Here we go again: more support for social and emotional classrooms

This time from David Brooks of The New York Times.

Citing statistics showing that "most people vastly overestimate the extent to which more money would improve our lives," Brooks concludes that "Most schools and colleges spend too much time preparing students for careers and not enough preparing them to make social decisions."

This conclusion betrays two fallacies:

1. The don't-make-educational-recommendations-without-visiting-actual-classrooms fallacy, which journalists and professors (especially education professors) repeatedly fall for (see here, here, here, here, and here).

2. The just-because-it-would-be-nice-if-students-learned-it-doesn't-mean-that-schools-can-actually-teach-it fallacy.

If David Brooks were to spend more time in grade schools, he would see that many schools actually shortchange material that would prepare students for careers in favor of activities designed to improve social skills.

And if he were to think about how one would go about teaching kids not to "overestimate the extent to which more money would improve our lives," he might consider how hard this is to teach, and that this is one area where experiential learning may be the only route to true understanding. 

Responses to comments on previous post

Something's up with blogger today, and my own comments are only occasionally appearing below, so I'm reposting them here.

To Barry Garelick:

Fascinating letters! Thanks for sharing them; there are several people I'd like to pass them on to.

To LexAquitas:
I hadn't consider the accountability angle on creativity and higher-level thinking. It also applies, I think, to "organizational skills."

To lgm:
Incredible story about reading level assessments. I've seen plenty of examples of this kind of Price is Right class participation affecting grades in general--but reading assessment???

To Beth:
I don't consider you the lone voice of dissent on this blog, and would be sorry to lose your voice here. 
I agree with you that kids need more free time for creativity. Indeed, that free time is the number one ingredient. Let's get rid of the homework in early grades, and let's have schools stop pretending that they can teach creativity, and pretending that it's ethical of them to grade students on creativity. They can't. It isn't.

I hope you didn't think I was presenting the Chinese system as the panacea for everything. Please reread me. However, since you bring up "my kids with autism," I will say that I imagine that high functioning kids like my son probably do better academically under the Chinese system than under the American one because of the emphasis on math and lack of mandatory group work in China. 

"In China, the group always trumps the individual."
This sounds like another one of those inaccurate stereotypes that Americans keep repeating about China. Chinese students can learn on their own; they are not forced into groups in the classroom. They are assessed as individuals, not as groups. I've taught in Hong Kong traveled extensively in China, and taught Chinese students here in the U.S., and while I do see some group effects in extracurricular socializing that are different from group effects in America, I never saw "the group always trumps the individual."

In the West "we celebrate the heroic individual who defies the group." 

I'd argue that this is less and less true in America today, especially in our schools.

"for decades the US has been known for its creativity and innovation." 

Yes, and many of those who've produced this creativity and innovation got their k12 education in schools that people now consider too "traditional"--whether they got this education in this country or abroad.

The stereotype of rote learning in East Asian classes

Time and again you hear Americans claiming that East Asian education is all about rote learning, including East Asian math education. Where does the East Asian rote learning stereotype come from?

At a book talk I gave at the Yale China Association two days ago, where several Chinese nationals were in attendance, this was one of the questions we addressed.

Is it simply an instance of sloppy, prejudicial stereotyping and American self-promotion?

Is it that the people who most strongly denounce rote learning tend to conflate it with other things they don't like that are true of East Asian education, like students sitting in rows facing a teacher and a blackboard, like highly-structured, teacher-directed lessons, and like hard work and after-school cram schools?

Is it that students from East Asia are often quiet in American classrooms, and that Americans assume this lack of participation stems from having nothing to say rather than from the kinds of cultural differences of which too few Americans have sufficient appreciation?

Is it that, in one subject in particular, there is, necessarily, a lot more memorization than in American classrooms--namely written Chinese, with its thousands and thousands of distinct characters--and that, again, people sloppily conflate this with everything else?

Or is it that American Constructivist advocates occasionally manage to find someone who was educated in East Asia who will politely tell them that they would have learned so much more if they had had the privilege of attending grade school in America, where there's so much more higher level thinking?  (This is a claim I've heard from several Constructivist advocates, though I have yet to meet the person they're talking about).

In addition to discussing these possibilities, I learned the following things about mainland Chinese k12 math education:

In the early grades, students only learn math and Chinese, with about 3 hours a day spent on math.  

Students do large numbers of problems that one person characterized as having certain patterns that students eventually get used to, but these problems are challenging word problems--especially involving trains and other moving objects--not columns and columns of pure calculation problems.  One student characterized these problems as extremely helpful for higher level mathematical thinking.

Curiously, while some American educators write off East Asian education as all about rote learning, certain Constructivist advocates point to Japan (and sometimes Singapore) as a paragon of group-centered, multiple-solutions based, discovery learning.  But, as one learns in The Learning Gap, the group in question is the whole class, and the person in charge of this group is the teacher, and the discovery comes about as a result of his/her Socratic dialogue with the entire class, and that while multiple strategies are entertained, the teacher ultimately helps the class understand why all strategies are not equal, and why one strategy (often one involving a standard algorithm) is often far better the others.

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

Introductory division problems:

From the end of 5th grade Investigations

From the beginning of 5th grade Singapore Math

The trouble with "The Trouble with Boys"

Peg Tyre's book does a wonderful job exposing the ways in which reduced recess time, early literacy expectations, writing-intensive activities, the decline in penmanship instruction, excessive homework, zero tolerance for aggressive play, and lack of male role models have contributed to a marked decline in how well boys do in school.

But in the process, Tyre creates a faulty impression of schools as drilling and killing and pushing kids harder in academics than ever before. As she writes on pp. 84-85:

Elementary school is a conveyor belt. It moves kids from the magical world of childhood toward a more complex universe where reading and writing, concrete reasoning, abstract thought, and time-management skills are the currency of the land. In the last ten years, that conveyor belt has been speeded up. Our children are being pushed to reach the milestones of literacy and arithmetic earlier and earlier.

If you doubt this is true, talk to any veteran kindergarten, first-grade, second-grade, or third-grade teacher. Fifteen years ago, kindergarten was a place or social and emotional development. Reading was reserved for first grade. First-graders were expected to learn their letters and slowly, over the year, master letter sounds, begin to recognize some words on sight, and read short sentences. Second grade was given over to developing math concepts and reading fluency. These days, in many schools principals urge parents to be sure that their incoming kindergartners already know the letters--uppercase and lowercase--and to make sure they have the corresponding letter sounds solidly under their Hello Kitty or Power Ranger belts. Many parents are warned that in order to stay at grade level, kindergartners should be able to read on their own by the end of the year. Today, first-graders are routinely pushed through a curriculum that fifteen years ago was considered standard for second or sometimes third grade.

Noting a "single-minded focus on standardized tests" in which there is "no time for blocks," Tyre cites findings by the Center on Education Policy (a Washington think tank) that nearly two thirds of elementary schools are spending more time on reading and math and less time on social studies, science, art, music, lunch, and gym.

She also cites children's book author Ralph Fletcher as saying that "there are so many curriculum mandates that writing has become so much more content driven and less about choice."

Her anecdotes include:

A mother whose son is "bored to death with the drill-it-till-you-kill-kit approach to math problems, which, in the mother's words, involve "the same problems, with the same numbers over and over again."

A teacher who bucks current trends because she is "determined to prevent filling out worksheets and quiet desk work from taking away from active play and hands-on learning."

Tyre's discussion ignores the reality that:

1. Reform Math has watered down math and science instruction as never before. Far from being two years ahead in math, as Tyre suggests, and far from being "pushed to reach the milestones of arithmetic earlier and earlier," as Tyre states, your average elementary student, by 5th or 6th grade, is actually up to two years behind in math.

2. Most No Child Left Behind tests set such a low bar, especially in math, that classrooms that focus on these tests set a lower academic bar than ever before.

3. While many schools have reduced or eliminated art and music, art is alive and well in all those "be colorful," "be creative" math, science, language arts, and social studies assignments, and all those large/interdisciplinary projects.

4. Blocks and other manipulatives are alive and well in today's Reform Math classes, extending further into elementary school than ever before.

5. Reform Math de-emphasizes worksheets and "quiet desk work" in favor of hands-on, cooperative group learning.

6. Reform Math eschews drill and kill as never before, such that fewer and fewer students are doing the same problems over and over again.

7. Assignments in general, and writing assignments in particular, are less and less content-driven, and more and more based on personal connections and reflections.

Finally, as accurate as Tyre's anecdotes surely are, they are one-sided. Where are the many boys who are bored with school because the math is too easy, or because the writing assignments are based more on personal feelings than on actual content, or because science is more about science appreciation than about solving hard science problems, or because math, science, and social studies assignments so often require him to produce "colorful and creative" illustrations, book covers, and posters?

The surprising preferences of many children

...and not just the left-brainers, perhaps:

How often have we heard professional educators claim that children are bored by drills, prefer projects to tests, prefer working with classmates to working on their own, and prefer sitting in groups with classmates to sitting in rows facing their teachers?

One reminder of how questionable such claims are comes from an anecdote recently shared on kitchentablemath.

Perhaps this boy is an outlier. But his words echo those of the children I interviewed for my book.

Well, perhaps it's only the hard-core left-brainers who feel this way. But even this I question. When I did after-school math enrichment with 1/6 of our school's 2nd and 3rd graders, I always let them to choose between working on their own and working in groups, and a surprising number (at least half, as I recall) would opt for the former. They also loved our rapid-fire, teacher-directed multiplication drills.

Of course educators shouldn't let children's preferences be the only thing that guides their teaching. But they should avoid making faulty assumptions about these preferences, and ensure that when they avoid the things that children prefer, they are doing so for a good reason.

Four "left-brain child" book talks in New Haven/Boston areas

Wednesday, March 24th at 6:00 PM, Yale bookstore in New Haven, CT.

Thursday, March 25th at noon, Miller Library in Hamden, CT.

Thursday, March 25th at 7:00 PM, Back Pages books in Waltham, MA.

Friday, March 26th at 4:00 PM, Yale-China Association in New Haven, CT.

Math problems of the week: 3rd grade Everyday Math vs. Singapore Math

1. The final division practice session in the "Multiplication and Division" chapter of the 3rd grade Everyday Math Student Math Journal Volume I, p. 84:

2. The final division practice session in the "Multiplication and Division" chapter in the 3rd grade Singapore Math Primary Mathematics 3A, p. 102:

3. Extra Credit: Should Singapore math students, like Everyday Math students, be solving 3rd grade division problems using counters?

The Constructivist selection bias

It has recently occurred to me that one reason why Constructivist classrooms appeal to so many people--including so many newspaper reporters--is because of their inherent selection bias.

Consider this.  Only in certain types of classrooms can the Constructivist dream become a reality.  Only in certain classrooms, that is, can you have groups of students spending so much of the day doing hands-on group activities without running up against either a shortage of materials or total chaos.  And only certain teachers and principals have been trained in the methods and supposed virtues of Constructivist classrooms. 

All the factors that favor Constructivism--small class sizes, well-behaved students, in-class parent volunteers, specially-trained teachers--correlate in turn with school district wealth, which correlates in turn with the socio-economic status of the families that enroll at the school.

And, as study after study has shown, high socio-economic status is correlated, independently of particular schools and their pedagogical practices, with academic achievement.

Thus, it's easy to connect the dots between Constructivism and academic success--and pleasant learning environments and compliant children and the crème de la crème of specially-trained teachers (those who win the opportunity to teach such desirable children in such desirable environments)--even though Constructivism per se cannot claim credit.

Meantime, with the majority of our inner-city students stuck with Reform Math programs in non-Constructivist classrooms, you've got the worst of both worlds: mindless filling out of poorly-sequenced, dumbed-down worksheets whose convoluted directions and nonstandard algorithms no one understands.  Of course, in this case it's easy--way too easy--to blame everything but the curriculum.

Do mathematicians mostly work independently?

That is, is it the case that when mathematicians collaborate, they do so by "divvying up the pieces, working independently, and only reconvening to present and tweak one another's solutions"?

That's the claim I make in my book, based on my observations growing up among mathematicians, and based on the affirmation of the mathematicians past whom I ran this hypothesis.  

But for some reason I didn't run it past one of my closest mathematician friends, Dr. Stephanie Frank Singer, who just wrote a generous review of my book in which she observes that, "While many mathematicians do work that way, many others work collaboratively."

Dr. Singer and I talked this over a couple of days ago in light of the common requirement by K12 teachers that students do math in groups--a requirement they justify by stating that "mathematicians work in groups," and that children need to develop their collaborative social skills.  

To what extent, I asked Dr. Singer, does successful mathematical collaboration require social skills? Not much, she replied. In such collaborations, what's primary is the mathematical content. The mediating effects of this content are such that, even when one or both parties has minimal social skills, those social deficits don't really get in the way. Perhaps, I proposed, this kind of content-driven interaction liberates those who lack social skills--an important idea to keep in mind when thinking about how to create social opportunities for individuals with Asperger's Syndrome.

Does this idea suggest a different reason to require students, especially the less social ones, to work in groups? Not at all. As I point out in my book. cooperative learning zealots forget that there's a huge difference between voluntary collaborations, in which people choose one another because they recognize that they can benefit from one another's insights, and involuntary collaborations, especially where the math (as in K12 Reform Math) is so simple for so many students, and where there's not enough interesting content to mediate social interactions.

Math problems of the week: 6th grade Everyday Math vs. Singapore Math

The final angles problems in 6th grade Everyday Math (first) and 6th grade Singapore Math (second):

Extra Credit: a. Compare the 1-3 step Everyday Math problems with the 4-6 step Singapore Math problems. Why does only the former request explanations for answers? b. Relate your answer to (a) to the Everyday Math "Time to Reflect" questions that follow this section, in which pride, challenge, and learning are supposed to be made explicit: Which activity in this unit do you believe is an example of your best work? Why do you think so? Which activity in this unit did you find the most challenging? Why? What is something new you learned about geometry in this unit?

Autism and reading comprehension: the parents as experts

One of the ways in which the usual rules don't apply when teaching autistic students is in picking appropriate reading assignments. Consider the following two passages:

Nobody gave The Treatment like Farquar. Palmer knew a kid who had his arm in a sling for a week after. Yet Farquar himself was maddeningly unpredictable. Some birthday boys he seemed to totally ignore, passing them on the street as he usually did, as if they were dog doo. On the other hand, he had been known to walk halfway across town, knock on a door and say sweetly to a surprised parent, "I hear there's a birthday boy in here."

Some kids turned into quivering zombies. They kept their birthdays as secrets as possible. In school, if their teacher announced their birthday, they denied it, claiming that it was a mistake. They refused to have parties. They stayed inside their house for a month so they would not bump into Farquar.

But there was another side to it. There was the honor. There was the respect you got from other kids, the kind of respect that comes to soldiers who survive great battles...

(From The Wringer, by Jerry Spinelli.)

Instead of fighting with weapons, Ghandi and the Congress Party began to use other methods of resisting the British. They taught the Indians to resist with "noncooperation"--meaning that Indians simply refused to pay taxes to the British government. They encouraged Indians to "boycott" British goods (refuse to buy anything made in Great Britain). Gandhi told his followers to make their own handmade cloth for their clothes, rather than buying British cotton. When the British put a tax on salt, Gandhi led his followers on a march of 240 miles to go collect salt from the sea, rather than buying the taxed salt. He started with seventy-eight people. By the end of the march, thousands of people were following him.

Gandhi told Indians to take their children out of British schools. He asked them to give up privileges given to them by the British. He himself sent back a medal that the British government had given him for his work in South Africa. When a factory refused to give its workers enough money to live on, Gandhi went on a hunger strike. He refused to eat until the factory owners agreed to the raise. It took too three days for the factory owners to give in and agree. They didn't want to be responsible for Gandhi starving to death!

(From The Story of the World, Volume IV, by Susan Wise Bauer).

Both The Wringer and The Story of the World are intended for the 9-12 age range. And according to the usual measures--vocabulary, sentence length, and sentence complexity--the second passage is unequivocally the more difficult of the two.

But in terms of the work the student must do to fill in the gaps in literal content to make sense of the text, the first passage is much more challenging. In particular, nowhere is it stated that Farquar beats kids up on their birthdays. If you don't infer this, you then won't understand why kids try to keep their birthdays a secret. And without this, and a grasp of the social meaning of "honor," you'll be completely baffled by the second paragraph of the excerpt.

In the second passage, on the other hand, much more is spelled out. The explanatory asides, while they contribute to the length and complexity of the sentences, offer useful definitions of key terms ("noncooperation" and "boycott.") In general, much less filling-in is necessary to understand the connections between sentences.

These differences between texts make sense when we consider their different settings. One is set close to home, and centers on schoolboy dynamics with which most neuro-typical children are familiar. Because of this, it can leave many things unstated and still make sense to most readers. The other text, on the other hand, is set in a faraway time and place, and involves issues that 9-12-year olds cannot be assumed to be familiar with. Thus, much more needs to be made explicit. For children with autism, many of whom pick up much less of the social dynamics of everyday life, this has the effect of leveling the playing field.

Because of this phenomenon, readings centering on other times, places, and issues tend to be much more accessible to those with autism than readings centering on everyday life. Unfortunately, however, in their zeal to make everything "relevant" to students' purported "personal lives," today's educators are biasing their reading selections more and more towards realistic texts about everyday life.

Any parent who spends any time reading with their autistic child knows about the problems this creates. But too few of those who teach autistic children in school settings--be they regular ed or special ed teachers--have either the training or the experience with one-on-one reading support to have much of an inkling about how autism affects reading comprehension.

Teachers must therefore be willing to hear suggestions from autism parents about appropriate reading assignments. But are they? I'm still waiting to find out...

Revenge against the nerds--by teachers

ChemProf's comment about teachers bullying socially awkward children made me think of a recent post on the Math Investigations (TERC) website in which a teacher points out that a certain type of student is languishing under Reform Math, and, while pointing this out, uses an all-too-familiar negative caricature:

There is another population that I think we are in danger of leaving behind, a population that used to do well in school mathematics: tidy math fans.

What is tidy math? Worksheets containing orderly rows of computation problems, all essentially the same problem, but with different numbers. Textbooks or teachers that cleanly demonstrate a method step by step and then ask students to do thirty problems using that same method. These are examples of tidy math.

Who are tidy math fans? Students who are neat and well-organized. Students who may not be too creative, but who pay attention and follow directions well. Students who are satisfied with knowing how and who are not bothered by not knowing why. Students who grow up, meet math teachers like myself at parties, and say "Oh, I've always liked math. I love how there's always one right answer to a problem." These are tidy math fans.

Neat, organized, not-too-creative directions-followers who don't ask why and want everything cut and dried. Yes, we all know who we're talking about here. Not people we'd want to be friends with, of course, but (as per Equity) we shouldn't totally abandon them either.

Notice also the tired caricature of traditional math (for which the most recent counterexample on this blog is this post).

Our teacher continues:

Tidy math fans do well in what we now call "traditional" math programs. But as some schools adopt new programs like Investigations, some of these students face a sudden drop in status, from one of the best math students in the class to an average, sometimes struggling student. Their self-esteem about their math ability plummets. It's no wonder that some of their parents (who themselves grew up with tidy math) put up a fuss about the new program and teaching style that is causing their children's loss of confidence.

The rules for success and the very definition of what it means to do math have changed on them. Math is much harder now.

I can't help detecting just a whiff of schadenfreude here. After all, what's more satisfying than bringing down the type who would have out-shined you back when you were a student?

You might argue that this change is for the students' good. What tidy math fans were successful at before really wasn't mathematics anyway, and we do all students a favor by showing them what doing mathematics is really about. "Doing math has to do with thinking and reasoning about problems or situations that call for applying mathematical ideas and skills . . . Skills should be learned in the context of problems and situations and should not exist isolated from the problems and situations that give them their purpose." (Burns, p. 69.)

The mathematicians I know consider Traditional Math far more mathematical than Reform Math, but why ask them?  After all, they are all tidy math fans.  Surely math educator and children's book author Marilyn Burns has a much better handle on what mathematics is really about.

In Beyond Arithmetic, Investigations authors advocate that students work on nonroutine mathematical problems. "With nonroutine problems, students should expect "messiness." There may be different paths to a solution, and there may be several different good solutions to a problem . . . Doing mathematics often means rough drafts, tentativeness, challenge, and hard work." (Mokros et al., p. 53.)

And surely math education specialist Jan Mokros is a much better source on what doing mathematics involves than tidy, correct-answer-obsessed mathematicians are.

Our teacher goes on to express concern about the mixed blessings that Investigations has brought (which apparently include making math more enjoyable to most students--a constituency of students whom I have yet to meet):

Most students LOVE Investigations, messiness and all. I am excited about the many students who are turned on by Investigations, students who used to think math is boring. I'm thrilled to hear the stories of students who would rather continue with math time than go to recess. But I am also troubled by the few students who liked math better the old way.

We need to recognize how hard the adaptation to "messy math" is for a few children. To achieve our vision of equity, we must support these children too, but how?

I have a few suggestions, but I'm afraid they may be a bit too tidy for the Powers that Be.

A Singaporean's perspective on Singapore Math

I just came across an online article by a Singaporean named Justin Lee, the founder of two education businesses in Singapore.  In reaction to many articles "fussing about Singapore Math on the Internet," Lee writes: 

While many authors bemoaned or even whined about the difficulty American kids had with Math, it made me at times sympathetic or even amused. You see, Math in Singapore was highly enjoyable in my time and we dreaded other subjects like English and Science instead. Why is this so?

One reason, Lee points out, is that, for about 50% of the Singaporean population, English is not the native language.  As a result:

Math in primary school (for 7-12 year olds) was one of the easiest subjects to ace. It did not involve language application as extensively as Science. Although the word problems in Math papers still involved the English language, it required us only to write one-liners as conclusions. Many friends of my age then scored above 80 marks out of a 100 in Math on a regular basis. Being able to score so highly in Math (as opposed to barely passing English or Science) easily made Math our favourite subject in school!

This, of course, makes me think of all the language impaired math buffs who suffer under Reform Math's much more language-intensive "story problems" and verbal explanations requirements.

Lee goes on to lament a development in Singapore that is taking math standards in Singapore in the opposite direction as that which American math standards have followed.  Apparently, "there has been a rising trend of schools setting impossible-to-pass Math tests and examinations in the late 2000s." Instead of parents being upset that standards are too low, Singapore parents are upset that standards, which have long been higher than ours, have now risen too high.

Lee proceeds to describe how he and his classmates found Singapore math to be easy and enjoyable, with plenty of time left over for fun:

It is true that the Mathematical concepts are built year upon year and concepts that have been taught are not taught again, but merely revisited briefly. This is as opposed to the slightly incoherent system in the US, where kids can sometimes wonder why they are doing the same things again. While this arrangement may appear to be harder on Singapore students, I actually felt it was very easy on us. In fact, we felt that it was a gift from heaven to be able to do fractions at primary 6 again, right after we learnt something similar the year before.

It might appear as though a Singapore student would have had to spend many hours poring their beady eyes other Math textbooks and Math problems to acquire such ‘astounding’ proficiency in the subject. The truth is, the pace of learning was rather fine. I could do quite well in school without having to attend extra lessons (tuitions), and school only lasted from 730am to 1pm, Monday to Friday. There was still ample time for monkey business after 1pm.

To sum up, I am positive that Math in primary school was enjoyable for most students in the 1990s. This may not be so after internal Math examination standards were revised upwards in the late 2000s, but we shall address this issue in another article.

I look forward to more!  In our self-absorbed, American-exceptionalist country, the Singaporean perspective, which should be a key element in the debate over math reform, is all too often overlooked.

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

I. The last 4 fractions problems in the 4th grade Everyday Math Student Math Journal, volume 2 fractions unit, "Fractions and Their Uses: Chance and Probability," pp. 227-8.

Write 5 fractions equivalent to 1/6.

Divide. Write the remainder as a fraction.

769/15 =

Suppose you had to explain to a first grader how to read the fraction 1/6.  What would you say?

When discussing fractions, why is it so important to know the value of the whole or ONE? Give an example to support your answer.

II. The last 5 fractions problems in the 4th grade Singapore Math Primary Mathematics 4A, fractions unit, "Fractions," pp. 108-109.

Sara bought 40 m of material. She made 6 curtains from the material. She used 2 m to make each curtain. What fraction of the material did she use for the 6 curtains?

Travis had 160 mangoes. He sold some at $2 each and made $240.

(a) How many mangoes did he sell?

(b) What fraction of his mangoes did he have left?

Mary bought a roll of ribbon.  After using 5/8 of the ribbon to decorate some packages, she had 15 ft of the ribbon left. How many feet of ribbon did she buy?

John bought some stamps. He used 3/5 of them to mail letters. He had 12 stamps left. How many stamps did he use?

III. Extra credit: 

Comment on the ability of a math buff with Asperger's Syndrome to answer the third and fourth Everyday Math questions, as opposed to the third and fourth Singapore Math problems.

Comment on the ability of an Everyday Math student to answer the third and fourth Singapore Math problems.

Comment on the ability of grade school students in general to satisfactorily answer the third Everyday Math question without the benefits of a math methods class at an education school.

On teasing and bullying

I've been researching this question for an online class I'm designing on High Functioning Autism/Asperger's, and found what I've learned to be applicable to bright, quirky, socially awkward children in general--and their parents. Here's what I've written up.

Studies suggest that sensitive, socially awkward children are particularly vulnerable to persistent teasing--of the sort that people now classify as bullying. Being academically gifted, further setting the child apart from his classmates, may make matters even worse.

Encourage your child to talk about the situation; just talking and being heard may help him feel better. It will also build trust between the two of you, and give you a sense of the issues.

In advising your child, you can avoid making him more self-conscious about his differences by shifting the spotlight from him to his bullies. Explain to him what motivates them: bullies thrive on getting a reaction; those who tease him are trying to make him cry.

Then empower your child. Explain that while we can’t control bullies, we can control our reactions to them and how often we cross their paths.

Help your child brainstorm ways to avoid the bullies. Perhaps there are particular places at school where bullies hang out, or specific groups of kids that he could avoid spending time with. It may turn out that some of the children he considers his friends are among those who tease him. In this case, you need to convince him that friends don’t make their friends feel bad, and that if his friends won’t stop teasing, or stand up for him when other friends tease him, he needs to start looking for new friends.

Advise you child, as well, on how to best to react to teasing. As bullying researchers have repeatedly found, ignoring the perpetrator doesn’t work; it will just make him try harder to get a reaction. Instead, advise you child to give a different reaction from that which the bully is seeking.

Effective responses include the direct, honest, retort: “Why are you saying cruel things about me when you know it upsets me?” or “It hurts my feelings when you tell people that I suck my thumb when I don’t.” Alternatively one can direct the insult back at the bully: “I know, it must really bother you that I dress this way,” or “Does making me feel terrible about myself make you feel better?"

After presenting these options to your child, help him brainstorm a handful of ready responses that he is comfortable delivering. Whichever ones he chooses, it’s crucial that he speak his lines with confidence. He should enunciate them clearly in a sufficiently loud voice, standing up straight and looking directly into the eyes of the bully. Message delivered, he shouldn’t wait around for a reaction, but calmly walk away.

Many socially awkward children will find it difficult to deliver their lines with sufficient confidence. Role playing the interaction at home will help them tremendously. Start by having your child play the bully, modeling his chosen response yourself. Then change roles and practice until your child shows the requisite confidence.

Some victims of bullying may be too self-consciousness to share their plight with their parents. If you suspect that your child is a victim and are unable to encourage him to talk about it, it’s still important to act: persistent teasing and bullying can have profound, long-term effects on mood and self-esteem. Many reluctant children are ultimately relieved when things are brought out into the open; the more so, of course, once they’re actually dealt with.

If your child is reluctant to admit to being bullied, present your advice in general terms. You might say that all children have to deal with teasing, and here are some things you learned to say when you yourself were teased.

Besides advising your child, there is much you can do without involving him directly. Telling the teacher and principal right away is crucial; don’t assume that school officials are necessarily aware of the situation. Request ways to minimize the opportunities for bullying—e.g., by having recess or cafeteria aides keep a close eye on your child, or by changing his classroom seating arrangements, assigning him to a different group during group activities, or allowing him to work independently instead of in a group.

You can also request that school officials convene meetings with the bullies and their parents. Many schools have official anti-bullying protocols. Many parents have no idea that their children have bullied others and are eager to do what they can to set things right.

Finally, it’s important to address the root causes of your child’s victimization. Some awkward children unwittingly irritate others in ways that invite teasing. Discretely observe your child during play dates or other interactions and see if he provokes others through behaviors that are under his control to alter. If so, give him constructive feedback later on, perhaps role playing specific interactions.

The most effective antidote to bullying, however, is building self confidence. Show your child love and understanding. Help him develop his talents and focus on his positive qualities. Help him improve his social skills through regular play dates, carefully chosen extra-curricular activities, and/or social skills classes. Help him find true friends by inviting over like-minded peers who share his quirks, or kind, socially responsible classmates who will stand up for him when others tease him. By helping your child develop his social self-confidence, you not only reduce his susceptibility to bullying, but strengthen his ability to cope with all sorts of other social challenges that life eventually presents.