Wednesday, September 29, 2010

The humanely arranged classroom

When I entered my daughter's classroom at back-to-school night the other week, I almost wept with joy. The desks were arranged.... in rows facing the teacher. No wonder my daughter, for the first time ever, was retaining her teacher's words and reporting to me what she'd learned from her. Finally she had a teacher up in front, easy to see and hear. Why did she, along with various other highly distractible classmates, have to wait until 4th grade for this?


When I saw those desks in rows, what moved me was a sense of humaneness. This was a classroom that takes education seriously; one in which the teacher views teaching as her top priority, and herself, not her students, as the one ultimately responsible for ensuring that everyone learns--in spite of all those education fads that dictate otherwise.

Here's what Teach Like a Champion, Doug Lemov's marvelous survey of highly effective teachers, has to say about classroom seating:
Teachers in many classrooms seat their students in pods of desks that face each other because they believe that students should be socialized to interact in school. This is a general (in fact overgeneralized) belief about the nature and philosophy of schooling. With the exception of the fact that some teachers realign desks for tests, this classroom layout often doesn't change even if critical parts of the class period involve, say, taking notes on what the teacher writes on the board. This often erodes outcomes. Though students should interact in school, the time when they are supposed to be constructing a record of key information in writing may not really be the time for that. And with desks in pods, some percentage of the students must now look over their shoulders to see the information they are accountable for and then swivel to write it down in front of them. Furthermore, students must ignore the student directly across from them to attend to the teacher behind their desk. If the teacher's goal is to be attended to for much of the lesson, she has created a strong disincentive for that. The classroom layout has made the primary lesson objective harder to accomplish in deference to philosophy.
All the more so when distractible, pod-seated students receive low grades on tests (or "authentic assessments") based on material covered only in class, a common occurrence in our textbook-eschewing primary schools.

Monday, September 27, 2010

Does the logical pursuit of clear answers lead to terrorism?

Or, more precisely, to a disdain for ambiguity and compromise that, in turn, leads to terrorism?

At least among engineers?


So concludes a study by sociologists Diego Gambetta and Steffen Hertog as reported in Slate, and, more recently, the New York Times Magazine. Examining more than 400 radical Islamic terrorists from more than 30 nations in the Middle East and Africa, Gambetta and Hertog found engineers three to four times more likely to become violent terrorists than doctors, scientists and financiers. "The next most radicalizing graduate degree, in a distant second," writes Slate reporter Benjamin Popper, was Islamic Studies."

Reportedly teasing out the effects of engineers being particularly well-qualified to become terrorists,
Gambetta and Hertog write about a particular mind-set among engineers that disdains ambiguity and compromise. They might be more passionate about bringing order to their society and see the rigid, religious law put forward in radical Islam as the best way of achieving those goals.
As the Times Magazine reports, their conclusions apply to right-wing groups in general: 
Gambetta and Hertog found engineers only in right-wing groups — the ones that claim to fight for the pious past of Islamic fundamentalists or the white-supremacy America of the Aryan Nations (founder: Richard Butler, engineer) or the minimal pre-modern U.S. government that Stack and Bedell extolled.

Among Communists, anarchists and other groups whose shining ideal lies in the future, the researchers found almost no engineers. Yet these organizations mastered the same technical skills as the right-wingers. Between 1970 and 1978, for instance, the Baader-Meinhof gang in Germany staged kidnappings, assassinations, bank robberies and bombings. Seventeen of its members had college or graduate degrees, mostly in law or the humanities. Not one studied engineering.
The Times Magazine sums up Gambetta and Hertog's conclusions as follows:
The engineer mind-set... might be a mix of emotional conservatism and intellectual habits that prefers clear answers to ambiguous questions — “the combination of a sharp mind with a loyal acceptance of authority.” 
As for the direction of causality:
Do people become engineers because they are this way? Or does engineering work shape them? It’s probably a feedback loop of both, Gambetta says.
Either way, according to Slate:
Terrorist organizations seem to have recognized this proclivity... A 2005 report from British intelligence noted that Islamic extremists were frequenting college campuses, looking for "inquisitive" students who might be susceptible to their message. In particular, the report noted, they targeted engineers.
At least two engineers have raised questions about this study. As the Times Magazine article reports:
William A. Wulf, a former president of the National Academy of Engineering, is, no surprise, no fan of the Gambetta-Hertog theory... The sample of militants Gambetta and Hertog used was simply too small for them to be sure they haven’t stumbled into a meaningless numerical accident, he says. The theory, according to Wulf, misrepresents what engineers are about. “A person who is rigid,” he says, “is a bad engineer.”
And in a letter published in this week's Times Magazine, Julio M. Ottino, Dean of the Robert R. McCormick School of Engineering and Applied Science, writes:
Most leading universities in the U.S. are cultivating thinking skills completely opposite to what they state as a preference for “clear answers to ambiguous questions.” The goal of my own school — and I know that we are not alone in this — is to produce whole-brain thinkers. We want to produce engineers who are firmly grounded in analysis, logic and rational thinking but who also have intuitive and metaphorical thinking skills — the kind that open up new avenues of thought.
This last remark leads my clear-answer-seeking mind to the following question: Is intuition really less likely to lead to radical beliefs than the logical pursuit of clear answers is?

Saturday, September 25, 2010

Barry Garelick on traditional vs. modern math instruction

Coalition for World Class Mathematics co-founder Barry Garelick attempted, twice, to post the following comment in response to this week's Problems of the Week comparison. Apparently, it's too long for Blogger Comments. However, it's such a great comment that I'm delighted to be posting it as today's post. Here is Barry Garelick:


This discussion of CPM reminds me of a similarly atrocious math program called IMP. IMP is an “integrated” math program that spans the four years of high school. It was funded by NSF in a grant totaling $11.6 million to San Francisco State University in the early 90’s.  Sherry Fraser, a co-directof of IMP made a public statement on November 6, 2006 before the National Mathematics Advisory Panel, a Presidential appointed panel charged with drafting recommendations on how best to prepare students. The opening lines of her statement were as follows:
How many of you remember your high school algebra? Close your eyes and
imagine your algebra class. Do you see students sitting in rows, listening to a
teacher at the front of the room, writing on the chalkboard and demonstrating
how to solve problems? Do you remember how boring and mindless it was?
Research has shown this type of instruction to be largely ineffective. Too many
mathematics classes have not prepared students to use mathematics, to be real
problem-solvers, both in the math classroom and beyond as critical analyzers of
their world.
I wrote to Ms. Fraser explaining that I was writing an article on math instruction that prevailed in the 40's through the 60's. I asked if she would provide me the cites of the research that she claimed shows this type of instruction to be ineffective. Her reply was as follows:
I'm a firm believer in people doing their own research. I'm sure you won't have any trouble finding a number of sources to confirm this. I certainly didn't. I'd be interested in reading your paper when you've completed it. I'm familiar with math instruction in the 1950's and 60's but am now wondering whether the world war during the 40's had any impact on math instruction in that decade.
Well, I took her advice and did my own research and the result is a three part article found here:

An Exploration of Traditional Math, Part III

The file has become corrupted in parts due to technical glitches but it is mostly readable. The comments from readers are readable as well and are also informative on their own. Interestingly, math scores on the Iowa Tests of Basic Skills in the State of Iowa steadily increased from the 40’s through the mid-60’s in the lower grades, when it hit a decline and didn’t recover until the 80’s: a pattern seen not only in Iowa. That the decline was seen in lower grades takes away the usual explanation offered for the decline in SAT scores during the same time period that the population of people taking the SAT had grown to include minorities who had not been in the college pool before. And the changing demographics argument which is offered to explain the decline in test scores in lower grades doesn’t explain Iowa’s, since the shift in white population decreased from 99% in the 40’s to 97% in the 60’s. What did change in that time period was an increase in the edu-fads that are today very commonplace: student-centered classrooms, inquiry based instruction and a move away from drills and mastery of procedural knowledge.

Thursday, September 23, 2010

Math problems of the week: Traditional algebra vs. CPM Algebra

I. From the first and last assignments of the first chapter ("Definitions and Notation") of Wentworth's New School Algebra text (published in 1898), p. 9 and p. 14:

If a = 1, b = 2, c = 3, d = 4, x = 5, y = 6, z = 0, find the numerical value of:

1. 15x
2. 3ab
3. 7by
4. 5bd
5. 9y2
...

Perform the indicated operations, and find the numerical value of each expression, if a = 8, b = 4, c = 3:

1. (b + c) ÷ c
2. (a + b) ÷ b
...
10. (b2 - c2) ÷ b
11. (a2 - c2) ÷ c2
12. (a2 - b2) ÷ b2

II. The first and last assignments of the first chapter ("Getting Started: Working in Teams") of the College Preparatory Mathematics Algebra text, p. 4 and p. 17:

With your team, find at least three of the main ideas the authors wanted you to know about this course. You can find these ideas in the "Welcome Note" you just read. Make a list of them. Be sure that you put a copy in your algebra notebook.

Reflect on the study team activities you experienced the last few days. Which activities were your favorites? Why? What about your team makes you feel comfortable? What makes an effective team member?

III. Extra Credit:

Which problems better prepare students for 21st century mathematics?

Tuesday, September 21, 2010

"Scientifically tested tests"

In her latest New York Times Op-Ed piece on what's wrong in education (her third since February), Susan Engel faults No Child Left Behind testing for measuring the wrong things and failing to help schools improve.

Many, myself included, have specific concerns about the NCLB tests: they set too low a bar and too low a ceiling, dumbing down the classroom curriculum; sometimes, correct but unexplained answers to math problems get only partial credit, as do incorrect but explained answers; the tests aren't used to help teachers adjust to the immediate needs of particular students, or to help particular students and their parents know what they need to work on, in the course of a particular school year. 

But Engel dislikes multiple choice, fact-based tests in general:
There are few indications that the multiple-choice format of a typical test, in which students are quizzed on the specific formulas and bits of information they have memorized that year, actually measures what we need to know about children’s education.
Well, that depends on what your opinion is about "what we need to know about children's education."

For Engel, it seems, the priorities are the "higher level" thinking skills that, in Engel's words, are "the qualities of well-educated children":
The ability to understand what they read; an interest in using books to gain knowledge; the capacity to know when a problem calls for mathematics and quantification; the agility to move from concrete examples to abstract principles and back again; the ability to think about a situation in several different ways; and a dynamic working knowledge of the society in which they live.
As for science, Engel mentions understanding the concept of "controlling variables."

Completely absent from Engel's proposals is content knowledge--unless "dynamic working knowledge of the society in which they live" includes things like world geography, American history, and current events in Pakistan. This, despite the fact that the latest cognitive science research indicates that "higher level" skills neither develop, nor apply, independently of structured, information-rich content. 

Also absent are such specific skills as penmanship, decoding, sentence construction, foreign language fluency, balancing chemical equations, and finding the roots to quadratic equations. 

Specific skills; rich, structured, factual knowledge: these are things a decent multiple choice test could assess, assuming you cared about them.

Then there are the specific skills Engel proposes tests should assess. However important these skills may be, it's highly questionable whether they (unlike, say, geography and quadratic equations) can actually be taught by classroom teachers.

For example, Engel proposes randomly sampling student writing to measure vocabulary and grammatical complexity. But as every linguist knows, general vocabulary (as opposed to specific vocabulary words taught in the classroom) and, even more so, grammatical complexity are developmental skills, not academic ones. Neurologically typical native speakers increase their general vocabulary sizes and their grammatical complexity through a combination of incidental exposure and brain development. Neither regular classroom teachers, nor standard curriculum packages, do much to address these skills, and, to the extent that they do, they have very little effect on them.

The same goes for perspective taking skills. Engel suggests having children “Write a description of yourself from your mother’s point of view" in order to "gauge the child’s ability to understand the perspectives of others." Again, it's not clear what purpose this assessment serves--beyond identifying who is and who isn't on the autistic spectrum.

Similarly problematic is Engel's proposal to measure reading comprehension levels by having children do an oral reconstruction of a story to a "trained examiner." What about shy children; what about children were struggle to express themselves orally?  How does this testing not penalize them and their teachers for circumstances beyond their control?

Then there's the cultural bias we see in Engel's proposal to measure literacy levels by "testing a child's ability to identify the names of actual authors amid the names of non-authors." Unless these authors come from some sort of core curriculum--something that Engel does not support--how does this testing not penalize socio-economically disadvantaged children and/or those who teach them?

While there are lots of problems with NCBL testing, there are decent ways to test children that help teachers teach better and children learn more. Unfortunately, Engel's proposals lead us in the opposite direction.

Sunday, September 19, 2010

Today's grades

A = Substantially exceeds the standard
B = Meets the standard
C = Making progress toward the standard
D = Making less than acceptable progress toward the standard.
F = Does not meet the standard.

(Or so I'm sold by last week's back-to-school night hand-out.)

Our school district does not give out plusses and minuses, so there's no need to define A- or B+.

And yet... Besides the sinister, Orwellian overtones of "the standard", there's the unexplained overlap between D and F and the large gap between A and B.  

So here are my questions: 

1. Does someone who is considered to exceed the standard but not "substantially" receive an A or a B?
2. How can someone be identified as "substantially" exceeding the standard when most assignments and tests don't measure skills that exceed the standard?
3. How does the system ensure that subjective teacher judgments don't determine whether a standards-exceeding but not obviously "substantially" exceeding student gets an A or a B?
   

Friday, September 17, 2010

Math problems of the week: 5th grade Trailblazers vs. Singapore Math

I. From the final word problems in the "Adding and Subtracting Fractions" chapter of the 5th grade Math Trailblazers Student Guide, p. 184:


Shannon's mother spends 1/3 of her monthly salary on rent (which includes heat). Groceries for the month and her car payment add up to about 2/5 of her salary.

A. Do these bills account for about 1/2 of her salary, more than 1/2 of her salary, or all of her salary (1 whole salary)?

B. What fraction of her salary is spent after paying for rent, groceries and her car?

II. From the final word problems in the "Fractions" chapter of the 5th grade Singapore Math Primary Mathematics 5A workbook, p. 75:

Larry spent 1/2 of his his money on a camera and another 1/8 on a radio. The camera cost $120 more than the radio. How much money did he have at first?

III. Extra Credit:

A. In which problem set does a greater fraction of the challenge involve mathematical reasoning, and in which problem set does a greater fraction of the challenge involve reading comprehension?

B. Which skill is "higher level": mathematical reasoning, or reading comprehension?

Tuesday, September 14, 2010

Is there a left-brain learning style?

Several people who called my attention to last week's New York Times science section article did so because of what it says about left-brain learning styles: 

Take the notion that children have specific learning styles, that some are “visual learners” and others are auditory; some are “left-brain” students, others “right-brain.” In a recent review of the relevant research, published in the journal Psychological Science in the Public Interest, a team of psychologists found almost zero support for such ideas. “The contrast between the enormous popularity of the learning-styles approach within education and the lack of credible evidence for its utility is, in our opinion, striking and disturbing,” the researchers concluded.
 
Because my book is one whose title, "Raising a Left-Brain Child," strongly suggests that there is a left-brain learning style, I have followed this question closely.  What does the cognitive science research mean for the conclusions I draw in my book?

To answer this, let's turn to Dan Willingham, an increasingly prominent debunker of learning styles theory whose recent book, Why Children Don't Like School, has received a great deal of attention, and who now writes a frequent column for the Washington Post.

Willingham argues that for something to be a "learning style" in any meaningful sense, it can't simply be a difference in abilit(ies).  If someone is more "visual" than someone else only in the sense that they are better at remembering what things look like, creating visual representations, and rotating three dimensional objects in their heads, then that's not a learning style difference. For "visual" to be a learning style, your "visual students" would have to be, on average, as capable of learning reading, writing and arithmetics, etc., as their "non-visual" counterparts, but learn these skills better than other students do when they learn them through visual channels.  And Willingham shows quite convincingly that the experimental evidence contradicts this notion.

What about left-brain?  The protagonists of my book are children who are some combination of unsocial (shy, aloof, and/or social awkward), analytical (good at math, grammar, science, analytical writing), and linear/one-thing-at-a-time in their thinking (better at focusing on one thing in depth than many things in breadth). These traits largely reflect cognitive strengths and weaknesses, and, to some extent, personal preferences, and so, in these respects, don't constitute learning styles.  Luckily, that doesn't matter for any of the conclusions I draw in my book.

But I have wondered whether one vs. many things-at-a-time, in particular, might possibly be a learning style difference.  Personal and anecdotal experience suggests to me that different people are able to handle different amounts of simultaneously streaming information; that some people can keep track of more information at a given time than others can; that, at the extreme, you get "linear thinkers" who can only tune into one conversation at a time, and only handle one task at a time (I count myself among them). And, while this narrow bandwidth might be considered a disability, it seems to me (based again on personal and anecdotal experience) correlated with an ability to process things in greater depth.

In other words, might breadth vs. depth in information intake and information processing be a tradeoff, with different people achieving similar results depending on whether the material is presented in a breadth-first or depth-first way?  Broad bandwidth people, for example, might learn literary analysis better through large group discussions, while one-on-one discussions work better for their narrow-bandwidth counterparts.  Likewise, broad bandwidth people might learn and remember history better through a broad, thematic approach, while their narrow-bandwidth counterparts learn and remember it better through a more depth-first linear approach--even if the same material is ultimately covered.  

Much about learning styles has been debunked, but, to my knowledge, no one has debunked the idea of varying band-width, however much it might reflect abilities and preferences, also having an effect on optimal learning environments.

Monday, September 13, 2010

Is it bad to give children frequent tests?

Two recent New York Times articles fly in the face of conventional pop psychology and educational philosophy.


An article in last week's Science Section on study habits cites cognitive science research indicating that the act of taking a test can enhance learning:
The process of retrieving an idea is not like pulling a book from a shelf; it seems to fundamentally alter the way the information is subsequently stored, making it far more accessible in the future.
As Henry L. Roediger III, a psychologist at Washington University in St. Louis puts it, “Testing not only measures knowledge but changes it.” 

Next we have a front page article in this weekend's Week in Review on Testing, the Chinese Way, written by Elisabeth Rosenthal, whose children spent a year at the International School of Beijing where "taking tests was as much a part of the rhythm of their school day as recess or listening to stories." Citing personal experience, Rosenthal argues that:

>Young children aren't necessarily aware that they are being "tested."

>Frequent tests give children important feedback about how they are doing.

>Frequent tests offer a more meaningful way to improve self-esteem than frequent praise does.

On this past point, Rosenthal cites Gregory J. Cizek, a professor of educational measurement and evaluation at the University of North Carolina at Chapel Hill:
Professor Cizek, who started his career as a second-grade teacher, said the prevailing philosophy of offering young children unconditional praise and support was probably not the best prescription for successful education. “What’s best for kids is frequent testing, where even if they do badly, they can get help and improve and have the satisfaction of doing better."
Cizek's overall take on testing in schools? “Research has long shown that more frequent testing is beneficial to kids, but educators have resisted this finding:”

Rosenthal concludes on a particularly powerful note:
When testing is commonplace and the teachers are supportive — as my children’s were, for the most part — the tests felt like so many puzzles; not so much a judgment on your being, but an interesting challenge. It is a testament to the International School of Beijing — or to the malleability of childhood memory — that Andrew now says he did not realize that he was being tested. Will tests be like that in a national program, like Race to the Top?

When we moved back to New York City, my children, then 9 and 11, started at a progressive school with no real tests, no grades, not even auditions for the annual school musical. They didn’t last long. It turned out they had come to like the feedback of testing.

“How do I know if I get what’s going on in math class?” my daughter asked with obvious discomfort after a month. Primed with Beijing test-taking experience, they each soon tested into New York City’s academic public schools — where they have had tests aplenty and (probably not surprisingly) a high proportion of Asian classmates.

Saturday, September 11, 2010

Is it bad be quiet in class?

In the title of her recenly-published article in the Chronicle of Higher Education, Mary Reda asks a refreshing question: "What's the Problem With Quiet Students? Anyone? Anyone?" After conducting "a yearlong study of a first-year composition class in which students periodically wrote about their experiences of classroom silence, followed by a series of interviews with five students who self-identified as 'quiet,'" Redy discovered that, beyond boredom and lack of preparedness:

The overwhelming majority of the students in my study understand speaking in class to be a high-stakes testing situation in which they are expected to provide a right answer. The more pressure a professor creates through grading class participation, the more complicated it becomes for students to speak. By observing an instructor—how she interacts with the class, the kinds of questions she asks, and how she responds to their voices—they determine whether they are expected, in general, to reflect, speculate, and hypothesize aloud or to perform on an oral quiz.
Redy finds that "choosing silence" is also associated with certain types of of personalities and backgrounds:
Some students choose silence because it best fits their learning style, culture, or history. Much contemporary pedagogy lauds the calls for "student voice" as empowering. But students who are, for example, visual learners, or whose home cultures have taught them to value speaking and silence differently than the contemporary culture of American higher education does, often benefit from the inclusion of silence in the curriculum.

Some students are quiet because they are listening to others' views to integrate them into their own perspectives. Speech and contemplation may not happen simultaneously; those who don't come to the classroom already skilled in academic discourse need time and space to "translate" their thinking.
Redy's takeaway?
I have stopped automatically assuming that the silences in my classroom necessarily indicate failure. I work harder to communicate with my students about my expectations and theirs, particularly since for many students, my student-centered, dialogical classroom is the exception, not the rule, and the kinds of discussions—and silences—I invite may challenge what they think a classroom should look like
I now make time for occasional silence in my classes by assigning in-class writing and building deliberate pauses for reflection into our discussions. 
Redy's newfound wisdom, particularly if it spreads to others, is good news for the many "left-brainers" who find discussions difficult to contribute to--whether they are shy, socially awkward, or simply have trouble following the discussion closely enough to know exactly when to jump in.  As one commenter puts it:
I was extremely quiet all through my undergrad years and into graduate school. My professors unanimously agreed that I "needed to participate in class more often." I was quiet not so much because I was shy (though that was true during my first couple of years of college) but because I'm an introvert, and I need time to think before I put my ideas out there. I don't "think out loud"; my brain just doesn't work that way. The problem with a lot of class discussion is that it moves so fast that by the time someone like me is ready to chime in, the rest of the class has moved on to the next topic. That's not the only reason students don't talk, but I don't think my experience is at all unique.

I don't think I even realized all of that until I started teaching and had to confront student silence from the other side. One of the things I learned to do was to periodically ask the students to stop, reflect, and write down a few sentences about whatever topic we were discussing, and then share them out loud. It seemed to help turn classroom silence from something awkward and empty into something productive.
Another commenter was less sympathetic:
Shouldn't education be partially to facilitate students' maturity and comfort participating and contributing? Wouldn't the other students benefit from hearing a wider range of points of view? And wouldn't class discussions be more interesting with more participants?
Yet another commenter offered yet another reason for student silence: some students prefer the expertise of their professors to the inexperience of their classmates.  They keep silent and silently hope that their peers will, too.  

This last comment brought back memories from grad school. One of my classes lost two full weeks of content to two students who enjoyed the sounds of their own voices. My friend and I took to putting down our pens and sitting back in our seats until the professor finally returned to the syllabus.

Thursday, September 9, 2010

Math problems of the week: 4th grade Everyday Math vs. Singapore Math

I.The final two pages of the first of two 4th grade Everyday Math workbooks, Student Math Journal 1, pp. 186-186:




II. The final two pages of the first of two 4th grade Singapore Math workbooks, Primary Mathematics 4A, pp. 183-184:





III. Extra Credit
Are Everyday Math students better informed about other countries than Singapore Math students are?

Tuesday, September 7, 2010

Autism and abstract thinking

One of the assumptions commonly made by people who know, or think they know, something about autism is that autistic people tend to be concrete thinkers.  Since the high functioning autism population is full of mathematicians, engineers, computer scientists, and linguists, who reason in highly symbolic, abstract ways through highly abstract material, this assumption has baffled me.


When I teach classes on autism, I marvel at how frequently my students continue to make this assumption no matter how frequently I try to disabuse them of it.  As I consider the reasons why this happens, several thoughts come to mind:

1. For many people, abstraction is synonymous with fuzziness, flexibility, and open-endedness. Because autistic people tend to be rigid, ritualistic, precise, pendantic, and/or detail-focused, and because many of them don't do well when faced with open-ended questions or open-ended tasks assigned to them by other people, they do not look like abstract thinkers according to this misconception of "abstract." All too often, for example, people forget that the concept of "polygon" is no less abstract than the concept of "love."

2. Many people, especially in education, conflate logical inferencing with the sorts of inferencing that good readers engage in when making sense of a text.  As I've discussed in previous posts (here and here), many of today's assigned texts require the sorts of social inferences and and bridging inferences (integration of background knowledge) with which autistic children tend to struggle. These are not the same as inferring the contrapositive or doing a reductio ad absurdum.

3. Many people, as I discussed in a recent post, confuse labels with concepts and assume that a child who doesn't know the label for a given concept also doesn't understand the concept.  Many labels for abstract concepts and logical processes are difficult for autistic children to pick up on their own: they often require explicit vocabulary instruction that other children don't need. Unless and until they receive such instruction, many people will assume that they don't understand the underlying abstractions--e.g., that if he doesn't know the word "because," he doesn't understand causality.

Unfortunately, because so many people, in their confusion about what abstraction entails and how abstract concepts differ from linguistic labels, overestimate their own understanding of abstraction, they once again underestimate the capacities of great numbers of autistic children.

Sunday, September 5, 2010

Special Functions

The book is out!

Spread the word!

Friday, September 3, 2010

Math problems of the week: 2nd grade Investigations vs. Singapore Math

I. From a 2nd grade Investigations math homework sheet assigned 8/9 of the way into the school year:

II. From a multiplication assignment from the beginning of the second half of the 2nd grade Singapore Math curriculum:

III. Extra Credit

1. Should the child whose answers to the first problem set are recorded above be required to redo the problem with pictures of items repeated in 8 rows, 3 columns; 6 rows, 6 columns; and 7 rows, 4 columns? (Extra credit: how many pictures in total does that amount to?)


2. What about the Singapore Math students? Are they missing out on something by never being required, anywhere in the curriculum, to draw items repeated in rows and columns in order to "represent" multiplication?

Wednesday, September 1, 2010

Hard America, Soft America

Barry Garelick recently asked me a very thought-provoking question addressing what I've written about left-brainers and criticism:

In the conclusion chapter of your book, on p. 205, you make the point that compliments are favored over criticism, so students are really ill-prepared for the workforce ultimate, etc etc. Yet, on p. 115 of the book you make the point that left brainers get mediocre grades because they don't "participate" well nor do the "explanations" required, and so forth. Further, in that section of the book you talk about how in some areas, there is a grading system going from 1-4, and that no one gets "4's". This seems to contradict what you say later. There is criticism, some of it very harsh, both for the left brainers who can't play in the right brained world, and in grading systems for which the top grade is rarely, if ever, handed out. 

Perhaps the conclusion is that compliments are earned for doing superficial and non-academic, non-rigorous assignments, and that in some situations, criticism is so severe that everyone is ill-served.
Barry's question helped me significantly sharpen my question on this matter. So did a TV show I watched during one of my book tours. Here's how I responded to Barry:
I think part of what's going on is giving feedback vs. passing judgment. I most recently found this exemplified by a reality show I watched a couple of times along with some acquaintances during a mini-book tour. The show is So You Think You Can Dance, and the gimmick is that a group of young people each have to prepare and perform (individually) a bunch of different dances in different styles, and then have to stand on stage (here's where the voyeuristic element comes in) and listen to feedback from 3 different judges. Later even more drama ensues as all half dozen dancers stand on stage to find out which two of them are going to be eliminated before the next round. 

What struck me was how positive the feedback was--the judges (even the British one) seemed incapable of giving much in the way of criticism, and such criticism as there was was couched in so much positive that you barely noticed it. As a result, when they finally passed their judgment, regardless of who they eliminated, it was always a surprise, to all concerned. 

Not being a fan of reality competitions, I have no idea how common this protocol is, but it instantly struck me as emblematic of what happens in public schools. Tons of judgment (in highly choosy grades; in who gets to take violin lessons, in who gets gifted programming) but very little actual criticism--constructive or otherwise. And, yes, this makes the judgment all the harsher because you don't know the basis. On the other hand, when pushed by parents, teachers will insist that "a 3 is a good grade." (one reason I think they've moved from the standard letter grades to this less familiar number system--though parents now are catching on..) They also tell the kids that 3s are fine.

The second piece of the picture is that such criticism as does occur seems to me mostly not to target academic work, but behavior and social-emotional maturity. Here there in fact is a lot of criticism, as many teachers seem to mistake immaturity for willful disrespect and unkindness (which, in our zero-tolerance classrooms, seem to upstage the concerns about self-esteem that academic criticism raises). When I visited my daughter's kindergarten, I was astonished to hear this experienced and in many ways highly effective teacher call one boy out for turning away from his classmates towards the easel when explaining something to them: she felt he was being "disrespectful" by not facing his "friends" and speaking loud enough for them to hear him, when it seemed pretty clear to me he was just being a typical 5-year-old.

So in short I'd say we have highly hedged judgments instead of criticism, except when it comes to behavioral expectations.