Sunday, June 26, 2016

The Normal Children Locked Inside in lockstep with the Common Core Standards

I was recently talking with another autism mom about the various "normal child locked inside" takes on autism that predominate in the popular media: those stories of miraculous communication breakthroughs that generally occur thanks to some sort of facilitated communication:

1. a therapist providing "light support under the wrist" as a child supposedly moves his finger independently over a keyboard;
2. a keyboard that for some reason has to be held up to the child's fingers and whose letters need for some reason to be read out loud to the child as he types;
3. a child who, even though he does type independently, does so not to converse spontaneously (at least as far as we ever see), but to spontaneously type out poems that may have been composed by someone else and reproduced from memory.

None of these breakthrough stories have been validated by any controlled study, for all the many times that studies have invalidiated their underlying methodologies.

"But is there any real harm in believing in these stories," the autism mom was wondering. After all, they give parents and therapists hope, and the kids, instead of being given up on, get lots of loving attention. Maybe the "facilitation" approaches overestimate the kids' abilities, she said, but surely that's better than the way things used to be, when nonverbal kids were completely written off as having no potential at all.

She has a point. And while I've harped on the downsides of the miracle cure stories--how they raise false hopes and deter therapies tailored to the child's actual potential--that actual potential is never fully knowable, and it is arguably worse to underestimate it than to overestimate it.

Our different perspectives as autism moms may, to some extent, reflect the differences in our children's educational placements. Her child has been mostly in private special education schools; mine has been mostly in mainstream classrooms. In private special education schools, there's less pressure to push students towards mainstream educational goals and it can be easiest to keep expectations low. In mainstream settings, especially under the Common Core, it's a completely different story. Except for 1-2% of the most cognitively disabled children, all students are expected to meet the same goals. And while the Common Core website acknowledges that some students will need accommodations, the only specific type of accommodations it mentions is assistive technology.

As I was discussing this with the other autism mom, it occurred to me that the Common Core's assumption that all but 1-2% of students should be held to the same standards basically assumes a "normal child locked inside" model of all but the most severely impaired kids. It assumes, in other words, that assistive technology--serving as a sort of facilitated communication--can unlock the potential of most students with special needs.

Yes, assistive technology can provide enlarged screens to visually impaired students, screen readers to blind students, keyboards to students with impairments in fine motor control, and speech-to-text to deaf students. It's great, in other words, in providing access to children whose brains are basically neurotypical inside. But no assistive technology can make Shakespeare (required under Common Core English Standards) accessible to those students with the deep impairments in linguistic comprehension that characterize many otherwise high functioning individuals with autism.

The notion that most kids can be accommodated to fit one-size-fits-all standards, then, is yet another downside to those miraculous, "normal child locked inside" stories of autism. Yes, they may keep people from giving up on kids prematurely. But they raise false hopes, they deter appropriate therapies, and they support the strangleholds of the Common Core Standards.

Thursday, June 23, 2016

Math problems of the week: Common Core-inspired explanations requirements

From PARCC's Guide to Mathematics Released Items: Understanding Scoring:

From the Common Core Standards' Myths vs. Facts page:

Extra Credit:

Explain whether the above is a myth or a fact. In your explanation, you must use the time line of math education history--and, in the course of this time line, consider the use of the number line in lessons on multiplying fractions.

Monday, June 20, 2016

Autism diaries: taking responsibility

J has just entered his third decade, and things are looking a lot better than they were at the beginning of his second.

He's just finished up his first year of college and, incentivized by ceiling fans for B averages, he has done OK. The first semester he only managed to make it look like he'd gotten a B average--by dropping the classes he was failing and somehow doctoring the display of his grades on our local computer. The second semester he actually managed a B average, but only after going on a reduced schedule and then dropping his English class. (We still have to sort out the English requirement with the Office of Disability Services).

The third semester he also managed a B average (each time it's been down to the second decimal place). This time he did it without dropping any classes, but with only computer science and math on his roster. His math classes--where all the assignments and logistics were totally straightforward--went fine. His computer science classes--where both the directions and the turning-in process weren't so straightforward--were more problematic. In fact, he was all ready to drop one of them because he was in danger of a D or worse, but I insisted that he turn things around this time or no fans. And he did--entirely on his own.

In fact, the thing that impresses me the most about J's college experience is how well he's handling things independently. Except for the verbal challenges of complicated directions, and the social challenges of working in groups, he's managing quite well. He's finding his way around campus, getting to classes on time, checking in with professors about uncertainties, and taking pictures on his iPhone of important, ad hoc whiteboard announcements. Organization and transitions are commonly ranked among the top challenges for students with ASD. Not so for J.

For J, the issues are social and linguistic. But his language and social skills continue to grow. While I'm not sure what exactly goes on socially at school--except that he eats lunch in the cafeteria and attends a weekly chess club--he recently passed a milestone with me. He still lives at home, and in many ways our dynamic hasn't changed: I caught him in the act of lying in bed rather than cleaning up his room, which he had claimed he was doing. He immediately stated that he was starting with the things on his floor that were within reach of his bed. "Yeah, right" was my reply.

A common refrain about children on the spectrum is that they are literal minded and don't get irony. But J has heard "yeah, right" often enough from me that he has--for quite a while now--totally gotten my drift. What was different this time was that he made it clear that he actually cared--a lot--about whether I believed him. Even though he was facing no consequence for not cleaning up his room or for lying about it, he was so upset at my skepticism that he followed me around the house insisting that he really was cleaning up his room and trying to get me to convince him that he'd convinced me that he really was cleaning up his room from his bed.

Another milestone: J was recently called up for Jury Duty. They must have gotten his name off the voter roles: J (luckily) has no interest in driving, but he eagerly registered to vote two years ago when a form arrived in the mail the month he turned 18. The Jury Duty milestone had several remarkable features. First, the report date was actually convenient: two days after J's last final. Second, he was so eager to be picked that he showered and shaved more thoroughly than he had in a very long time. Third, I wasn't in a panic about how it would go: I gave him a few basic guidelines, two trolley tokens, and lunch money, and assumed it would all work out.

As it turns out, all he did was sit in a room for 6 hours--with a lunch break in between--and then collected a $9 check. But it was all pretty miraculous nonetheless.

After all, this was the same kid who was deemed by evaluators at a highly reputed autism center to be so highly impaired that only life skills classes were appropriate; and who, until just a few years ago, depended on one-on one-support to make it through his school days without getting into fights or disrupting or dozing through classes.

Friday, June 17, 2016

Math problem of the week: Common Core-inspired guidelines for explained answers

From EngageNY's released test items and scoring guidelines for the New York State's math assessment for 8th grade:

Extra Credit:
Is the 4th responder being held to a higher standard than the other responders?

Monday, June 13, 2016

What is really going on in our most segregated schools?

In our discussions of bathroom accessibility and micro-agressions and trigger warnings and privilege checking and the nuances of affirmative consent, we're neglecting some serious issues. One of these is the continuing segregation of our schools, which is arguably more pernicious than ever: a segregation in which our urban school districts are offering disadvantaged students what, in many cases, is a far worse education than ever before.

Because our public schools aren't really public, as in open to the public, it's hard for outsiders to get a close look at the classroom instruction that occurs (or fails to occur) in the schools into which our most disadvantaged urban students are segregated. Mostly what we hear about has to do with the dire physical conditions of the buildings, or the lack of librarians, nurses, and college counselors, or the shortage of basic supplies like paper and toilet paper. 

But every once in a while one hears an alarming eye witness report about what's actually going on in classrooms. And what one hears is far worse than a lack of music, art, or AP curricula. Consider high school math classes that consist of teachers showing students the different functions of the keys on a calculator; teachers who don't bother assigning homework because they're certain students won't do it; teachers who have given up on their students and essentially just babysit them; burned out principals who avoid hiring good teachers because good teachers might make them look bad (I know several great teachers who would love to teach disadvantaged students but have been turned away or discouraged by terrible principals). Not to mention: students who sit imprisoned for weeks or months in teacherless rooms thanks to shortages of "certified" teachers and substitutes. 

So it was refreshing to see the New York Times Magazine run an article this past weekend highlighting the continued segregation of the New York City schools. In this article, Nikole Hannah-Jones contrasts the general conditions of most of the city schools into which disadvantaged students are segregated with one which has managed to flourish:
P.S. 307’s attendance zone was drawn snugly around seven of the 10 buildings that make up the Farragut Houses, a public-housing project with 3,200 residents across from the Brooklyn Navy Yard. The school’s population was 91 percent black and Latino. Nine of 10 students met federal poverty standards.
Hannah-Jones credits P.S. 307's success to its principal, Roberta Davenport, who has, among other things, obtained money from a federal magnet grant that funds a science, engineering and technology program.

But she also credits Davenport with some other things that I find problematic:
she rejected the spare educational orthodoxy often reserved for poor black and brown children that strips away everything that makes school joyous in order to focus solely on improving test scores. These children from the projects learned Mandarin, took violin lessons and played chess.
Focusing solely on improving test scores vs. making learning joyous with extra subjects like music and foreign language is a false dichotomy that assumes no middle ground. Reading, writing, and math, taught well, are fun; Mandarin and violin, taught properly, can be grueling. Producing a decent enough violin sound to make music joyous; learning the Mandarin tones and characters well enough to make communication meaningful: these things demand extensive drill and practice.

Plus, as things currently stand, the pressure to improve test scores is one of the only disincentives we have against those teacher-free/teacher-as-babysitter classrooms that predominate more than ever in the most segregated of our urban schools.

Friday, June 10, 2016

Math problems of the week: Common Core-inspired answer explanations guidelines

From EngageNY's released test items and scoring guidelines for the New York State's math assessment for 5th grade:

Extra Credit:

Do the above "does not sufficiently explain" (sample 1) and "summation is not shown" (sample 2) demonstrate only "partial understanding of the mathematical concepts in the task"?

Wednesday, June 8, 2016

Follow up newsflash: another thing that matters is how rational you are!

In a recent post, I argued that our obsession with the shortcomings of IQ and other aptitude tests and our infatuation with "non-cognitive" skills ("grit", "emotional intelligence," "leadership") has us forgetting a number of cognitive skills: cognitive skills that aren’t measured by IQ and other aptitude tests, but that nonetheless factor into intelligence. These include:

--attention and observation: how much of the world around you do you sponge up?

--curiosity: do you notice what you don’t know and care enough to seek answers—asking, listening, reading widely and in depth?

--your patterns of reflecting later on what you learned earlier (regular recall and reflection promotes long term memory)

--the breadth of topics your mind ranges over: does it brood on a narrow range of fixed topics or does it wander widely and to new places?

--the breadth of new connections—logical, analogical, relational—that your mind makes among the things it ranges over.

All these factors feed into phenomena we clearly appreciate, in real life, as part of intelligence: the volume, organization, and connectedness of the facts someone knows, or how interesting, astute, and/or creative their questions, observations, and ideas are.

But I left out one big cognitive factor that also isn't measured by IQ: rationality. Discussed at length in the works of psychologist Keith Stanovich (I'm indebted to a fellow-linguist for alerting me to this research!), it includes the tendency to think a lot; to think, before acting, about the consequences of one’s actions; to be open-minded and objective; to eschew superstition and dogma; and to consider multiple perspectives, pros and cons, and nuance. It's also a function of certain types of knowledge: e.g.,  knowledge of statistics and scientific reasoning; awareness of the various common logical fallacies and self-serving biases to avoid.

As Stanovich notes in his chapter on Intelligence and Rationality (for the Cambridge handbook of intelligence):

Critics of intelligence tests are eager to point out that the tests ignore important parts of mental life—many largely noncognitive domains such as socioemotional abilities, empathy, and interpersonal skills, for example. However, a tacit assumption in such critiques is that although intelligence tests miss certain key noncognitive areas, they do encompass much of what is important in the cognitive domain.
But, though people often "define intelligence in ways that encompass rational action and belief," intelligence tests are “radically incomplete as measures of cognitive functioning” and completely neglect rationality.

Nor does rationality simply capture how much you resemble Mr. Spock. Rationality is a major determinant of whether people set reasonable goals and make reasonable decisions and judgments, and so is integrally connected with their happiness--and with that of those around them.

Stanovich makes a good case for the teachability of certain sub-skills of rationality--a much better case, indeed, that others have made for the teachability of non-cognitive skills. Stanovich also lays out a number of specific proposals about how one might go about teaching these skills.

But are schools likely to listen? Why should they? After all, it's so much easier to pretend to teach non-cognitive skills than it is to actually teach cognitive ones.

Saturday, June 4, 2016

Cold War Calculus vs. 21st Century Linear Algebra

I've been mulling on and off over a two-month old Wall Street Journal Op-Ed entitled Calculus Is So Last Century. The Op-Ed, co-authored by a data science firm CEO and a computer science professor, argues that Calculus is mainly useful for Cold War-era careers in physics that are now eclipsed by 21st Century careers in bio- and information-technology:

Calculus is the handmaiden of physics; it was invented by Newton to explain planetary and projectile motion. While its place at the core of math education may have made sense for Cold War adversaries engaged in a missile and space race, Minute-Man and Apollo no longer occupy the same prominent role in national security and continued prosperity that they once did.
The future of 21st-century America lies in fields like biotechnology and information technology, and these fields require very different math—the kinds designed to handle the vast amounts of data we generate each day. Each individual’s genome contains more than three billion base pairs and a quarter of a million genomes are sequenced every year. In Silicon Valley, computers store over 100 GBs of data—more information than contained in the ancient library at Alexandria—for every man, woman and child on the planet.

Accompanying the proliferation of new data is noise, and a major job for data analysts and scientists is to tease out true signal from coincidence and noise. Knowing when a result is due to chance versus when it is statistically significant requires a firm grasp of probability and statistics and an advanced understanding of mathematics.

We no longer think of outcomes as being triggered by a single factor but multiple ones—possibly thousands. To understand these large and complex data sets, we need an educated workforce that is also equipped with a firm understanding of multivariate mathematics and linear algebra. 
It had never occurred to me that the only useful applications of calculus were in missile technology and rocket science. So last weekend I checked with Uncle M, who is both a mathematician and an academic dean at a major university--and someone who has spent many hours engaged with issues relating to required courses and prerequisites. What did he think about this proposal?

Not much. Economics, engineering, and mathematical statistics, he pointed out, also require knowledge of calculus. Indeed, my oldest son, who just received a bachelor's in mechanical engineering, reports that differential equations--and not linear algebra--were crucial to his course of study.

Plus, Uncle M points out, calculus is a lot more challenging than the kind of applied linear algebra favored by the authors. They aren't explicit about this, but there's linear algebra, and then there's linear algebra. There's an abstract variety, taught by algebraists, in which one operates in n-dimensional space with complex numbers and proves theorems about domains, ranges, kernels, vectors, and eigenvalues. And there's an applied variety, often taught outside mathematics departments, in which one works with matrices populated with actual numbers and applies these to real-life situations. The two varieties are really completely different subjects. Abstract linear algebra, in my experience, is really tough: riddled with mind-bending abstractions and impossible to visualize. In comparison, applied linear algebra is a piece of cake. It's also easy compared with calculus. And the same is true of applied statistics.

They're not explicit about this, but it's applied linear algebra and applied statistics that our data science CEO and computer science professor are advocating for.

Since calculus is harder, argues Uncle M, it makes sense to introduce it gradually, starting in high school. Not doing so burns bridges--bridges to math, physics (which still exists), mathematical statistics (as opposed to applied statistics), engineering, and economics. It's far less clear that continuing to mostly not teach linear algebra in high school burns any bridges.

Finally, Uncle M observes, there is currently a glut of unemployed biologists. Maybe there are tons of jobs in biotechnology, but not enough for the biology majors. Career-wise, engineering (supported by Diffy Qs) continues to be the more promising field.

Naturally, few pieces about math education can resist claiming that part of the problem is rote learning:
Computers and computation are ubiquitous and everyone—not just software engineers—needs to learn how to think algorithmically. Yet the typical calculus curriculum’s emphasis on differentiation and integration rules leaves U.S. students ill-equipped at posing the questions that lead to innovations in computation. Instead, it leaves them well-equipped at performing rote computations that can be easily done by a computer.
Perhaps the authors mostly experienced calculus as a bunch of rules about differentiation and integration, but good textbooks and good teachers show otherwise. Indeed, even the authors say:
Calculus, like any rigorous technical discipline, is great mental training. We would love for everyone to take it. 
It's just that:
the singular drive toward calculus in high school and college displaces other topics more important for today’s economy and society. Statistics, linear algebra and algorithmic thinking are not just useful for data scientists in Silicon Valley or researchers for the Human Genome Project. They are becoming vital to the way we think about manufacturing, finance, public health, politics and even journalism.
Even journalism? That seems like a bit of a stretch: