Celebrating creativity?

Creativity is one of those things we say we celebrate--along with honesty, open-mindedness, critical thinking, neurodiversity, and diversity of opinion. But creativity also strikes me as one of those areas in which everyone has an agenda.

Here's another post from 2011.

The virtues of creativity

In this blog I've repeatedly complained about wrong-headed priorities involving creativity, explaining answers, learning styles, self-esteem, and relevance. In the next few blog posts, I'm going to argue that each of these things should still play some role K12 education. I begin, today, with creativity.

As regular readers of the blog know, I've repeatedly criticized the practice of grading students on creativity when there is no established protocol for teaching it or for measuring it objectively (beyond the crude, reductionist, and pointless tallying of things like "illustrations per page" and "colors per illustration"). Does that mean that creativity should play no role in K12 education? Not at all. Teachers can, and should, attempt to inspire creativity in their students and to be creative themselves in their teaching.

But inspiring creativity does not mean simply exhorting students to "be creative." Far more promising is helping students appreciate the creative works of others--in anything from poems, to stories, to essays, to paintings, to clever solutions to math problems. Or giving them inspiring assignments or prompts--e.g., extend such and such a bizarre opening sentence into the first of a story; or extend such and such a random squiggle into a page-sized illustration. Or taking them on exotic outings--topiary gardens; whirligig exhibits; kitchen instrument concerts; or La Compagnie Transe Express.

Teachers themselves can be creative, too, even in the driest of subjects, and without reducing the subject matter to meaningless mush. A friend of mine who teaches at St Ann's in Brooklyn--a school whose combination of a classical education and a creative teaching staff is perhaps unparalleled--dresses up every Wednesday like a puritanical schoolmarm, topped with a puritan cap and equipped with a dunce cap, teaches her 5th graders the fundamentals of grammar and style. They love it, and they learn it.

Ironically, at the same time that students are increasingly graded on "creativity," schools are inspiring it less than ever. They're increasingly more likely to punish than to reward teachers who don't adhere to their scripted lines. And, their language-policed, all-about-me curriculum, which prefers mirrors to windows, provides way too few windows, in particular, into creativity at its most inspiring.

 

Perhaps that's why America is less and less a land of innovation--except for first-generation immigrants, assuming they don't go back home.

Campaigning vs. governing, nth edition

The world would be a better place if successful campaigning and successful governing didn’t depend on such different skill sets.

Here’s an updated version of an old post

Narcissistic Leadership

Personality, of course, is a multi-dimension affair, and there are as many personality spectra as there are personality dimensions. But one possible spectrum I've been wondering about goes something like this:

Autism___________Asperger's__________Normal Range_________________________Narcissism

At both ends you see varieties of extreme self-absorption. In autistic spectrum disorders, the source and the essence are socio-cognitive: core to autism is difficulty inferring, automatically and accurately, the perspectives of other people. In narcissism, the source and essence are emotional: self-love interferes both with gut-level empathy and with the desire to consider others' perspectives. Source and essence aside, perspective taking deficits obviously impair pro-social behavior, including, for example, the ability to lead others.

But because narcissists are better at hiding (or “masking”) their disorder, it tends to be only those on the autistic side of the spectrum who strike employers as bad candidates for leadership positions. Indeed, because narcissists also exude confidence and charm, many of us consider them leadership whizzes. Wouldn't it be nice if a study cited in last week's weekend Wall Street Journal could make us think twice:

When narcissists get assigned to leadership roles, they impress their charges with authority and confidence. They also underperform, a new study finds.
...

Workers assigned to narcissistic leaders tended to report that they were authoritative and effective. But, in fact, narcissists-led groups shared information less effectively than the others and picked the wrong candidate more often.

The study offers a cautionary tale to businesses, the authors said: Narcissists are equipped to ace job interviews, for example, but are unlikely to live up to expectations.

At some level, this explains a lot of what's wrong in the world. But why does it not surprise me that many people who ace job interviews are "unlikely to live up to expectations"?

On the flipside, I suspect that many on the other end of the spectrum, while floundering in job interviews, would make great employees, if only someone gave them the chance.

The Rectangle: an appreciation

[A recently rediscovered 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:

Mr. Lim read 10 pages from his book on Monday. Mr. Smith read three times as many pages as Mr. Lim. Their friend, Mr. Samy, read 15 pages more than Mr. Smith. How many pages did Mr. Samy read from his book?

Rectangles are also a good way to visualize multiplication:

5 × 9:

74 × 368:

including the commutative law of multiplication:

And the distributive law:

 a (b  + c) = ab + bc:

And equivalent fractions:

And the factoring or multiplying out of quadratics:

And the area of triangles:

And the area under a curve:

Indeed, so versatile is the unassuming rectangle that I'm sure I've missed a number of other areas for which it is a powerful conceptual building block.

Is there really no Theory of Mind deficit in autism? Part I: is it all about language instead?

Cross-posted at FacilitatedCommunication.org.

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.

Of course, Gernsbacher and Yergeau’s argument depends, to some extent, on what exactly is meant by Theory of Mind (henceforth, ToM). To some extent, ToM has traditionally been defined by the long-standing tests used to assess ToM: false-belief tests like Sally-Anne test and the Smarties test; Happé’s Strange Stories; Baron-Cohen’s Mind in the Eyes test (which we’ll call “Eyes test” for short); and the Animated Triangles test. Here is a quick summary of the key tests:

• The Strange Stories Test measures the ability to deduce the social/emotional reasons for characters’ behaviors in a narrative sequence.

• The Eyes Test measures the ability to recognize emotions from facial information that is restricted to a rectangular region around the eyes.

• The Animated Triangles Test measures the ability to ascribe emotions to self-propelled, interacting shapes in a short animation.

•  The false-belief tests measure the ability to make inferences about the beliefs held by (or about) individuals who are missing key pieces of information. Two common examples are:

  • The Sally-Anne “unexpected location change”  test, in which Sally doesn’t witness Anne moving her marble from a basket to a box

  • The Smarties “unexpected contents” test, in which a candy box contains a pencil rather than candy

False-belief tasks are the most cognitively complex of the ToM tasks: they measure what we can call “cognitive perspective taking”—the ability to put oneself in someone else’s cognitive shoes and deduce their state of knowledge or beliefs. Gernsbacher and Yergeau begin their article by reiterating one of the arguments made in Gernsbacher and Frymiare (2005) about how failure in such tests correlates with language development rather than with autism. Typically developing children need to reach a certain level of language development to pass false-belief tests, and children with non-autism related language delays—e.g., deafness—are also delayed in passing false-belief tests. But Gernsbacher and Frymiare (2005), as I discuss in my *earlier post*, do not address the fact that autistic individuals need to reach a much higher language level than other groups do to pass these tests. This fact suggests that those autistic individuals who do pass false-belief tests may be doing so through an atypical mechanism—i.e., a more deliberative reasoning out, or “hacking out” through language.

Gernsbacher and Yergeau, on the other hand, do attempt to address the “hacking out” hypothesis. Their counterargument is that it is hard to reconcile the “hacking out through language” strategy with the language impairments common to autism. They ask: “How and why would autistic people preferentially use language to ‘hack out’ the answers while non-autistic people, without communication impairments, do not?” The answer, of course, is that language, given the challenges of autism, may nonetheless still be autistic people’s best option—assuming, of course, that they reach the requisite level of linguistic mastery. Moreover, the fact that the level of linguistic mastery required for autistic people to pass false-belief tests is considerably higher than that required for non-autistic individuals suggests that, when autistic individuals pass false-belief tests, language is doing more work—i.e., playing a bigger role—than it does for non-autistic people.

Gernsbacher and Yergeau also reiterate Gernsbacher and Frymiare’s (2005) arguments about the complex language involved in false-belief tests—and how, therefore, failing to pass false-belief tasks may merely reflect language difficulties. However, as I noted in reference to the 2005 paper, there are non-verbal versions of the false-belief tests—also called “implicit” false-belief tests—that rely only on anticipatory gazing (e.g., towards where Sally will look for her marble) as opposed to answering a complex question (e.g., “Where does Sally think her marble is”). One implicit false-belief experiment is discussed in Senju et al. (2009). They find that the autistic participants, unlike the non-autistic participants, failed to look anticipatorily at the location where Sally would look for her marble. Indeed, this is even the case with high functioning adults with Asperger’s who (as would be expected from their verbal mental ages) were able to the standard (verbal) ToM tests, including the Sally-Anne task and a second order ToM test called the “ice cream test”.

Instead of discussing these eye-tracking versions of the false-belief tests, Gernsbacher and Frymiare cite, as their only example of nonverbal false-belief tasks, the picture-sequencing experiment of Baron-Cohen et al. (1986). This experiment compared autistic and non-autistic performance on sequencing pictures into three kinds of sequences: mechanical sequences (e.g., a balloon rising into the sky and then being punctured by a tree branch),  behavioral sequences (e.g., a child entering a store and exchanging money for merchandise), and “intentional”/ToM sequences (e.g., a child putting some candy in the box, leaving the room, and then, after someone else opens the box and eats the candy, returning, re-opening the box, and looking disappointed). Regarding these findings, Gernsbacher and Yergeau say:

Four research teams, of whom we are aware, have published attempts to directly replicate these results—and none could do so. Using the same stimuli, procedures, and analyses, no other research team has replicated the finding that autistic participants perform significantly worse than typically developing participants on the “intentional” picture sequences.

The studies cited by Gernsbacher and Yergeau here are Ozonoff et al. (1991); Oswald and Ollendick (1989); Buitelaar et al. (1999), and Brent, Rios et al. (2004). And while all of them do indeed fail to replicate Baron-Cohen et al.’s results, some of their other findings do suggest that ToM deficits nonetheless characterize autism.

For example, Ozonoff et al. found “significantly poorer emotion perception abilities in this sample of autistic individuals.” They also found that a subset of the autistic group (as opposed to the Asperger’s group) performed significantly less well on the first order ToM test (the Smarties test) and that this performance correlated with the emotion perception scores.

Brent et al., meanwhile, found that the autistic participants “performed worse than typically developing controls on the mentalizing Strange Stories task and the Eyes task. Their conclusion: “children with ASD are impaired relative to typically developing children in advanced theory of mind abilities.”

 As some of these authors acknowledge, the picture sequencing tasks may not accurately capture ToM deficits. This is not the same thing as finding that ToM deficits do not exist.

Despite Ozonoff’s replications of relative difficulty for autistic people on first-order false-belief tests, Gernsbacher and Yergeau claim that “Baron-Cohen, Leslie, and Frith (1985)’s seminal study reporting that autistic participants are prone to fail first-order False Belief tasks… is also prone to fail replication.” Here they cite Dahlgren & Trillingsgaard (1996);  Russell & Hill (2001); Oswald & Ollendick (1989); Fitzpatrick et. al. (2013); Yirmiya & Shulman (1996); Yirmiya et. al. (1998); Moran et. al., (2011).

To the extent that these studies fail to replicate an autism-specific tendency to fail false-belief tasks, it is largely because of the linguistic confounds discussed above: all children fail the standard false-belief tests before they achieve a certain language level, and all children pass the standard false-belief tests above a certain language level. What’s specific to autism, as we discussed, is the need to achieve a significantly higher level of linguistic functioning than in other groups in order to pass explicit false-belief tests. Furthermore, Buitelaar et. al. (1999), cited elsewhere in Gernsbacher and Yergeau’s piece, found that performance on first-order false-belief tests correlated with autistic traits as measured by a standard measure of autism symptomology (the CARS).

Gernsbacher and Yergeau then turn to second-order false-belief tasks. These are tasks that involve calculating what one character will believe about another character’s (faulty) belief (“Where does Anne think that Sally will look for her marble?”). Here they point to studies showing that autistic participants are no more prone to fail second-order false-belief tasks than other populations are—a fact that is indeed borne out by the various studies. However, there are some key things to keep in mind. First, since passing a first-order false-belief test is a prerequisite for passing a second-order false-belief test, these studies only include individuals who pass first-order false-belief-tests. In autism, as we discussed, passing first-order false-belief tests means having achieved a significantly higher verbal mental age than in other groups. And what the studies (e.g., Tager-Flusberg & Sullivan, 1994) propose is that, at this point, challenges other than autism-specific challenges like mentalizing figure most importantly. Prime candidates are executive functioning (EF) challenges like working memory and cognitive load/processing demands.

In addition, the ability to pass second-order false-belief tests does not rule out ToM difficulties in the real world. For example, Leekam & Prior (1994), despite finding that the autistic participants were no more prone than other groups to fail second-order false-belief tests and could “make appropriate social judgements about lies and jokes”, also found difficulties, as per parent reports, in real-world ToM skills. These reports turned up difficulty both with lying, in particular white lies, and with joking—and here there was no difficulty between second-order “passers” and “failers.” Overall, Leekam & Prior’s result support that “theory of mind development is delayed relative to the mental age of normal children”.

Similarly, Bauminger & Kasari (1999) report that, despite the similar performance by autistic and non-autistic participants on second-order false-belief tests, “the autistic children, as a group, gave more irrelevant or wrong responses when asked to explain their answers to the belief question.” (Such explanations are not generally part of standard false-belief tests). Such performance, they note, suggests the ability to pass second-order false-belief tests does not rule out deficits in social understanding. They cite similar findings by Ozonoff & Miller (1995) and others. As Bauminger & Kasari put it, “Even very able children with autism, or children with Asperger syndrome, have difficulties in applying theory of mind when faced with a real social situation.”

One theory of mind task that is intended to measure real-world skills are Happé’s Strange Stories—stories that involve real-world mentalizing situations. But here, too, Gernsbacher and Yergeau argue that there has been a failure to replicate—a failure, specifically, to replicate Happé’s (1994) finding that autistic participants who pass first- or second-order False Belief tests nonetheless fail the Strange Stories test.

But once again there is the confounding role of language. The Strange Stories, by their very nature, are grounded in language and involve much more verbiage than false-belief tests. Even if the syntax isn’t as complex, there are a greater range of vocabulary words. Consistent with this, Sheeren et al. found that age and verbal abilities (as well as general reasoning abilities), not autism diagnosis, were the determining factors for success with Strange Stories. Consistent, in turn, with Sheeren et. al., those studies that found no deficiencies with Strange Stories involved adults with high functioning autism or Asperger’s (Senju et. al., 2009; Schuwerk et. al., 2018; Ponnet et. al., 2004).

As for younger children, Gillotte et. al., (2004) report that, despite similarities in overall performance between autistic and non-autistic groups, the former gave significantly more inappropriate mental state answers (e.g., angry instead of sad) to the Strange Stories questions. This suggests, Gillotte et al. propose, that many children with autism, despite “severe ToM difficulties”, had “learned to apply generalized compensatory strategies such as offering an explanation in terms of mental states to any question as to why a person acted in a particular way.”

Another study involving younger children, cited by Gernsbacher and Yergeau as failing to replicate Happé (1994)’s Strange Stories results, is White, et. al. (2009). While children with autism who showed ToM impairment on other tests performed “significantly more poorly” than controls on the Strange Stories tests, they also performed more poorly on counterparts in which the stories were based on animals. Perhaps this suggested to Gernsbacher and Yergeau, inasmuch as animals don’t have minds, that the issue was something other than ToM. White et al.’s explanation, rather, is that “a mentalizing [ToM] deficit may affect understanding of biologic agents even when this does not explicitly require understanding others’ mental states.”

Returning, now, to autistic adults, even those highly verbal autistic participants who performed well on the Strange Stories tests struggled with other ToM measures. Schuwerk et. al. (2018), for example, report that such participants scored significantly lower on the Eyes test and also showed less accurate anticipatory looking in an eye-tracking-based implicit false-belief test akin to the one discussed above. Schneider et. al. (2013) also found that, despite similar performance on explicit ToM tests, autistic individuals showed no evidence of anticipatory looking (“tracking”) in an implicit false-belief test, “even over a one-hour period and many trials.” They conclude that “the systems involved in implicit and explicit ToM are distinct” and that “impaired implicit false-belief tracking may play an important role in ASD”.

Furthermore, Murray et. al. (2017) show that, when the Strange Stories are substituted with an animated counterpart in which language is less of a confounding factor, the differences between autistic and non-autistic performances increase, with the former showing more relative difficulty. As Murray et. al. note,

Adults with ASD had lower scores, indicating difficulties with social cognition that could not be explained by general cognitive factors (e.g., verbal ability) and were specific to understanding the intentions behind nonliteral language in communication.

Ponnet et. al., (2004)’s findings were similar. On the standard “static” versions of both the Strange Stories and Eyes tests, the adults with Aspergers performed similarly to typically developing adults. But in the more naturalistic empathic accuracy task, in which participants attempted to infer a person’s thoughts and feelings in a videotape of that person in a naturally occurring conversation with another person, the individuals with Asperger’s performed significantly worse. Roeyers et. al., (2001) obtained similar results in similar experiments with adults with pervasive developmental disorder (PDD).  As they put it:

These findings suggest that the mind-reading deficit of a subgroup of able adults with PDD may only be apparent when a sufficiently complex naturalistic assessment method is being used.

One study cited by Gernsbacher and Yergeau as failing to replicate Happé (1994)’s Strange Stories results, Spek et. al. (2010), in fact did replicate it. They found that HFA and Aspergers adults “were impaired in performance of the Strange Stories test and the Faux-pas test [which taps the ability to detect social blunders] and reported more theory of mind problems than the neurotypical adults.” It was only their performance on the Eyes test—which, as we noted earlier, tests the ability to infer specific emotions from the eye-region of faces—that their performance was equivalent to the other groups.

As for the Eyes test, Gernsbacher and Yergeau note, correctly, that it involves sophisticated vocabulary (words like “envious” and “fantasizing”)—though we should add that word definitions are often provided as part of the test. Gernsbacher and Yergeau then cite research, both on autistic individuals and on individuals with non-autistic language challenges, that shows that “the best predictor of Reading-the-Mind-in-the-Eyes” is vocabulary. But one of these studies still shows connections, if weaker, to cognitive empathy and emotion perception (Olderbak et. al., 2015). In addition, as we’ve discussed earlier, vocabulary itself is grounded in social engagement: early vocabulary development is a function of frequency of responses to Joint attention (RJA). Given how subsequent vocabulary builds on earlier vocabulary, it could be that vocabulary levels, even late in development, correlate with early (and even current) social engagement—the more so with words like “envious” and “fantasizing”. If so, then there may be an underlying social variable that underlies both vocabulary, especially socio-emotional vocabulary, and performance on the Eyes test.

This blog post has gone on long enough. For those who’ve made it this far, here’s a quick recap:

• Some ToM tests use language as a testing medium, and thus require a certain threshold level of linguistic comprehension. This can result in language skills being a bigger causal factor in test performance than mentalizing/perspective-taking skills are—except when we consider the causal role played by mentalizing/perspective-taking skills in the acquisition of those language skills.

• Autistic individuals need to acquire significantly more language than non-autistic individuals do before they can pass false-belief tests. This suggests that autistic individuals are using language to reason through these tests in a more deliberate way than their non-autistic counterparts do.

• Second-order false belief tests (“Where does Ann think that Sally will look for her marble?”) appear to be primarily measuring something other than social reasoning skills (e.g., working memory and cognitive load/processing demands). But second-order false belief tests are generally administered only to those who pass first-order false-belief tests—those, in order words, who have already reached a significant social-cognitive milestone.

• Second-order false belief tests aside, the patterns of performance on ToM tests observed in autistic vs. non-autistic individuals, including in the articles cited by Gernsbacher and Yergeau, consistently indicate ToM difficulties in autism.

• The most impaired ToM skills are those involving

  • automatic (as opposed to deliberate) perspective-taking (e.g., automatic gaze shifting to where Sally will look for her marble)

  • socially naturalistic settings.

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REFERENCES

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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 post on this phenomenon.

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, for 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.

Crowds vs. herds, redux

I was delighted to re-discover this old post. 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

In my first book I draw a distinction between "cooperation" and "collaboration," defining the former as people working while interacting, and the latter as people working on joint projects, but not necessarily in one another's presence or with much productive interaction. In collaborations, after the work is divvied up, participants might spend the majority of their time working independently. 

I argue, furthermore, that this is what typifies most successful real-world collaborations. Except for those of us working on construction sites or film sets, we tend to get most of our work done at desks in private offices or cubicles; not at conference tables.

It turns out that there is a good reason for this. In an article in last weekend's Wall Street Journal, Jonah Lehrer reports that:

The good news is that the wisdom of crowds exists. When groups of people are asked a difficult question—say, to estimate the number of marbles in a jar, or the murder rate of New York City—their mistakes tend to cancel each other out. As a result, the average answer is often surprisingly accurate.

But here's the bad news: The wisdom of crowds turns out to be an incredibly fragile phenomenon. It doesn't take much for the smart group to become a dumb herd. Worse, a new study by Swiss scientists suggests that the interconnectedness of modern life might be making it even harder to benefit from our collective intelligence.

The experiment was straightforward. The researchers gathered 144 Swiss college students, sat them in isolated cubicles, and then asked them to answer various questions, such as the number of new immigrants living in Zurich. In many instances, the crowd proved correct. When asked about those immigrants, for instance, the median guess of the students was 10,000. The answer was 10,067.

The scientists then gave their subjects access to the guesses of the other members of the group. As a result, they were able to adjust their subsequent estimates based on the feedback of the crowd. The results were depressing. All of a sudden, the range of guesses dramatically narrowed; people were mindlessly imitating each other. Instead of canceling out their errors, they ended up magnifying their biases, which is why each round led to worse guesses. Although these subjects were far more confident that they were right—it's reassuring to know what other people think—this confidence was misplaced.

The scientists refer to this as the "social influence effect." In their paper, they argue that the effect has grown more pervasive in recent years. We live, after all, in an age of opinion polls and Facebook, cable news and Twitter. We are constantly being confronted with the beliefs of others, as the crowd tells itself what to think.

This research reveals the downside of our hyperconnected lives. So many essential institutions depend on the ability of citizens to think for themselves, to resist the latest trend or bubble. That's why it is important, as the Founding Fathers realized, to cultivate a raucous free press, full of divergent viewpoints.

The ideal, then, isn't group think, but independent thinking followed by a compilation of people's thoughts. 

Jonah Lehrer, however, neglects to mention one reason why the social influence effect has grown in recent years:  all the time that today's students are forced to work in groups in K12 classrooms, and, increasingly, in college classrooms as well.  In this case it's not the hyperconnectedness of our wired and wireless lives that's responsible, but the group think of the education world, with its systematic confusion of "cooperation" with "collaboration."

Computer programming-- an optimal pedagogy

It has long struck me that the most suitable courses for online learning are programming courses.

Not only that, but programming itself provides optimal learning, even without a human instructor. Quoting from one of my earlier posts:

• Programming exercises provide immediate feedback: as soon as you run your code you see whether it works, and if not, where the problems are.
• Learning is active: it's still up to you to figure out how to fix the problems. 
• Standards are high: Computer programming is unforgiving--even of tiny errors. The program simply won't run if you make any mistakes. 
• In particular, you must express things clearly and logically, without any syntax mistakes, missing steps, inconsistencies, or undefined terms.
• There's consistent, effective reinforcement: when you get it right, the gratification is immediate and intrinsic (your program works!) 

Can't we make all learning this way--and stop saying it's bad to have high standards, unforgiving feedback, and the ever-present authority of an absolute truth that won't let you get away with anything?

An absolute Truth, indeed, that is Out There: when a program doesn't behave as it should, there generally *is* a solution, and if you persevere systematically and scientifically (generating and testing hypotheses), you'll eventually find it.

Thoughts on Relevance: How much relevance is relevant?

I was reminded of this old 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?

to learning, that is?

Today's educators tell us that students learn best from material that relates to their personal lives. But has anyone bothered to ask students how they feel?

If anyone had asked me how I felt when I was a student, I would have replied that quite often I prefer the exotic and abstract to the personally relevant.

In English/Language Arts, this meant fantasy, science fiction, and historical fiction.

In social studies, faraway times and places.

In science, cosmology and the intricacies of cell life and natural selection.

And in math, base 8, formal proofs (what made 9th grade Geometry so refreshing), and polar coordinates.

Often, the further removed from family, community, peers, current events, and "all about me" the better.

My favorite teachers weren't those who showed how everything related back to daily life and current events, but those who knew how to guide us to the most exotic nuggets and help to make them crystal clear.

They made things personally relevant in the best sense: not by making us relate them back to ourselves, but by helping us care enough about them, and understand them deeply enough, that we made them a part of ourselves.

Isn't the best teacher, after all, one who helps our minds expand to embrace new material, rather than one who limits new material to what he/she thinks our current minds can personally relate to?

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. 

Consider the term "borrow," as in "borrow 1 from the 10's digit."  And consider the autistic spectrum child who understands neither the word "borrow," nor the underlying (socially-grounded) concept. In the course of helping my autistic son realize his mathematical potential, I've thought long and hard about how to simplify and mathematize the accompanying language. Now, in teaching regrouping to my daughter, I'm revisiting what I came up with for my son. 

We start by exploiting a common counting error: "Twenty-one, twenty-two, twenty-three, ....,twenty-eight, twenty-nine, twenty-ten, twenty-eleven, twenty-twelve, twenty-thirteen,...." 

Then we look at a particular problem: 

31

- 8

I let my child notice how you can't subtract 8 from 1. Then I remind him or her of the counting error, and discuss how thirty-one is the same as twenty-eleven.  Then I have him or her rewrite the problem accordingly: 

211

- 8

First I apply this renaming to the most straight forward problems (where the top number is between 30 and 99). 

Then I introduce the teens:  "onety-one, onety-two, onety-three,... onety-eight, onety-nine, onety-ten, onety-eleven, onety-twelve..."  ' (My daughter now regularly--tongue in check--refers to 11 as "onety-one", and 21 as "onety onety"). 

Then I introduce the ones:  "zeroty-one, zeroty-two, zeroty-three..., zeroty ten, "zeroty eleven." (And my daughter renames 11 as "zeroty onety"). 

Then I introduce, via 90, numbers over 100:  "ninety, tenty, eleventy, twelvety..." 

Next I translate specific numbers in the hundreds:  705 is "six hundred and ninety fifteen;" 821 is "seven hundred and twelvety-one" or "seven hundred and eleventy eleven." 

Lastly I introduce numbers over 1000, which don't sound so odd to our ears in translation: "ten hundred, eleven hundred, ..." 

Finally, I have my child translate specific numbers in the thousands:  1111 is "eleven hundred and eleven" (for carrying from the thousands place to the hundreds place), "ten hundred and eleventy one" (for carrying from the hundreds place to the tens place), or "eleven hundred and zeroty eleven" (for carrying both from the thousands place to the hundreds place and from the tens place to the ones place." 

Or, translating directly into numbers, one can write 1111 as: 

1111             (eleven in the hundreds place, useful when subtracting 900)  

10111    (eleven in the tens place, useful when subtracting 90)  

11011            (eleven in the hundreds and in the ones place, useful when subtracting 909).  

For my quirky kids, all of this has been surprisingly straightforward.