Social-emotional studies

From the U.S. history book American Vision, the text used in Philadelphia's public high schools:

A.P. update: what does it take to show your work?

We learned last week that J managed to get a 5 on his AP BC Calculus exam, defying expectations about whether he'd be able to step out of his shoes enough to show his work. None of his practice tests earned 5s, and so it's very satisfying to see this one, especially as it bodes well for his potential to show his work in college-level math classes this coming year.

On the other hand, he only got a 3 on the AP Computer Science exam, which presumably means there's more work to do in making sure his programs (which he dashes off quickly, and which get the job done, but are often quite lacking in clarity) conform to specifications. Apparently, this is even harder for him than showing his work in math.

Except that there's another possible explanation for J's superior performance on the BC Calculus exam--and for his uncharacteristic eagerness to find out his score. It turns out that his math teacher had promised the class to organize a lunch at Dave & Buster's if they all did well.

And Dave & Buster's--you guessed it--has lots and lots of ceiling fans.

Do American secondary school contribute to radicalization?

I've written frequently here and elsewhere about how America's K12 schools are particularly challenging for unsocial children. The uniquely American quantity of extra-curricular school-based activities--sports, clubs, student government, athletic events, dances--have transformed American junior high and high schools into institutions that are much more social in nature than their counterparts in other countries. American high schools are major centers of social gravity, with social hierarchies based more on athletic skills, extracurricular activities, and leadership than on academic interactions. Factor in the rise of mandatory group work inside and outside of American classrooms, and the social pressures are inescapable. From this, the quirky, unsocial introvert, in comparison with his counterparts in other countries, will find little refuge.

On top of this, there seems to be something particularly trying about American teenagers in particular. One Asperger dad I know sends his son to a Canadian summer camp because, as the son has observed, Canadian teenagers are nicer.

All this makes me wonder about the role played by American junior high and high schools in marginalizing, and thereby radicalizing, certain psychologically unstable and susceptible kids: the school shooters, the skin heads, and the ISIS recruits. Of course, there are plenty of other factors at play here, from the availability of guns here in America, to homegrown homophobic, White Supremacist ideologies, to the lure of the Caliphate in the Middle East. But it's worth appreciating what nasty settings those institutions that concentrate together large numbers of teenagers can potentially be--especially when child-centered ideologies empower kids to create and run the social hierarchies in settings where the adults should really be in charge.

Math problems of the week: more Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states: the next three problems on the sample 4th grade practice test.

Extra Credit

Discuss the relative roles played by language skills (knowledge of labels, careful reading) vs. math skills in these problems.

Going "deep" with Common Core algebra

It's time for another exegesis of an article in Edweek, this one on what the Common Core is doing for algebra students:

Under the Common Core State Standards, Algebra 1 is a much tougher course than what was taught previously in most states, teachers and standards experts say, in part because many of the concepts that historically were covered in that high school class have been bumped down into middle school math.

Actual Common Core-inspired algebra problems tell a different story.

Some say those changes could complicate efforts around the country to put 8th graders in Algebra 1—a still-debated trend that's grown over the past two decades.

And thus the Common Core, besides all the other fashionable K12 practices it endorses, has become yet another excuse not to accelerate students, but rather to impose a one-size-fits-all on everyone based on their calendar age.

And while that kind of move can disappoint some parents, educators point out it doesn't mean 8th graders aren't learning algebra.

Well, that depends on what you mean by "algebra."

"There's big confusion between the Algebra 1 course with a capital A and algebra, the mathematical subject," said William G. McCallum, a mathematics education professor at the University of Arizona, in Tucson, and one of the lead writers of the common standards. "If you follow common core, there's now tons of algebra content in the 8th grade."

Well, that depends on what you mean by "algebra."

"Traditionally in Algebra 1, a lot of time was spent looking at linear functions," said Diane J. Briars, the president of the Reston, Va.-based National Council of Teachers of Mathematics. "But a lot of that work now has been moved into 8th grade common core."

Right. Kids in 8th grade (and younger) are filling in input and outputs on function charts, guessing and checking and plotting points on grids, and solving for x in simple equations involving minimal mental (or algebraic) manipulation. Then there's ratio and proportion.

"The common core… built much higher expectations for conceptual understanding regarding ratio and proportional relationships [in 8th grade] to prepare students to understand the ideas of slope and rate of change."

It sounds pretty impressive:

Simultaneous linear equations and functions and their graphs—concepts also typically taught in Algebra 1—are now also taught in 8th grade under the common core.

The catch is that those simultaneous equations never have more than two variables in them, even in today's Algebra 2, and that they require little in the way of symbolic manipulation.

The idea is that by the time students get to Algebra 1, they will have developed deep understanding of some basic algebraic concepts, and can dive into more complicated coursework.

The "complicated coursework," though, is about applying these concepts to "real-world" situations, not to situations of mathematical complexity:

Students are focused on applying the algebra they're learning, rather than seeing it as a series of procedures and algorithms.

For instance, rather than doing a set of problems from the textbook, Mr. Ryan said, students in Algebra 1 might collect data on the weight of students' backpacks, plot them on a graph, and model them with an algebraic function.

What's challenging about math, however, often isn't the concepts themselves. How hard, after all, is the concept of a function, or a slope, or an algebraic "model" of a simple, real-world situation like the weight of students' backpacks?

What's challenging about math, rather, is the mathematical complexity and abstraction that emerges from applying functions, slope, and algebraic models, not to real-world situations, but to mathematically complex situations, with layer upon layer of abstractions, abstract patterns, and symbolic manipulations. What students need practice mastering is this emergent property of complex, abstract math, and not the building-block concepts themselves--or their real-world applications. Yes, students need to engage with the concepts in action, but most especially in an abstract, mathematical way that few are seeing today.

Here are some examples of what they are missing, and will miss--throughout their years of Common Core-inspired high school math:

--simultaneous equations involving more than two variables.
--simultaneous quadratic equations.
--equations involving abstract quadratic patterns.
--real-world situations that take some real mathematical thinking to model mathematically.

Autism diaries: the question of authorship

"I just assumed you were coming back to the kitchen," says J. "In fact, I did not even think of trying to leave the fan on all night."

In fact; assume--to my ears, coming out of J's mouth, these words sound almost miraculous. Not only are they the sort of subtle, conversational terms that are supposed to elude even higher functioning Aspies and auties, they're also words J's picked up on his own, simply by overhearing people use them. Nearly all the words in his vocabulary, until recently, had to be deliberately pointed out or defined for him, sometimes repeatedly. Now, through the incidental learning that typifies most neurotypical language learners but eludes most individuals with autism, these words have become fully J's own.

I've written frequently about the question of authorship in autism. While this question arises most especially vis-a-vis the "facilitated communication" of nonverbal individuals, where it's for from clear who (or what) is actually doing the communicating (see here, here, and here), it also arises with verbal kids who communicate independently. Kids on the spectrum often have copious memories and can regurgitate verbatim large tracks of memorized discourse and large bodies of memorized facts. Some of them go through intensive behavioral therapy that drills them in prepackaged conversational phrases and formulas. Autism autobiographies may undergo extensive re-writing by editors--even if those editors manage to maintain, more or less, the original authorial voice. Those rewrites, in turn, may be memorized and regurgitated by the original authors in book talks and other post-publication speeches.

The flat facial affect, flat tone of voice, and overall lack of expressivity of autistic speakers only heightens the question of who is really communicating. Is it the individual with autism, drawing spontaneously on internally processed knowledge, and putting words together independently and extemporaneously? Or is what we're hearing ultimately the product of a facilitator, a behavioral script, a book editor, a word-button or word-prediction program, or an author of a text that has been read and reread out of obsessive autistic interest?

It's often hard to say--and the line between the two extremes is often fuzzy. It's probably somewhat fuzzy even for neurotypicals: all of us do some cutting and pasting of other people's words.

In J's case, however, the same things that have limited him over the years have minimized questions about authorship. He doesn't sit for drills; his verbal memory is poor; he reads very little by choice; his only obsession is ceiling fans, and even this tremendously high-interest topic doesn't inspire much reading; nor does he publish memoirs and give book talks.

What this means is that what comes out of J's mouth or his various keyboards really is J--through and through. There's absolutely no illusion whatsoever...

Except that there is--at a whole new level.

Yes, what comes out of J's various keyboards really is J, through and through. But, as we've seen repeatedly, he often tries to pass off his words as belonging to someone else. He's regularly, and often successfully, impersonated each of his parents, along with a few others--for example, those lucky individuals whose email accounts he's hacked.

At his "best," in other words, J not only isn't echoing others, but is surpassing even himself.

Math problems of the week: Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states.

Extra Credit:

Discuss how these problems exemplify the phenomenon (discussed earlier) that often the "deep concepts" are relatively easy, while more complex calculations involving those concepts (conspicuously absent in these problems) are where the real challenge emerges.