The rectangle: an appreciation

[A recently rediscovered Out in Left Field post from 11 years ago]

Only the Triangle gets a course to itself, but, as a tool for teaching math concepts in general, the Rectangle (including the special case of the Square) is, as it were, unparalleled.  Rectangles are, of course, the basic constituent of Singaporean bar modeling, substituting for x and y in word problems that might otherwise require algebra:

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Theory of Mind deficit in autism? Part I: is it all about language instead?

(Cross-posted at

In this post and five subsequent posts, I review the final article in my series on Morton Gernsbacher’s FC-friendly articles on the nature of autism. In this last article, Empirical Failures of the Claim That Autistic People Lack a Theory of Mind, Gernsbacher and Yergeau (2019) go further than any of Gernsbacher’s previous articles in making the case against autism as a socio-perceptual, socio-cognitive disorder. In particular,  Gernsbacher and Yergeau claim that the original studies that showed Theory of Mind deficits in autism have failed to replicate and been overturned by later studies.

Morton A. Gernsbacher, Professor of Psychology, University of Wisconsin

Gernsbacher and Yergeau open with a straw-man characterization of what Theory of Mind proponents purportedly have said: “The assertion that autistic people lack a theory of mind—that they fail to understand that other people have a mind or that they themselves have a mind—pervades psychology”. The more common claim, rather, is that autism involves some degree of deficit in the recognition/awareness of emotions in other people (e.g., attending to and recognizing facial expressions, or deducing specific emotions from behavior), combined with some degree of deficit in socio-cognitive perspective taking: in figuring out how to respond appropriately to another person’s emotional needs; in deducing the belief set of another person when those beliefs conflict with one’s own.

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Fund what you know, redux

When funders fund stuff we know better than they do, it’s painful to think of the opportunity costs. Stuff I know includes math and literacy education, and I’ve found Bill Gate’s endeavors here downright excruciating. Adding injury to the opportunity costs is the damage done to America’s school children. (See, for example, Emily Hanford’s recent exposé on Balanced Literacy.) 

Here’s my original OILF post on this phenomenon.

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Crowds vs. herds, redux

I was delighted to re-discover this old post from Out in Left Field. In the age of social media–and in light of everything Jonathan Haidt has observed about what’s happened to public discourse since the emergence of the “like” and “retweet” buttons–the Swiss study I quote from here seems more relevant than ever.

p.s. I should note that my source on this study, not long after writing about it, was disgraced for self-plagiarism and inaccurate reporting–though not for his reporting on this study.

p.p.s. re “rediscovery” of old posts, I recently figured out why Out in Left Field has kept disappearing–and have ensured it won’t happen again. And I’ve also recently figured out where to find a number of my old posts.

p.p.p.s. Oh, and as for my related issues pertaining to Twitter, you can now find me on Mastodon, where, fwiw, there are “favorite” and “boost” buttons instead of “like” and “retweet” buttons.

Crowds vs. Herds

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Progressive education was anti-algebra

For some reason, I missed this episode in the history of progressive education. (I need to finally read Left Back.)

William Heard Kilpatrick, one of the most influential pedagogical figures of the early twentieth century, would have felt right at home in today’s educational culture wars. Back then, as now, the traditionalist defense of math education came from the idea that the subject created order and discipline in the minds of young students. The child who could solve a geometric proof, for example, would carry that logic and work ethic into his professional life, even if it did not entail any numbers at all. Kilpatrick, a popular reformer who was known as the “million-dollar professor,” not for his salary but for the huge tuition-paying crowds his lectures drew, dismissed that idea. Algebra and geometry, he believed, should not be widely taught in high schools because they were an “intellectual luxury,” and “harmful rather than helpful to the kind of thinking necessary for ordinary living.” Not everyone was going to need or even have the intelligence to complete an algebra course, Kilpatrick reasoned. Why bother teaching it to them?


Kilpatrick’s ideas were taken up by the progressivist movement in education, a powerful force in the early twentieth century inspired by the work of the philosopher John Dewey and guided by a set of principles that included “freedom for children to develop naturally,” “interest as the motive of all work,” and “teacher as guide, not taskmaster.” These ideas had their roots in the University of Chicago but ultimately went mainstream when they were championed by professors at the Columbia University Teachers College, where Kilpatrick and Dewey taught. The coalition of anti-math parents and academics had a steady influence on education policy for decades. From the start of the twentieth century to after the Second World War, the percentage of high-school students enrolled in algebra fell. In 1909, roughly fifty-seven per cent of high-school students were enrolled in algebra. By 1955, that number had been cut by more than half to about twenty-five per cent.

How Math Became an Object of the Culture Wars by Jay Caspian King, The New Yorker, 15 Nov. 2022.

Thoughts on Relevance: How much relevance is relevant?

I was reminded of this old Out In Left Field post when hearing about a poor grade an autistic student earned for the “personal connections” response he made to a Harry Potter book. His response went something like:

I never drank polyjuice potion before. I never did magic before. I liked that chapter because Harry and Ron realized that Draco Malfoy is not the heir of Slytherin. 

His teacher’s comment to the parent:  

Maybe your son should find a book that he can make connections with to make the reflection section more meaningful.

It would seem that only neurotypical notions of personal relevance pass muster.

(This is the kind of problem that the neurodiversity world should be focusing on–as opposed to whether we should use terms like “severe autism” and “has autism”).

Autism aside, there’s the question of whether students in general really prefer to harp on questions of personal relevance, as opposed to being transported far away from their personal lives.

Thoughts on Relevance: How much relevance is relevant?

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How to teach subtraction without linguistic barriers

An ancient post from Out in Left Field, relevant to Students with Autism.

How to teach subtraction without linguistic barriers

Too often, Reform Math lets language get in the way, whether in its convoluted, poorly written directions, its convoluted, poorly written word problems, or in its relentless demands that children explain their answers. But, for students whose math skills far exceed their language skills, even traditional math poses problems. 

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Is there really nothing inherently atypical about language development in autism? Part II

(Cross-posted at

Following up on my previous post on the FC-friendly claim in Gernsbacher, Morson & Grace that there is nothing inherently atypical about language development in autism I now turn to Gernsbacher, Morson & Grace’s 2016 paper.

This paper looks at three linguistic factors that have been claimed to be characteristic of autistic speech: pronoun reversals, echolalia, and a smaller-than-to-be-expected lag between comprehension and production. Gernsbacher et al. argue that none of these is unique to autism, and therefore that “none can or should serve as diagnostic of autism.” They furthermore suggest that, while they also occur in typical development, these factors are only seen as pathological in autism because of the pathological way in which we view autistic people.  

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Common Core-inspired grammar fallacies, and why we need paper graders

I was just talking with an AI professor at a Halloween party, and he told me that he now requires his students to run all their papers through Grammarly before turning them in.

That reminded me of this old Out In Left Field post; it also made me wonder to what extent we can all learn from the feedback–imperfect though it is–provided by automated editors like Grammarly.

Common Core-inspired grammar fallacies, and why we need paper graders

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Social emotional learning and academic slippage in the post-Pandemic era

In the years since I originally posted this on Out in Left Field, the emphasis on social-emotional learning is greater than ever. Somehow the pandemic has become an excuse for shifting the balance away from straight-up academics towards even more social emotional learning, even as declines in academic skills are at least as worrying as declines in socio-emotional maturity.

Social emotional learning for everyone, or special interventions for disruptors?

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Autism in America: gratuitous barriers to productive employment, Part II

Addendum: in the end, the way around the English requirement was a waiving of the school’s rules against undergraduates taking online classes. The online version of the English classes bypassed some of the problems with group work. 

Indeed, it turns out that online classes in general eliminate many autism-specific, classroom-based barriers.

Without a well-timed global pandemic, graduation may have remained elusive.

Cross-posted at Out In Left Field:

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