriting it.  While mathematical guess and check procedures often emerge out of real-world application, in general, real-world mathematical application has lagged several hundred years behind pure mathematical theory.  As irrelevant to today's non-mathematicians as today's mathematical advancements may appear to be, they may turn out in several centuries to be crucial to solving real-world problems in anything from cryptography to quantum computing to the generation of sustainable energy.  Assuming, of course, that future scientists and engineers are still getting adequate training in basic high school math.

Math problems of the week: 1900s Algebra vs. Interactive Mathematics Program

I. The 21st homework assignment in Wentworth's New School Algebra (published in 1898) [click to enlarge]:

II. The 21st homework assignment in Interactive Mathemetics Program: Integraded High School Mathematics Year 1 [click to enlarge]:

III. Extra Credit:
Estimate the ratio of effort to learning in each problem set. Draw a diagram that indicates how well each one works.

Accelerating within grade level with new new new Math: more strikes against math-inclined students

First, the "new new new Math." Pearson, the publisher of TERC Investigations, has collaborated with the power brokers at the highly-reputed, top-scoring Montgomery County School District (MCSD) to create a new "integrated" math program, eventually to be marketed around the country with help from MCSD's academic cachet. It's hard to track down specific details about this curriculum, which debuts this coming school year in Montgomery County, but, judging from its fifth and sixth grade objectives it looks suspiciously like Investigations. These objectives make no mention of standard algorithms like long division, instead emphasizing data, "representations," probability, statistics, and measurement. Nor do we see terms like "calculations," "automaticity,"  and "mastery"; rather, we find repeated instances of "explore", "examine," and "extend understanding." All good things, in theory; bastardized over the years under Reform Math, they also raise red flags.

Also suspiciously Reform-like are (1) the elimination of the "math pathways" model of grade acceleration wherein capable Montgomery County students could attend above-grade level math classes, and (2) a letter to parents sent out by the principal of Laytonsville Elementary School explaining why grade acceleration has been eliminated for "nearly all" students:

The new standards require students to develop deeper level of understanding in mathematics. Memorizing and repeating formulas will always be part of learning mathematics, but will not be sufficient in order to demonstrate deep understanding. Students will be expected to show understanding, computation, application, reasoning and engagement in a mathematical concept to be ready to move on to a new topic... In addition, the new standards are more challenging at each grade level. For example, many of the standards now in Grade 1 were previously in Grade 2 or higher or were not taught in the prior Montgomery Public Schools Curriculum. Therefore, the practice of grade skipping acceleration in mathematics will not be necessary for most students. Almost all of our students will be working at the challenging grade level standards this year and not in the next grade up.

To ensure that the needs of students who require more challenge are met, MCPS has developed enrichment and acceleration within the grade level curriculum that goes beyond the requirements of new standards. Students who have consistently demonstrated proficiency of a mathematics concept will be able to enrich their understanding of a grade-level topic or accelerate to a higher-level topic.

Ah, yes, deep understanding, application, engagement: why are these always associated with the most dumbed-down of math curricula? Even more oxymoronic is the concept of "acceleration within the grade level curriculum"--right up there with "differentiated instruction in heterogeneous groups."

One MCSD parent, whose daughter, then a 3rd grader, was deemed two years ahead in math in last year and placed in a 5th grade math class, suspects that her daughter would be "bored to tears" if kept at grade level under the new curriculum.

But eliminating ability-based grouping reflects one of the key findings of the Montgomery County Mathematics Working Group. Citing a study published in the Journal for Research in Mathematics Education, they note:

Mixed-ability grouping results in higher achievement for average and lower ability students and does not significantly affect achievement levels for higher ability students.

Montgomery County, of course, is part of a larger drive to eliminate ability-based grouping around the country. Montgomery County's new superintendent, Joshua Starr, succeeded in eliminating it in Stamford, Connecticut; where will he go next after he finishes up in Maryland? Perhaps he could come to Philadelphia, where we're currently looking for a new superintendent, and eliminate our magnet high schools.

Good studies on the effects of mixed-ability vs. ability-based grouping on math-inclined students are hard to find.  But one study suggests that gifted kids in particular benefit when grouped with like-minded kids and given material tailored to their abilities. And what is perhaps the one truly controlled study ever conducted anywhere in the world suggests that ability-based grouping is good for everyone.

There's at least some evidence that ability-based grouping has worked out well for Montgomery County in particular. Perhaps the lingering effects of that success will help Pearson sell its integrated Montgomery Math curriculum to the rest of the country.

Is the world right-brained or left-brained, IV: The end of linearity

If today's popular texts are to be believed, we live in an increasingly right-brained world. Most credited with originating this idea is Daniel Pink, the author of the 2005 Wired Magazine article, Revenge of the Right Brain and the follow-up best seller, A Whole New Mind: Why Right-Brainers Will Rule the Future.

The education world, of course, decided this long before Pink did. But Pink, a professional writer, makes his case more compellingly, and this has made him a much sought-after speaker at education world events. You'll find him, for example, as the keynote speaker at Solution Tree's first annual Authorspeak Conference this fall (Solution Tree being "a leading provider of educational strategies and tools that improve staff and student performance," which "for more than 20 years ... ha[s] helped K–12 teachers and administrators create schools where all children succeed.").  I know about this conference because Solution Tree placed two page ad about it in the middle of this past week's Education Week.

In other recent developments, there's Cathy N. Davidson's just-published, "Now You See It," already a top-seller on Amazon. Davidson is a Duke University professor specializing in American literature, and, as such, she explores the consequences of the new, ever changing 21st century world, and the resulting new, 21st century brain--a brain which (surprise, surprise!) is being rewired for relentless multi-tasking instead of linear thinking. According to the review in this past weekend's Wall Street Journal:

The author takes us on a journey through contemporary classrooms and offices to describe how they are changing—or, according to her, should change. Among much else, we need to build schools and workplaces that match the demands of our multitasking brains. That means emphasizing "nonlinear thinking," "social networks" and "crowdsourcing." 

Like so many people who haven't spent time in contemporary classrooms, Ms Davidson confidently notes 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. 

Following this observation, as always, is the breathless description of the antithesis: the supposedly pioneering innovator. In this case:

Duncan Germain's classroom at Voyager Academy, a charter school in North Carolina, where learning is made to resemble a collaborative game. Self-organized teams engage in a contest to build the best bridge out of Popsicle sticks. Along the way they learn for themselves not just principles of engineering but also strategies of management—just what they need to thrive in the new world of work. Students in such a setting, Ms. Davidson writes, "are mastering the lessons of learning, relearning, and unlearning that are perfectly suited to a world where change is the only constant."

Reviewer Mark Changizi, a neurobiologist, is somewhat skeptical of some of Davidson's claims. She appears, he notes, to derive many of her conclusions, as well as her title, from the "gorilla" experiments of Daniel Simons and Christopher Chabris, where subjects were asked to watch a video of basketball players and to count the number of times they passed the ball. With their brains focused on this task, many subjects failed to notice a man in a gorilla costume wandering through the frame. Davidson concludes, among other things, that inattentional blindness is rampant, and that therefore students should work in groups so that multiple viewpoints can help them compensate.

No matter that inattentional blindness would suggest that our brains, however 21st century they are, remain inept at multi-tasking. For, if you've set your mind on a particular task--say, proving that the today's classrooms should be right-brained so as to reflect today's brains--you will fail to notice the metaphorical man in the gorilla costume, whatever he may represent.

Everything but the curriculum, III

Two more places where discussion of curriculum is conspicuously absent: the New York Times and Wall Street Journal reviews of Steven Brill's school reform book, Class Warfare.

(So far as I can tell, the same is true of Brill's book, which focuses primarily on teachers' unions.)

Math problems of the week: 1900's math vs. Interactive Math Program

I. The 14th homework assignment (and preliminary "Story") from the Interactive Math Program: Integrated High School Mathematics, Year 1 [click on pictures to enlarge]:

II. The 14th homework assignment (and preliminary discussion) in Wentworth's New School Algebra (published in 1898) [click on picture to enlarge]:

III. Extra Credit
What would today's high school English classes look like if they contained and solicited as much mathematics as the amount of narrative and verbiage contained and solicited by today's high school math classes?

Fund what you know

One of the most common pieces of advice given to would-be writers is "Write what you know." Substitute "write" with "fund," and you get something that many more would-be philanthropists need to hear.  This is particularly true of a brand of super-wealthy gift-givers whom Diane Ravitch, in her latest book, dubs "venture philanthropists."

Consider, full example, Bill Gates. How well does he know the issues in k12 education? Judging from the many millions of dollars that he has wasted on ventures that often only make matters worse, not very well at all. Included in his projects are the misbegotten School of the Future in Philadelphia, which emphasized technology over curriculum; the Blueprint program in San Diego (discussed at length in Ravitch's book), which mandated balanced literacy throughout San Diego's schools and also featured Reform Math; and, most recently (thanks to Barry Garelick for alerting me to this one), an online math education project with Pearson Publishers, the publisher of the infamous Investigations Math curriculum, among the worst of the Reform Math programs. 

If only Bill Gates were to take a close look at balanced literacy (or at how parents feel about it vs. other reading programs when it comes to spending their own money) or to compare Reform Math problems with traditional ones (for example here), he might direct his funds elsewhere.

Instead of funding what he knows, Gates appears to be relying on the advice of "experts." The problem is, if you're a famous outsider seeking advice on where to direct vast sums, hundreds of people will try to advise you, and only the most well-connected insiders will reach you. Even if you try to hear out everyone, unless you know the issues, you won't be able to assess competing claims, and so you will default to those with the most connections and credentials. In education (among other arenas), this is a very bad idea.

Instead of funding what he knows, therefore, Bill Gates is merely further enabling the mainstream Constructivist forces that miseducate everyone, and that particularly disadvantage the more analytical, left-brained students. To the extent that rumors about Bill Gates having Asperger's Syndrome are true, his involvement in education has, ironically, made school in general, and math in particular, decreasingly hospitable to his fellow eccentrics on the autistic spectrum.

The lost art of rational debate

Two articles in this week's New York Times Sunday Review touch on the rapidly disappearing art of rational debate.

In his front page article, Neal Gabler discusses how:

It is no secret, especially here in America, that we live in a post-Enlightenment age in which rationality, science, evidence, logical argument and debate have lost the battle in many sectors, and perhaps even in society generally, to superstition, faith, opinion and orthodoxy.

Gabler's culprits? Academic insularity and hyper-specialization, visual culture, social media, and, ultimately, information overload. But he omits two of the biggest causes. One is the precipitous decline in analytical writing and debate at the k12 level.

The other one emerges just 4 pages later in a piece by Sheryl Gay Stolberg. Citing Bill Bishop of The Big Sort, Solberg discusses how:

Americans now choose “in their neighborhoods and their churches, to be around others who live like they do and think like they do — and, every four years, vote like they do.”

Political sorting extends even to retail:

David Wasserman, of the nonpartisan Cook Political Report, recently calculated that 89 percent of the Whole Foods stores in the United States were in counties carried by Barack Obama in 2008, while 62 percent of Cracker Barrel restaurants were in counties carried by John McCain.

And even, I'd argue, to jobs. Consider academia (especially the humanities, social sciences, and education schools) vs. business (big and small), not to mention the starkly divided nonprofit and political sectors.

The more we live, work, shop, and play with--and even "friend"--only those people who appear to agree with us, and the more we keep our mouths shut whenever we find ourselves in a tiny minority of dissidents within an increasingly intolerant majority, the less we engage in rational debate about anything. And (the more so because our k12 schools have abdicated their role in nurturing it) the worse we become at it.

Math problems of the week: Interactive Math Program vs. 1900's Math, Part II

I. The first two pages of the 8th assigment in Wentworth's New School Algebra, published in 1898 [click to enlarge]:

I. The 8th homework assignment in Interactive Mathematics Program: Integrated High School Mathematics, Year 1 [click to enlarge]:

III. Extra Credit

a. What happens if you answer question 5, above, by saying that the more time you spend on homework, the less you benefit from participating in your group?

b. The Interactive Math Program assignment says that its questions are "designed to help you." The Wentworth assignment doesn't. Discuss.

Autism diaries XXVII: roundup of the latest experimentation and mischief

Let's order 3 lbs of squid from the fish counter while Daddy's not looking. Surprise: the fish guy fills my order!

While Daddy's driving, let's rig his cell phone to forward all calls to W's cell phone (W's has 10 ceiling fans so I have her number memorized). That way, when Mommy tries to call Daddy from the train to find out where to meet him, (surprise!) she'll instead be calling W.

Let's put my Malen vibrating bed-wetting alarm on my floor, angle my Radio Shack solar panel eastwards, and hook the one up with the other in such a way that the electricity generated by the latter triggers the wetness sensor on the former. That way when the sun rises my parents below me are awoken by a loud, low rumble overhead unlike anything that's ever woken them up before.

Let's put a tomato in the freezer and see what happens.

How leadership and community service requirements bedevil students with autism

From a letter posted by a parent on a listserv discussion about autistic students and leadership and community service requirements:

I do hope that others will recognize what a big stumbling block this is for our older children with Asperger's. My son also did not make the National Honor Soceity the first year, even though he was tied for the highest gpa all through jr high and up to that point in high school. The last year he did make it, but only after I helped him with the application and we went through anything we could think of that could be called leadership or communityservice. At the time, he wasn't yet dx with Asperger's.

If your child goes on to college, you may find the same problem arises in the form of scholarship and award applications. It has for us, at least. Our son's grades are still very good. However, he does not belong to campus clubs, does not hold a leadership position, etc. In fact, he recently applied for a National scholarship specifically for students with Autism. I was hoping he'd get some assistance through that one. But, no, he was told he was *required* to show Community Involvement / Social Activities. They also required letters of recommendation from close friends in his field or professors who knew him well - in order to submit a completed application. Well, the only people who know his character well are family or perhaps doctors. It is very frustrating and will affect many of our kids as they progress through school and college.

Community service requirements are on the rise everywhere, affecting everything from high school graduation  criteria to college scholarship decisions--even, apparently scholarships specifically for students with autism.

How many people have considered what these means for the autistic students we are supposedly trying to include? How broad an interpretation of "community service" are the Powers that Be wiling to consider? For example, would posting helpful  tips on programming on online discussion boards count as community service?

More "science appreciation"

The National Research Council just published its "Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas". As explained in its Executive Summary:

The overarching goal of our framework for K-12 science education is to ensure that by
the end of 12th grade, all students have some appreciation of the beauty and wonder of science; possess sufficient knowledge of science and engineering to engage in public discussions on related issues; are careful consumers of scientific and technological information related to their everyday lives; are able to continue to learn about science outside school; and have the skills toenter careers of their choice, including (but not limited to) careers in science, engineering, and technology.

It's telling which goal comes first and which comes last. Even more telling is which one the New York Times chooses to cite:

One of the big goals, the committee said in a 282-page report, is “to ensure that by the end of 12th grade, all students have some appreciation of the beauty and wonder of science.”

Ultimately, of course, what really matters is which of these goals our k12 schools choose to emphasize. Any guesses?

Math problems of the week: Interactive Math Program vs.1900's Math

I. The first homework assignment in Interactive Mathematics Program: Integrated High School Mathematics, Year 1 [click to enlarge]:

II. The first assigment in Wentworth's New School Algebra, published in 1898 [click to enlarge]:

III. Extra Credit

a. Which assignment is more tedious?

b. What grade should you get on the first assignment if you cite it as one of the experiences that you do not like, and list only disadvantages for group work.

c. Should you expect your teacher to respect your preferences for group work vs. working alone?

A left-brained take on depression

Yesterday's Philadelphia Inquirer Health Science section reports on evoluationary psychologist Paul Andrews' unorthodox take on depression:

Andrews, an assistant professor at McMaster University in Hamilton, Ontario, thinks depression, miserable as it is, serves a positive role, much as fever does in fighting infection.

He argues that the lethargy, lack of appetite, sleeplessness, and rumination that accompany depression help people focus on and ultimately solve their problems.

"Depressed mood states seem to promote an analytical processing style," Andrews said, that helps people break complex problems into smaller bites.

In other words, according to Andrews, depression promotes left-brained thinking, which is key to solving the problems that caused the depression in the first place.

Andrews' theory implies that taking medication, on the other hand, is counterproductive because, in as much as it alleviates the depression, it also curtails the analytical, problem-solving mindset. The problems persist, and once the patients go off the anti-depressants, the depression returns. Indeed:

In an analysis of 46 previous studies published last month in Frontiers in Evolutionary Psychology, Andrews and colleagues found that patients who used antidepressants were twice as likely to relapse when they stopped as those who were on placebos.

This is the first time I've ever read of a placebo being more effective than the drug!

As the rest of the article makes clear, Andrews is talking not about the kind of debilitating, physiologically based depression that hits certain people regardless of what's going on in their lives, but about situational depression:

Most depressive episodes come in response to specific events such as a breakup or job loss, Andrews said. Depending on the study, 15 to 40 percent of people say they have had major depression, the kind in Andrews' study, but almost everybody has had milder forms.

What does this mean for patients? "It looks like, if you can get better without taking antidepressant medication, you'll have a much better chance of not having a relapse," said Andrews, who is not a clinician.

The Inquirer is skeptical, but, if Andrews' study is accurate, the burden is on his detractors to explain why, when it comes to certain sorts of depression, the placebo outperforms the drug.