Wednesday, April 29, 2015

The "normal child inside" (fourth installment): being autistic vs. "having autism"

There have long been two mutually incompatible views of autism. There’s the view of the scientists—the neuroscientists and cognitive scientists--in which autism involves deep neurological differences that specifically impair the more complex aspects of socio-cognitive reasoning. And then there’s the view of the sensation-seeking public, in which autistic individuals have neurotypical social and cognitive capabilities but are trapped inside bodies riddled with sensory-motor impairments. In a nutshell, the AS child doesn’t communicate and socialize neurotypically either because his mind isn't so suited (science), or because his body won’t let him (sensation seekers and wishful thinkers, along with their assorted panderers).

Two generations ago, the “normal child trapped inside” model was also that of some of the self-styled empirical scientists. Psychoanalysts like Bruno Bettelheim made it their job to coax socially withdrawn children into normal sociability by liberating them from the “refrigerator mothers” who had "willed" them into "nonexistence." (Back then it was mothers, rather than uncooperative bodies, that were responsible for autism). But when it comes to clinical psychology in general, neuroscience and experimental psychology have long since discredited the normal child trapped inside.

Special education circles are another matter, as I recently discovered. Some of the more compelling locked-in child stories have penetrated special education programs and are treated as reliable windows into autism.

And these stories are quite compelling. Their star is a nonverbal individual whose inner self has been painstakingly unlocked, emerging as an eloquent, empathetic personality eager to share with us what it’s like to “have autism.” The costar, however, is no longer the psychoanalyst, but some sort of facilitated communication system. This consists of a low or high-tech keyboard and either a human or computerized facilitator. The human facilitates either by supporting child’s wrist, or by holding the keyboard up to the child’s fingers; the computer facilitates via word prediction and word completion software. Some these children appear in YouTube videos or shows like 20/20. Here we see short, often carefully edited clips of the child's fingers touching letters or buttons that spell out short messages, and we hear fluent, expressive voiceovers of longer texts whose actual production we aren’t privy to: soliloquies that typically show levels of eloquence, introspection, and empathy that belie everything that scientists have discovered about autism.

They’re not communicating things like How many ceiling fans do you have in your house? or I have a special computer internet which radio ways are quadrillion light years per second. Rather, they're communicating things like People look at me and assume that I am dumb because I can’t speak and I knowingly contribute to my looking retarded by carrying around a plastic spoon, but spoons are my comfort.

You watch these children’s eyes (to the extent that the videos let you), and you see little or no evidence of focused or coordinated eye gaze; you see eyes that seem to flit all over the place, or to stare upwards or outwards at nothing in particular (and often not at the keyboard that their fingers are pushing against). Perhaps all this can be explained by sensory-motor problems rather than socio-cognitive impairments. But then you have to ask: how can kids whose eyes seem not to be able to track pointing gestures or eye gazes, and who would seem therefore to have no way to deduce what people’s words refer to when uttered, have managed to learn the words for the various things in their everyday environments? Not to mention the more advanced words that have somehow entered their soliloquies, poetry, and memoirs: words like “assume” and “knowingly”? More advanced learners can pick up words from texts alone, but to jumpstart the process you (however neurotypical or neurountypical you are) need real-world connections. Before you can read for meaning, that is, you need a critical mass of basic vocabulary that you’ve actively linked to the outside world. And linking those basic words to the outside world--in other words to their meanings--requires of you (however neurotypical or neurountypical you are) a certain threshold of sustained and appropriately targeted auditory and visual attention.

Here's what Wikipedia has to say about Facilitated Communication (FC) and its promoters:

As early as 1991… more than 40 empirical studies published in peer-reviewed journals involving more than 400 people with autism not only failed to demonstrate FC's efficacy, but indicated that any success reported by proponents of the technique was due to facilitator influence.

Despite claims from FC promoters that autism is a motor control and emotional (i.e. confidence) problem that can be overcome with physical support, autism is, largely, accepted in the academic and clinical arenas as being a neurological problem often accompanied by intellectual disabilities. A core feature of autism is severe communication problems which cannot be overcome simply by supportively holding onto someone's hand.
Misconstruing autism as a disorder that can be unlocked by keyboards and facilitators ignores the science, the much more promising therapies based on that science, and, most of all, the pressing needs of the most vulnerable people involved.

Monday, April 27, 2015

Homeschooling update

The homeschooling schedule need not have any clear-cut beginnings or endings. Every once in a while, however, a bunch of things conclude at more or less the same time, and a bunch of new things begin. And then it's time for a homeschooling update.

In Literature, we recently moved on from Arthur Lang's King Arthur to Bullfinch's The Age of Fable; from assorted works of Washington Irving (Tale of Old New York, Rip Van Winkle, Sleepy Hollow) and Poe (The Cask of Amontillado; The Masque of the Red Death; the Black Cat) to To Kill a Mockingbird and Animal Farm; from Little Women to Good Wives; from The Hound of the Baskervilles, The Strange Tale of Dr. Jekyll and Mr. Hyde, and Macbeth to Frankenstein; and from Kings to Chronicles.

In history she recently finished Gombrich's A little History of the World and is now reading Outlines of European History.

In science we recently finished a McGraw Hill earth science text and The Way Life Works and are now working our way through our various science experiment kits.

In French she recently moved on from Level II to Level III in A-LM French, and from Astérix le Gaulois to Astérix et la serpe d'or.

Sadly, the three after-school art classes she takes at the Pennsylvania Academy of the Fine Arts are about to conclude this coming week.

Finally, in what is her biggest academic accomplishment this year, she just finished Wentworth's New School Algebra (which has made numerous appearances on this blog), doing nearly every problem in the book (skipping some of the really messy problems at the end), and is about to embark on an alternation of Weeks & Adkins Geometry (my husband's high school text) and A Second Course in Algebra (my mother's high school text), which includes some trig and pre-calc.

Not everything is new: I have her scanning the New York Times every morning, reading a poem once a week, working her way through a long American History text (Glencoe), Wheelock’s Latin, and music theory. Music lessons and ensembles continue, and this summer she looks forward to doing the six-week piano program at the Interlochen Center for the Arts.

Saturday, April 25, 2015

“Asian” collectivism vs. “Western” individualism: what does the fish tank experiment really show?

If you show an American an image of a fish tank, the American will usually describe the biggest fish in the tank and what it is doing. If you ask a Chinese person to describe a fish tank, the Chinese will usually describe the context in which the fish swam.
Skeptical about whether modern Chinese culture really is less individualistic than modern American culture, I was going to offer an alternative explanation for the results of the fish tank experiment, as discussed, for example, by David Brooks. What I like about this explanation, besides the fact that I can claim it as my own, is that the variable it targets also accounts for that other common stereotype about Chinese culture: that the education system is based mostly on rote memorization.

The variable I have in mind is the Chinese writing system.

In my earlier post, I wrote that the rote memorization in Chinese schools stems mostly from the logographic system of written Chinese. The thousands of characters prerequisite for literacy in written Chinese require many thousands more hours of memorization than the few dozen sound-symbol correspondences of written English.

But learning the Chinese vs. the English writing systems doesn’t just involve quantitative differences in time spent memorizing things. Also at play are qualitative differences in the memorization process. Learning an alphabet means attending to the symbols’ most salient features: the big lines and curves rather than the little serifs (or lack thereof) around the edges. Learning Chinese characters means attending to everything: the big lines and curves, but also the patterns of smaller lines and dots all around them. If Chinese people are more aware of the context of a fish tank, perhaps it’s because learning the Chinese writing system trains you in a certain attention to visual detail; in particular, to the details that surround the larger, more visually salient elements.

I liked this explanation so much that I was sorry to find out just now that, along with all the other experiments that supposedly show today’s Chinese to be less individualistic than their Western counterparts, the fish tank experiment fails, across many dimensions, to support not only the broader claims that I’m skeptical of, but the proximal claims about who reports what about the fish tank. The details are found in a 2008 post by Mark Liberman on the Language Log—a post so delightful and interesting that, for me at least, it more than makes up for my sorrow at having to abandon something I really, really wanted to believe.

Thursday, April 23, 2015

Common Core-inspired high school exam questions vs. Chinese and Finnish counterparts

From America's PARCC (The Partnership for Assessment and Readiness for College and Careers, a consortium of 23 states involved in developing Common Core tests):

From the Chinese Gao Kao

From Finland's National Matriculation exam:

Extra Credit:

Perhaps I'm cherry picking. Prove it by finding Common Core-inspired high school test questions as mathematically challenging as the ones above from China and Finland.

Tuesday, April 21, 2015

The stereotype of rote learning in East-Asian classrooms, III

(Third in what's become a series.)

This installment begins with a few more thoughts on Fareed Zakaria’s recent Why America’s obsession with STEM education is dangerous--which, for all its problems, is certainly thought-provoking:

Americans should be careful before they try to mimic Asian educational systems, which are oriented around memorization and test-taking. I went through that kind of system. It has its strengths, but it’s not conducive to thinking, problem solving or creativity. That’s why most Asian countries, from Singapore to South Korea to India, are trying to add features of a liberal education to their systems. Jack Ma, the founder of China’s Internet behemoth Alibaba, recently hypothesized in a speech that the Chinese are not as innovative as Westerners because China’s educational system, which teaches the basics very well, does not nourish a student’s complete intelligence, allowing her to range freely, experiment and enjoy herself while learning.
Jack Ma was born and educated in China and lives there now; thus creatively undernourished, how is he qualified to talk about creativity? For that matter, how qualified is the Indian-educated Zakaria, who, as he himself claims, went through a system oriented around “memorization and text-taking.”?

The fact that there are plenty of creative individuals educated in India and China should make us wonder whether the claims of these two particular Chinese and Indian-educated individuals--not to mention so many of us native-born Americans--are actually true.

When it comes to China in particular, Americans have hopelessly incoherent opinions. On the one hand, with our stereotype-confirming fish tank experiments, we think the Chinese (along with Asians in general) are more into group harmony than we Westerners are; on the other hand, with their competitive exams and tiger moms, we think they are more into competition and individual success. We carry on about how steeped in memorization the Chinese education system is, ignorant of how most of this is an artifact of a logographic writing system that demands thousands more hours of memorization than what our alphabetic system demands. Those hours do limit how much time Chinese K12 schools spend on a broader curriculum—e.g., on history, science and art—but, when it comes to math, their curriculum is akin to the highly conceptual Singapore Math.

Americans carry on about China’s college entrance (Gao Kao) exams, conflating stiff competition with rote memorization. Yes, the exams are highly competitive, and students study very hard for them, and, like most exams the world over, they favor the wealthy. And, by the time they take these exams, exhausted, sleep-deprived students may feel like mindless zombies.

But the exams aren’t rote. Both the Chinese and English sections include essay questions, and the problems on the math sections are highly conceptual. In many ways the Chinese Gao Kao exams are more demanding of conceptual understanding and creativity than America’s Common Core exams.

Sample essay question for the Chinese section of the Gao Kao can be found here and include questions like:
"You can choose your own road and method to make it across the desert, which means you are free; you have no choice but finding a way to make it across the desert, which makes you not free. Choose your own angle and title to write an article that is not less than 800 words."
Sample essay questions for the English section, found here, include:
A pencil laughs at a shorter pencil, which is almost used up, saying: "You're nearing the end!" You are discussing a picture with an English friend. Describe your understanding of the illustration, and the reason why.
And sample math questions, found on the slideshow on this site, include:

Critical thinking and conceptual understanding, anyone?

It took me only an ounce of skepticism and a handful of clicks to track down this information. But most Americans (including, apparently, naturalized Americans like Zakaria) are so sure that the Chinese system amounts to mindless rote learning that it hasn’t occurred to them to spend a few seconds verifying what their own mindless rote learning has taught them to take on faith.

Sunday, April 19, 2015

...And to teach reading, study math instruction

In her recent Edweek commentary To Teach Math, Study Reading Instruction, Marilyn Burns asks:

How can we connect literacy and math, so that teachers bring the strengths they have with language arts instruction to their math teaching? How can teachers make links between mathematics and language arts pedagogy that will enable them to engage children with math in the same way they bring children to the wonder of reading?
One way, she proposes,
is for teachers to think about leading classroom discussions in mathematics as they often do when teaching language arts. Probing students' thinking during math lessons is valuable, so that the goal is not only getting correct answers, but also explaining why answers make sense.
Asking students why answers make sense: this idea is so novel that it apparently hasn’t occurred to most math teachers. Along these lines, Burns advises, it’s important
even when [students’] answers are correct to ask: "Why do you think that?" "How did you figure that out?" "Who has a different idea?" "How would you explain your answer to someone who disagreed?"
Naturally, Burns is also a fan of verbal explanations and peer tutoring:
It's useful to have students comment on their classmates' answers as well, asking them to explain what a peer said in their own words, or asking students if they have a different way to explain the answer. If students are stuck, it's sometimes useful to have them turn and discuss the problem with a partner and then return to a whole-class discussion.
Her takeaway?
There's much for us to think about to help teachers teach math more effectively. But I think we can make headway if we take the two most important areas of the curriculum—reading and math—and look at them side by side to analyze what's the same, what's different, and what we can learn from one to enhance the other.
I agree. And so here are some of my suggestions about how good math instruction (the kind done in countries that outperform us in math) can teach us about reading instruction (so as to make it more closely resemble that done in countries that outperform us in reading):

1. Basics first, learned to mastery: just as good math instruction teaches basic arithmetic facts and procedures to automaticity; reading instruction should teach phonics to automaticity. Since many students, even older ones, currently lack automatic symbol-to-sound decoding skills, this means much more time on phonics than is currently occurring.

2. Focus in depth on the one best method(s) rather than covering a bunch of less effective methods superficially. Just as the best math classes focus on standard arithmetic and algebraic algorithms rather than drawings of groups of objects, digit splitting, skip counting, number bonds, repeated addition, repeated subtraction, landmark numbers, and lattices, reading classes should focus on phonics, vocabulary acquisition, and close readings rather than on sight word recognition, context clues, text-to-world references, and text-to-self references.

3. Make sure students have sufficient background knowledge: just as good math instruction waits until students have mastered relevant concepts before having them do novel applications in novel problems, good reading instruction should provide relevant background knowledge to new books (e.g., for Pride and Prejudice, information about English hereditary law; for the Great Gatbsy, information about the Jazz Age).

4. Keep it content-focused: just as good math instruction doesn’t focus away from the actual math via verbose word problems, verbose explanations, and overly concrete, detailed, real life situations, reading instruction should focus on inferences within the text, rather than on inferences that take readers out of the world of the text--and, worse (in the case of “text-to-self” references), distract or annoy them with the task of having thoughts about themselves rather than about what they’re reading.

Friday, April 17, 2015

Math problems of the week: Common Core-inspired quadratic structure problems

A sample high school math problem from PARCC (The Partnership for Assessment and Readiness for College and Careers, a consortium of 23 states involved in developing Common Core tests):

PARCC's discussion of how this problem aligns with Common Core Standard MP.7:

A more challenging set of "seeing quadratic structure" problems from over a century ago (Wentworth's New School Algebra):

Extra Credit:

1. Are there other useful structures one could recognize the PARCC problem as having other than Q2 + 2Q = 0? For example, might recognizing it as having the form a*a = b*a be an alternative, non-brute-force way of seeing its solutions?

2. If "seeing structure in a quadratic equation" warrants a special Common Core standard (MP.7), why aren't students getting more challenging quadratic structure problems like those in Wentworth above?

3. Was "seeing structure in a quadratic equation" even more important a century ago, before we needed the Common Core authors to remind us of how important it is?

Wednesday, April 15, 2015

Teaching Math in the 21st Century

Barry Garelick's new book is out!

Also available on Amazon.

An insider's account of math education in the Brave New World of the Common Core standards. Fans of Barry's Conversations on the Rifle Range series here on this blog will very much enjoy this compilation. More broadly, it is a must-read for anyone concerned with 21st century math education, STEM education, and "21st century skills."

Monday, April 13, 2015

But is he really ready for college?

In my previous post (below), I wrote about all the efforts that got J where he is now. But I left out one key thing. None of the social skills training, none of the GrammarTraining, and none of the educational strategies and opportunities would have gotten him anywhere without external incentives and external consequences. Even now, J would be happy to spend the entire day doing ceiling fan stuff. When he got his first college acceptance letter (by email), he didn’t tell me about it for four days—not until I thought of asking him whether he’d heard anything. Excited though he was to talk about it, in the grand scheme of things it simply wasn’t that important to him.

The same goes for doing well in school: he cares somewhat, but not that much. And the main reason he cares are all the external incentives we’ve attached-most of which boil down to ceiling fans.

In elementary and middle school, his dependence on parent-administered incentives for scholastic success created constant tension between us and J’s teachers. We could only incentivize assignments we knew about; we could only reward him for remembering to turn in his assignments if teachers let us know whether he had managed to do so; we could only reward him for good grades on assignments and tests if teachers communicated these to us shortly after the fact. But parent-teacher communication and online gradebook tools were not (to put it mildly) the school’s strong suit, and so we were constantly finding out, too late for timely incentives, that things were going badly.

“He needs to learn to be more organized,” said the school, repeatedly.

“He needs external incentives to be more organized,” said the mom, repeatedly. “We can’t provide these unless we know about problems as they arise. And you can’t punish a kid whose lack of organization is part of his disability by giving him low grades.”

If I hadn’t kept repeating this, J’s grades would have been low enough that he wouldn’t have gotten into the math and science magnet he now attends. The alternatives—the one remaining dysfunctional neighborhood high school, or a vocational tech school that has since been shut down—wouldn’t have led anywhere good.

Even at his current school, J has his egregious moments of minimal effort, maximal disorganization, or failure to notice and follow important directions, and teachers remind us of how important effort, organization, and following directions are in college and the workplace. Some of them say that it’s reasonable for the consequences for these shortcomings to match what the consequences will be in college or the workplace. It’s high time, surely, for J to stop depending on external motivations for effort, etc.: after all, to function in the real world, independently of hovering parents, he should be prepared for built-in, real-world consequences.

But had his high school grades fully reflected all his moments of minimal effort and maximal disorganization and failure to notice and follow directions, he wouldn’t have gotten into college.

Perhaps, then, J isn’t ready for college. But what is the alternative? If he’s not mature enough for college, he’s certainly not mature enough for the work place. He could theoretically stay in high school until he’s 21, but he’s taken all there is in the way of math and computer science classes, and we don’t want those skills, his most promising ones, to stagnate. Does it really make sense for him to ride out the next few years of his life in a holding pattern until he (eventually, hopefully) crosses some threshold of emotional maturity, when what he needs is a structured setting in which to further develop his most promising skills?

So, yes, he is ready for college. He is ready, in particular, for the best college he got into: one with an autism support program and minimal distribution requirements. One that, equally importantly, is within walking distance of home--where he will continue to live, and where, yes, we will be monitoring him very closely and continuing to give him all the external incentives it takes for him to continue to succeed.

As for the real world, we will cross that bridge when we come to it.

Saturday, April 11, 2015

Autism diaries: between "glimmers" and "miracle cures"

Towards the end of last calendar year, I posted the following questions:

The SAT Critical Reading score of Applicant X is 3/8 of his SAT Math score. There is a 500 point difference between the two scores.
1. Assuming that Applicant X grew up among native English speakers, what is his likely diagnosis?
2. Should you admit him to your engineering school?
The schools in question have now given us their answers, but first, a bit of background.

When J was four years old, he was downgraded by a autism specialists at one of the top autism research centers, after an extensive evaluation using the then-new ADOS tool, from PDD/“mildly” autistic to “moderately” autistic. One of the evaluators suggested we focus on life skills.

“He already has life skills,” I said. I described how J had figured out, on his own, how to operate the bread machine, and how he had recently tracked down an apple slicer at the grocery store so he could slice his apples the way they did at school.

The evaluator looked momentarily surprised. But then, delicately and diplomatically, she explained that “There may be glimmers.” Glimmers of specific abilities. She didn’t need to elaborate: we’d all seen Rain Man. Clearly she was thinking of parents who observe their 2-year-olds writing phrases like “FBI warning” with sidewalk chalk and assume that all would be well; kids who turn into adults who can tell you, in an instant, the day of the week of your great-grandfather’s 40th birthday, but can’t make simple purchases or pass job interviews. Equally clearly, I was not the first parent whose hopes she’d had to check with this reality.

But rather than life skills, we opted for a language support classroom, a year of neurofeedback, years of classroom-based tss support, years of daily extracurricular social and academic tutoring, and about three years of training in all 109 lessons of GrammarTrainer. By 6 J was functioning OK in mainstream classrooms, and by 16 he was fully included, with no tss support, at the first school to welcome rather than fear him--which also happens to be the best math and science magnet in the city (and one of the city's 3 top schools over all, with some of the best teachers I've ever seen).

So what has our moderately autistic four-year-old turned into? Among other things, a high school senior with high scores in math and computer science and writing skills not far below the neurotypical average. With a great sense of direction and extensive knowledge of the city transit system; with extensive experience conducting independent transactions at stores and negotiating fan visits and decommissioned fan donations from neighbors; and with hundreds of dollars earned through snow shoveling, yard work, household repairs, and, (somehow!), Google Ads, he has life skills galore. Such are his “glimmers.” But this is no miracle cure. J’s diagnosis hasn’t changed: recent tests confirm that his autism is still, not “mild,” but “moderate”; he still lags far behind in language comprehension, social skills, and emotional maturity.

So is he ready for college? 15 years ago, no one, even his hopeful parents, would have predicted it, but the answer, according to three different admissions offices, is yes!

Thursday, April 9, 2015

Math problems of the week: Common Core-inspired 5th grade geometry

From PARCC (Partnership for Assessment and Readiness for College and Careers), a consortium of 23 states involved in developing Common Core tests:

Sample Mathematics Item: Grade 5 “Two Aquarium Tanks”:

PARCC's rationale for this assignment in terms of Common Core Standards:

Extra Credit:

1. Discuss the ratio of mathematical challenge to nonmathematical challenge in solving these two problems.

2. Discuss the ratio of the effort involved in coming up with problems like these to the effort involved in justifying them--i.e., explaining how effective they are in meeting the Common Core standards (from "Evidence Statement" all the way down to "Scoring Information").

Tuesday, April 7, 2015

The SentenceWeaver(TM) in action

At Autism Language Therapies:



Soon to be up on iTunes for usability testing!

Sunday, April 5, 2015

Why learning isn't stylish

In Why Don’t Students Like School and elsewhere, psychologist Dan Willingham discusses experiments suggesting that what some people view as qualitative differences in learning styles really amount to quantitative differences in skill levels. And, I would add,variations in needs and preferences, particularly as a function of K12 classroom circumstances.

But learning styles theory is alive and well among current and would-be teachers—some of whom are my students. If I had time to do justice to their misconceptions, I would begin with the following re-definitions:

You’re an “auditory learner” if you depend on oral language (or text-to-speech programs) because you don’t read fluently at grade level. Some might call you dyslexic; others might call you a victim of deficient instruction in phonics.

You’re a “visual-spatial learner” if you’re good at visualizing things, or, alternatively, if you can’t sustain attention and need non-fleeting text-based language and/or pictures that you can repeatedly go back to and review.

You’re a specific subtype of “visual-spatial learner” if you have general language comprehension problems (impairing your comprehension of both spoken and written words) and rely on pictures and diagrams for communication. You’re even more “visual-spatial” if you also have trouble sustaining attention. Given that language and attention problems are highly common in autism, we see why so many people claim that autistic kids are “visual learners” who “think in pictures.”

You’re a “bodily kinesthetic learner” if you’re good at gym, or, alternatively, if you, in clinical parlance, have ADHD, or, in non-clinical, non-edu jargon, aren’t getting enough opportunities to run around—and/or are bored out of your mind at school.

You’re a “musical-rhythmic” learner if you’re good at music and rhythm, or, alternatively, if you restlessly strum your fingers, tap your feet, or hum during class time.

You’re an “interpersonal learner” if you’re good at socializing or like to socialize, or, alternatively, if you can’t/don’t like to do classroom tasks by yourself and rely on help from peers.

And you’re an “intrapersonal learner” if you get along with yourself better than with your classmates, or, alternatively, if you don’t want to share personal reflections in class and just want to be left alone.

And you’re a “verbal-linguistic” or a “logical mathematical” learner if you are, in what is still the most commonly used sense of the term, “smart.”

Friday, April 3, 2015

Math problems of the week: Common Core-inspired introductory geometry problems

The opening exercises of New York State Common Core Geometry Curriculum

The opening exercises of Weeks Adkins A Course in Geometry (1970 edition)

The following exercises provide situations in which deductions can be made. Consider carefully the way in which a supporting argument may be developed.

1. Two coins of the United States have a total value of 30 cents. Can you deduce the names of the coins?

2. Three coins of the United States have a total value of 60 cents. Can you deduce the names of the coins?

3. Three coins of the United States have a combined value greater than 70 cents and less than 80 cents. Can you deduce the names of the coins, if no two of them have the same value?

4. The sum of two whole numbers is an even number. One of the numbers is even. Can a deduction be made about the other number?

5. The product of two whole numbers is an even number. One of the numbers is even. Can a deduction be made about the other number?

6. Can a deduction be made about Tom from the statements that follow?
(a) All dogs have two ears. Tom is a dog.
(a) All dogs have two ears. Tom has two ears.
(a) All dogs have two ears. Tom has no ears.

7. In a class of 30 students everyone must take at least one of the languages French, Latin. If 20 are enrolled in French and 17 are enrolled in Latin, how many students are enrolled in both?

8. If x,y are whole numbers and x-y is an odd number, can a deduction be made about x + y?

9. A, B, C, D are four towns. A route runs through each pair of towns and no route runs through more than two of the towns. What deduction can be made about (a) the number of routes through each town, (b) the total number of routes?

Extra Credit

1. Are the Weeks Adkins exercises, above, irrelevant to 21st century mathematics?

2. The Common Core Math Standards include this one:
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples…
(I've omitted the "critique the reasoning of others" part of this goal.)

Try to find a Common Core-inspired problem in which:

A. the primary challenge, as with the 1970s Weeks Adkins problems, is in the construction of viable arguments
B. the logical challenges are similar to those of the Weeks Adkins problems.

Wednesday, April 1, 2015

Neurotypicals are autistic!

This striking conclusion, announced by autism researchers early this morning, is based on the new DSM criteria for autism:

A. Persistent deficits in social communication and social interaction across multiple contexts
B. Restricted, repetitive patterns of behavior, interests, or activities
C. Symptoms must be present in early development
D. Symptoms cause clinically significant impairment in social, occupational, or other important areas of current functioning.
E. These disturbances are not better explained by intellectual disability or global developmental delay.
Here, criterion by criterion, are their findings:

A. It turns out that most socio-linguistic communication by neurotypicals consists of utterances that are impoverished of real content (i.e., of new and interesting information), full of meaningless fillers like “so,” “like,” “really”, and “yeah,” and frequently insincere. Insincerity also pervades non-linguistic social communication, which consists mostly of fake smiles, insincere laughing sounds (so-called “social laughter”), and meaningless gestures.

B. Most subjects are of zero interest to most neurotypicals, especially beneath their superficial surfaces: quantum physics, astrophysics, geology, cell biology, organic and inorganic chemistry, materials science, civil engineering, history (whether intellectual, political, military, or even social), baroque music, renaissance art, Chinese philosophy, geography, and current events—to name just a few examples. One indication of this is how little most neurotypicals know about any of these subjects. Few, for example, can even locate Nigeria on a globe, let alone say anything about today’s election results. To paraphrase Temple Grandin, most neurotypicals seem content to sit around and chat about absolutely nothing.

C. Studies of social interactions among young children indicate these symptoms appear extremely early in neurotypical development.

D. These symptoms impair the quality of social interactions; they also impede occupational function and important life skills, as seen in the widespread incompetence (illiteracy, innumeracy, overall ignorance, poor planning skills, and susceptibility to bogus statistics, false logic, and quack theories) of so many fully-grown adults. Take the education world, for example. Or the world of autism. Indeed, these symptoms have severely impeded the occupational functioning of researchers hung up on narrow, rigid theories of autism, and therapists (particularly of the armchair variety) deficient in Theory of Autistic Mind (or the ability to empathize with autistic individuals—or their parents).

E. Given the pervasiveness of these symptoms in the neurotypical population, they cannot be better explained by intellectual disability or global developmental delay—unless we are going to say that nearly all neurotypicals are intellectually or developmentally disabled.