Sunday, January 30, 2011

Sunday Baffler: Is the world right-brained or left-brained, V

First we have the findings of over a decade ago by psychologist Daniel Goleman. As summarized in the Harvard Business Review:

In his research at nearly 200 large, global companies, Goleman found that while the qualities traditionally associated with leadership—such as intelligence, toughness, determination, and vision—are required for success, they are insufficient. Truly effective leaders are also distinguished by a high degree of emotional intelligence, which includes self-awareness, self-regulation, motivation, empathy, and social skill.
Here, empathy is "the ability to understand the emotional makeup of other people" and "skill in treating people according to their emotional reactions," while social skill is "proficiency at managing relationships and building networks" and "an ability to find common ground and build rapport."

Then, in the current issue of Harper's Magazine, we have an essay by Thomas Frank that opens with a précis of recent research on "society's winners":
One 2009 study in Psychological Science found that, in conversations with strangers, higher-status people tend to be more doodling and fidgeting and also use fewer "engagement cues"--looking at the other person, laughing, and nodding their heads.

A 2010 paper published in the Journal of Personality and Social Psychology found that "lower-class individuals" turned out to be better performers on measures of "prosocial" virtues as generosity, charity, and helpfulness."

A third study found that those of higher status were noticeably worse at assessing the emotions of others or figuring out what facial expressions meant.
In other words, while Goleman's research suggests that those on the autistic spectrum can never be "truly effective" leaders,  the more recent studies cited by Frank suggest that high-status individuals in fact have autistic-like tendencies. 

How do we resolve this apparent contradiction?

Is it that "high-status" is a broader category than "effective leader"? Perhaps it includes effective professionals in general, not just leaders. Goleman's findings, however, extend to high performers in general:
When I calculated the ratio of technical skills, IQ, and emotional intelligence as ingredients of excellent performance, emotional intelligence proved to be twice as important as the others for jobs at all levels.
So there must be some other constitutent of "high status" that is dragging down the average emotional intelligence of this group.  But who are they exactly, and are their numbers really large enough, and their "prosocial" skills low enough, to have this effect?

Another possibility is that "high status" individuals actually have all the social skills that Goleman deems essential, but that, having used them to attain their status and then been corrupted by this very status, they choose frequently not to apply these skills, or to misapply them, on the many, many occasions in which it is more tempting to go off on a power-trip than to be a hero to one's valet.

But this does not explain why "high status" individuals are "worse at assessing the emotions of others or figuring out what facial expressions mean."

The other mystery, of course, is why the rest of us are so willing to keep bestowing high status on such nasty individuals--a mystery that dates at least as far back as junior high school.

Friday, January 28, 2011

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

I. From the 4th grade Investigations "Assessment: Numbers to 1,000", given in late January:

1. Listen to the 3-digit number and write it down.  [623]

What is 1 more than the number?
What is 1 less than the number?
What is 10 more than the number?
What is 10 less than the number?
What is 40 more than the number?
What is 40 less than the number?
What is 200 more than the number?
What is 200 less than the number?

2. Put these numbers in order from least to greatest.

108 80 784 39 487

II. From very beginning of the 4th grade Singapore Math curriculum (Primary Mathematics 4a, pp. 15-16):
(a) _____ is 1000 more than 42,628
(b) 263,240 is 10,000 more than _____
(c) _____ is 100 less than 90,000
(d) 86,000,000 is 100,000 less than _____
(e) 45,600 is _____ more than 45,500
(f) 384,000 is _____ less than 394,000
(g) 29,409 + _____ = 30,409
(h) 2,483,000 - _____ = 2,482,000


5. Arrange the numbers in increasing order.
(a) 3695 3956 35,096 30,965
(b) 345,760 296,870 503,140 462,540

III. Extra Credit

My daughter received a B on the Investigations Assessment last week because she wrote that 200 more than the number (623) is 1023. I have no idea why she did this, nor does she. As for her teacher, she simply marked my daughter's answer as incorrect and wrote in the correct answer. Last week my daughter also completed Singapore Math's 4th grade Challenging Word Problems booklet, accurately completing such problems as:
Erin has $2.55 more than Roy. Jason has 4 times as much money as Eric. The 3 boys have $24.15 altogether. How much money does Jason have?
Speculate on the intended and actual value of assessments like the Investigations "Assessment."

Wednesday, January 26, 2011

Speaking of projects: how one parent handles those mindless assignments

I've been meaning for quite some time to repost this comment from Glen at kitchentablemath. It's one of my all time favorites:

I have my fourth grader do a hundred fraction problems while I do his "cut pictures out of magazines" homework for him. I have him work through middle school math contest problems, tossing him hints when he gets stuck, while I draw on his poster board. I had him learn every country in Europe while I built miniature teepees in a shoebox diorama.

He gets good grades on his schoolwork, but other parents--I mean kids, of course--often cut and paste better than I do.

His teacher thinks he's a "natural" at math, but there's nothing natural about it. It's man-made. It's training--the same sort of training you'd do if you needed to teach someone to cut hair or build birdhouses: show them how, help them a few times, and put them to work.

She would be shocked if she actually knew the level of difficulty of the math and science work he can do, but we're careful not to let her find out. Last year the teacher found out and was nasty to him for the rest of the year. She liked him when she thought he was a natural, but when she found out that he had to work at math, she was outraged.

"It's not fair to me that you are willing to do that much work for your father, but aren't doing the same for me!" I thought that I--I mean my son, of course--was cutting enough pictures out of enough magazines for her, but she apparently thought she deserved more.

She wanted to discuss the "problem" with me. She was concerned about how I was using his time. (How ironic.) She said that their Everyday Mathematics emphasized "conceptual understanding" and was concerned that my approach might not lead to "actual understanding." The previous night he had solved,

"We have four times as many cows as horses on our ranch. If we sold 280 cows, we'd end up with twice as many horses as cows. How many cows do we have?"

He was in third grade. I almost asked her to go to the board and show me how SHE would have taught him to solve it, with "actual understanding," but that would have been cruel. I held my tongue to keep my son out of trouble and said that I tried my best to help him understand. We left it at that.

This is one of the top 5% of elementary schools in Silicon Valley, so almost all the kids are performing at grade level--and that's where they want to keep them.

And I've now found out that at higher levels, middle school and high school, it's almost standard practice for parents to take the mindless homework load off their kids' shoulders to free up time for them to do the portion of homework that is actually useful.

Monday, January 24, 2011

Other parents (and other children)

After a grueling weekend coaching my 4th grade daughter through her first big science project, I wondered what it was like for other parents. Many, I know, find the experience as grueling, and its ratio of effort to learning as maddening, as I do. But there are plenty out there who don't mind these projects at all. Somehow, even though the projects demand a level of organization and executive functioning that many 4th graders simply haven't yet attained, the pro-project parents seem to have kids who not only enjoy doing them, but are able to do them painlessly on their own. 

While I envy this somewhat (it would have been nice to have had a more enjoyable weekend with my daughter), what really gets my goat is when the pro-project parents (just like the pro-project teachers) can't understand why anyone would object to such projects, or why my child wouldn't be sufficiently motivated to do them on her own.  Worse yet is the implicit judgment that often accompanies this lack of empathy. After all, their children had no difficulty. Surely there must be something deficient about my child, or perhaps about my child-rearing.

A similar message has been reiterated during the whole of this weekend by a commenter on a recent thread on kitchentablemath. Far from being a pro-school-project parent, though, this particular guy is an anti-establishment anarchist who believes that schools and society are so corrupt and corrupting that all of us should be home schooling. Where his children--and all the children he says he knows of--have no difficulty, it seems, is in mastering the three Rs and everything else worth learning without any being pushed by their parents. Here is some of what he has to say:
Our kids started composing their own pieces (sort of pop neo-romantic classical, I suppose) when they were nine, without any suggestion at all from anyone that they do so (I guess they encouraged each other).


My kids play recitals; in a few weeks they will be part of a “Baroque Festival” run by the local university, as will some of their friends: I expect they will have fun.

And, that is the point, I expect they will have fun... Of course, they practice, of course they struggle over the correct fingering. But, it does not make them miserable, they are not “pushed.”

I’m well aware that most kids will not teach themselves special relativity when they are twelve-years-old, as I did. I view that fact with sadness, but, after all, it is rather besides the point. Very few people need to know special relativity. 
Having established that he has wonderfully bright, creative, self-motivated children and that he himself was astonishingly precocious and values learning tremendously, he starts generalizing:
...based on my own experience as a child and on my kids’ experience: I think kids innately want to learn, but that that desire is squeezed out of them by our society (parents, schools, and pop culture).
Ah, but. What if you have a narrowly focused child who doesn't want to learn everything that is necessary for functioning in society? What if your kid was this way from the beginning, before school; indeed, what if this child's narrow focus includes an obliviousness to pop culture? Again, there's that implicit judgment: either my kids are aberrant, or (assuming I've adequately sheltered them from toxic society) I shouldn't be pushing them because they're naturally curious like all (normal) kids are (or would be, if only...) 

Here's what I wrote in response:
While it may be true that *most* kids innately want to learn *something*, one should not take it on faith, or on anecdotal evidence drawn from ones own personal experiences, that *all* kids innately want to learn *all* that they need to in order to function independently in society.

Take, for instance, the many kids on the autistic spectrum who have no innate interest in interacting with other people and in learning basic social interaction skills, or even, in many cases, of learning the fundamentals of spoken and written language. Indeed, it's because of this deficiency in innate interest that many of the most effective therapies for autism involve high degrees of structure, teacher/therapist control, and extrinsic reinforcers.

I suspect that AS children are not the only ones who lack innate interest in learning certain sorts of skills that most of us would deem essential for independent living. Among the diversity of personalities that constitute humanity, I imagine that there are some who have (through no fault of pop culture in particular or society in general) no innate interest in learning how to read, in how to write intelligibly, and/or in how to keep track of their finances.

Especially if one is lucky enough to have smart, good-natured, broadly inquisitive children, it's important not to generalize from one's own parenting experiences and assume that, if only others would just follow in our footsteps, their children would turn out just as well as ours do.
Here's part of the extremely long reply I got in response:
Of course, I meant the vast majority of kids, those with normal intelligence, not suffering from debilitating mental disabilities. etc.

Well… of course, there are other forms of mental disabilities than autism.
My reply:
For a someone who prides himself on his ability not to take things on faith, you have a remarkable amount of faith in the idea that the only children who don't have an innate desire to learn *everything* their parents might deem important are mentally disabled.

Unless this is your definition of what a "debilitating mental disability" is? But then I'm not sure"vast" is the right word for your "majority". Also, I think it's important to draw a distinction between abilities and interests.

Can you guess what one of the things is that most demoralizes the many parents of eccentric children, narrowly-focused children I know who feel they must push their children quite hard in certain areas? The judgments of parents of kids who *are* innately interested in pursuing these things on their own and who assume that every child must share these innate interests. The fact that these judgments often stem from ignorance does not erase their sting.

It's important to note that many of the children I've written about do broaden their interests later on in life, but that if one waits for the innate interest to show up on its own, the resulting delay in mastery may frustrate not just the parent, but the child him or herself. For example, not every 5, 6, 7, or even 10-year old boy wants to learn how to read, even if he or she is not mentally disabled, and even if he recognizes the importance of reading later on and wishes he had started earlier.
His reply:
First, I think there is not just faith but very strong (not admittedly, conclusive) evidence that most kids are naturally willing to learn a great deal, but that our society has distorted that natural inclination.

I alluded to some of that evidence above: There is little trouble in our society in getting kids to want to learn how to drive. Historically, aside from the modern West and mandarinate China, teaching kids what they need to know to function in their society does not seem to have provoked enormous resistance or rebellion on the part of the kids. Everyone knows that toddlers tend to be curious about just about everything (including a lot of things they should not be curious about for safety reasons), but that this curiosity tends to get squeezed out of American kids before adolescence.

And, in my own personal experience, watching kids I know – family, friends, etc. – as they develop, the process by which the schools squeeze out the children’s natural curiosity has been fairly obvious: some of the kids have even been rather explicit in telling me that this is the case.

As a scientist, I look for simple hypotheses which fit all the facts I can uncover. This hypothesis seems to best fit all the facts I know of.

My second point relates to your mentioning kids’ not having an “innate desire to learn *everything* their parents might deem important.” You’re right, of course, but my sympathies do not lie with the parents on that! Sure, most kids would not voluntarily read The Scarlet Letter. Why should they? 


Perhaps, most people should not learn history, literature, etc. in their teens. Perhaps, most people can’t.. Perhaps, you grok “Macbeth” or The Scarlet Letter better when you have some life experiences than as a callow teen. Or, perhaps, both are not really ever worth reading at all.

What kids really need is the three Rs. Americans once knew how to teach the three Rs rapidly, in four years or less, as my great-grandmother’s generation proved, and there was much less of a “youth culture,” “adolescent rebellion,” etc. back then than there is now.


If you’re suggesting that most American kids really would like to avoid acquiring the basic knowledge of the “three Rs” that my great-grandmother already had acquired when she dropped out after fourth grade circa 1893, well… how on earth could we have produced children who do not want to know that? It is not normal for children to so hate their society that they do not want to acquire the very basic knowledge required to live in that society, and, indeed, American kids are (notoriously!) eager to learn how to drive, how to use credit cards, etc.
My reply:
I'm not, of course, talking about MacBeth and the Scarlet Letter. Nor am I talking about learning how to drive. I'm talking about basic skills for functioning independently in society of the sort that may require of kids a tremendous amount of discipline to master, and time (yes, four years of time): yes, the three Rs. What is your evidence that kids in general--not just your great grandmother-- used to master these things without forced to by adults? What about all those rebellious farm boys we read about in the Laura Ingalls Wilder books--or are you referring to an even earlier golden age of education? That most people have a love of learning that has been squeezed out of them by school (a point with which I agree) does not imply that only mentally disabled children resist learning the three Rs.

It would seem that you haven't met many children whose love of learning is channeled into narrow, esoteric interests; I've met tons. Families share genes; friends share personality traits; family and friends do not represent the gamut of personality types. People don't realize this, think they've seen everything, and then make toxic judgments about other parents.


Glen, on a different thread, puts it beautifully:
"There is a value conflict between the little people my kids are today and the adults they will one day become. The little people fight for what they value today, but who represents the adults they will become?

"That has to be me. I'm like an agent representing the interests of faraway clients with whom I can't communicate. I have to do my best to figure out what they would want me to do and act on their behalf while still protecting the interests of the kids in front of me. I can't let either side take too much advantage of the other.

"Many years from now I'll meet those adult "clients" face to face and have to justify my actions. There will be some second guessing. They'll have the benefit of hindsight and won't fully understand how things were. But, overall, will they be pleased at how I took care of their interests?

"That's a question I try to keep in mind when deciding how hard to push."

And many other parents as well, especially, I imagine, those of us with kids whose "natural willingness to learn" is focused on a narrow range of esoteric topics.

Unlike the evil schools, we don't try to squeeze out these interests, but we do push, often harder than other parents do--and however much they might frown on us.
But our anarchist home schooler continues to insist that:
Teaching reading is stunningly easy: all you need is a couple books and an adult who can read. sane societies, it is not that big of a deal to get kids to learn the basic things they need to function in society


Teaching a kid to read is really, really, really easy. I strongly suspect that anyone who thinks otherwise has never successfully taught a kid of normal intelligence how to read. It’s easier than changing diapers.
Addressing someone else, he also notes, in reference to Rousseau vs. the Enlightenment philosophers whom he says support his views, that "distinctions matter," and, in reference to a purported division of humankind into neocons or Rousseauists, that "the human race is a wee bit broader than that." 

My final reply (before it became clear that this debate was going nowhere--see below): 
"Distinctions matter."
But not, apparently, when it comes to mental disabilities vs. narrow interests, being highly curious vs. being broadly curious; and objects of natural curiosity vs. skills pertaining to artificial systems like written language.

"The human race is a wee bit broader than that."

But not, apparently, when it comes to learning how to read.
In response, our faith-free scientist professes to believe that he's already addressed these points:
Already settled issues, Katharine: asked and answered, as the lawyers say.
Just like that. If only life were so simple for the rest of us. And if only more people would realize that it simply is not.

Saturday, January 22, 2011

Is the world right-brained or left-brained, IV

Digesting the latest cognitive science research in this past week's New Yorker, David Brooks appears to conclude that, deep down inside, we're all right-brainers, and that it's the right-brained stuff that makes all the difference:

Intelligence, academic performance, and prestigious schools don’t correlate well with fulfillment, or even with outstanding accomplishment. The traits that do make a difference are poorly understood, and can’t be taught in a classroom, no matter what the tuition: the ability to understand and inspire people; to read situations and discern the underlying patterns; to build trusting relationships; to recognize and correct one’s shortcomings; to imagine alternate futures. 
The cognitive revolution of the past thirty years... emphasizes the relative importance of emotion over pure reason, social connections over individual choice, moral intuition over abstract logic, perceptiveness over I.Q.


There’s a debate in our culture about what really makes us happy, which is summarized by, on the one hand, the book “On the Road” and, on the other, the movie “It’s a Wonderful Life.” The former celebrates the life of freedom and adventure. Research over the past thirty years makes it clear that what the inner mind really wants is connection. “It’s a Wonderful Life” was right. Joining a group that meets just once a month produces the same increase in happiness as doubling your income. According to research by Daniel Kahneman, Alan B. Krueger, and others, the daily activities most closely associated with happiness are social—having sex, socializing after work, and having dinner with friends. Many of the professions that correlate most closely with happiness are also social—a corporate manager, a hairdresser.
The inner mind. Left out of Brooks' discussion is any sense of human diversity; any notion that there may be significant exceptions to these general trends. 

In particular, if what Brooks writes is really true of all of us, it's really bad news for the individuals on Autistic Spectrum out there who don't do well in groups, don't have tons of friends, and tend not to succeed in social professions. (Brooks' note about social jobs is also bad news for writers like himself; will he quit his OpEd gig to become a hairdresser?).

But are writers, solitary travelers, and people like Temple Grandin really less happy than the rest of humanity?  Or might the cognitive science research show us something different if it didn't lump all of humanity together?

Ironically, Brooks' other recent piece, his OpEd on Amy Chua in last week's New York Times, has the opposite problem: in places it is more applicable to Aspies than to their neurotypical counterparts. For here he claims that:
Practicing a piece of music for four hours requires focused attention, but it is nowhere near as cognitively demanding as a sleepover with 14-year-old girls. Managing status rivalries, negotiating group dynamics, understanding social norms, navigating the distinction between self and group — these and other social tests impose cognitive demands that blow away any intense tutoring session or a class at Yale.
Um, I imagine most neurotypical 14-year-olds find sleepovers less cognitively demanding than four hours of focused attention.

On the other hand, Brooks repeats the tired fallacy that "most people work in groups," confusing, as do so many of his colleagues in education, the notion of collaboration (where large projects are divvied up and people typically spend most of their time working apart) with cooperation (the much less common practice of co-workers spending most of their time working together, in groups, in the same place at the same time--e.g., sitting around a conference table and talking for hours on end and somehow being productive).

One can only imagine how Brooks' pieces, both of them anticipating his forthcoming The Social Animal, will be used by educators to further justify current practices. I wonder whether any of these people will notice (and remember) the one direct mention Brooks makes of classrooms:
The traits that do make a difference [the ability to understand and inspire people; to read situations and discern the underlying patterns; to build trusting relationships; to recognize and correct one’s shortcomings; to imagine alternate futures] can’t be taught in a classroom. 
[Italics, emphatically, mine].

Thursday, January 20, 2011

Math problems of the week: 1990's vs. CPM algebra

I. The last two problems in the "Simple Equations" chapter of Wentworth's New School Algebra (published in 1898), p. 32:

A man bought 10 yards of calico and 20 yards of cloth for $30.60. The cloth cost as many quarters per yard as the calico cost cents per yard. Find the price of each per yard.


A man has a certain number of dollars, half-dollars, and quarters. The number of quarters is twice the number of half-dollars and four times the number of dollars. If he has $15, how many coins of each kind has he?

II. The last two problems in the "The Math Club: Solving Equations" chapter of College Preparatory Mathematics Foundations for Algebra: Year 2, pp. 202-203:

Tom is buying new computers for his writing team. He can buy the first five at a dealer discount. The other fifteen will be purchased for an extra $50 each. The cost of the computers comes to a grand total of $11,750. Find out how much each of the discounted computers cost. A Guess and Check table might be useful. Write an equation.


Below is a list of Tool Kit entries from this chapter.

MC-8 Equations
MC-119 Mixed Numbers

Review all the entries and read the notes you made in your Tool Kit. Make a list of any questions, terms, or notes you do not understand. Ask your partner or study team members for help. If anything is still unclear, ask your teacher.

III. Extra Credit

Approximately what percentage of CPM students will be able to solve the Wentworth problems, assuming they are armed with Guess and Check tables and Tool Kits?

Approximately what percentage of CPM students would have to list the Wentworth problems under things they "do not understand"? Approximately what percentage would find that the solutions are "still unclear" after talking to their "partner or study team members" and therefore have to ask their teacher?

Tuesday, January 18, 2011

Specific rules for civil conversation

Since fostering civil discussion has become one of our national priorities, I thought I'd add my two cents. Too much of what public figures and political commentators are suggesting, in my opinion, resembles the overly vague goals of today's schools (Approach learning as a lifelong process; Appreciate diverse disciplinary and interdisciplinary perspectives and approaches to knowledge; demonstrate receptivity to new knowledge; blah, blah, blahthat ultimately go nowhere.  Really listen to the other person; Show respect for alternative view points; Treat the conversation as a common search for truth rather than as a battlefield--people tend to think they're already doing these things. Surely it's only those on the other side that need to reform. 

So how about these concrete "left-brained" rules instead:

1. No time limits: Allow a large, open-ended amount of time for discussion. Don't start a debate when you have less than an hour left with someone, unless you schedule ahead of time a follow-up meeting to resume the discussion.

2. No interruptions: Knowing that there's plenty of time left, let the other person go on and on and on as long as s/he wants to. Take notes on what you'd like to say in response to specific points rather than interrupting at that moment because you might forget it later.

3. Keep it specific. Avoid statements like "But s/he is a member of the Heritage Foundation," or "that sounds like socialism." Start with a particular issue and discuss it in as much detail as possible.

4. Check facts rather than argue over them. Have an internet device handy for looking up specific points of factual contention. If sources are contradictory, keep looking things up.

5. Use your "indoor voice."

Sunday, January 16, 2011

Why we can't trust math professors...

At least on k12 math education...

Consider the following math professors: Keith Devlin (Stanford), who wants grade schools to de-emphasize calculation skills; Dennis DeTurck (Penn), who wants grades schools to stop teaching fractions; and Jordan Ellenberg (University of Wisconsin) and Andrew Hodges (Oxford), who criticize grade school math as overly rote and abstract. And consider all the math professors featured in these three recent Youtube videos (an extended infomercial for the so-called "Moore Method," yet another re-branding of guide-on-the-side teaching and student-centered discovery learning--thanks to Barry Garelick for pointing me to these!).

Every last one of these math professors sounds like yet another apologist for Constructivist Reform Math. Each one of them can be--and in some cases is--readily cited by Reform Math acolytes and by the Reform Math-crazed media as such. And, yet, had these professors actually been subjected to Reform Math when they were students, it's hard to imagine that any of them would have enjoyed the subject enough to pursue it beyond grade school. 

Indeed, unless the mathematician in question has actually sat down and looked at the Reform Math curricula in detail, and imagined him or herself subjected to it, year after year, in all its slow-moving, mixed-ability-groupwork, explain-your-answer-to-easy problems glory, we should not trust what he or she has to say about it. Indeed mathematicians in general, unless (like Howe and Klein and Ma and Milgram and Wu) they take the time to examine what's going on with actual k12 math students in actual k12 classrooms, are especially unreliable judges of current trends in k12 math. Here's why:

1. Grownup mathematicians remember arithmetic as boring and excessively rote, and tend therefore to downplay the importance of arithmetic in general, and arithmetic calculations in particular, in most students' mathematical development.

2. Unable to put themselves in the shoes of those students to whom math doesn't come as naturally as it does to them, they tend also to downplay the importance of explicit teaching and rote practice. Some mathematicians take this a step further, imagining that if one simply gave grade schoolers more time to "play around" with numbers, they'd make great mathematical leaps on their own.

3. As more and more college students show worsening conceptual skills in math, mathematicians tend to fault k12 schools for failing to teach concepts and "higher-level thinking," not for failing to teach the more basic skills that underpin these things.

4. In upper-level college and graduate math classes, attended disproportionately by those who are approaching expert-level math skills, student-centered learning is much more effective than it is in grade school classrooms, where students are mathematical novices. Not enough mathematicians read Dan Willingham and appreciate the different needs of novices and experts.

Now there are two specific ways in which mathematicians can provide valuable insights for k12 math instruction:

1. They are perhaps the best source on what students need to know in order to handle freshman math classes. 

2. To the extent that they remember what it was like to be a math buff in grade school, and to the extent that they take a detailed look at what's going on right now in k12 math classrooms, they can offer insights into how well suited today's curricula and today's classrooms are to the needs and interests of today's budding mathematicians.

But the fact that mathematicians are really, really good at math does not, in itself, make them reliable sources on what works in k12 math classes. Quite the contrary.

Wednesday, January 12, 2011

Math problems of the week: subtraction strategies in Investigations vs. Singapore Math

1. From the 4th grade Investigations Student Math Handbook, pp. 13-15, given out in January:

2. From the 3rd grade Singapore Math Primary Mathematics 3A Textbook, about midway through the first half of 3rd grade, pp. 54-59:

3. Extra Credit:

Are the six demonstrations of a single algorithm, as seen in the Singapore Math textbook, an instance of "rote" teaching--as opposed to the single demonstrations of four different methods in the Investigations handbook?

By 5th grade, Investigations students are two years behind Singapore Math students. Is it because of "Chinese mothering," or might there be some other factor at work here?

More media attention for "innovative" constructivist classrooms

Even when the results are unequivocally negative, the press finds reasons for enthusiasm--assuming all the fashionable ingredients are there. Consider the following excerpts from an article in yesterday's Times about a classroom in the New American Academy in Crown Heights, which consists of "four teachers in large, open classrooms of 60 students":

Sixty children in a first-grade class can get loud — sometimes too loud for a teacher to explain a lesson.
So, while waiting for her teacher to come by, one little girl arranged the pennies she had been given to practice subtraction into a smiley face. Another shook her pennies in a plastic bag. A high-pitched argument broke out over someone’s missing quarter.
“We don’t know what we are supposed to be doing, but we are learning about math,” Thea Burnett, 6, said.
When [teacher Jennifer McSorley] leaned forward out of her chair to write a word on an easel, a 6-year-old boy moved it, and she fell when she tried to sit back down.
...Then another boy ran off to hide under an easel. Someone grabbed someone else’s pennies. The noise snowballed.
In the front of the room, Kathleen Kearns, a first-year teacher, strained to get her 20 students to understand how to use a chart to classify similarities and differences between two characters in a book. About half a dozen students refused to sit in their places.

“I need you here; your job is here,” she said to one, trying to be heard. After class, she said, “I am exhausted at the end of the day.”
In the first two months of school, a student pulled a chunk of an adult’s hair out, and an ambulance crew was called twice to calm a child. Eight weeks into the year, the only student work visible on the blue-painted walls was a poster with finger-painted hand prints and the words “Hands Are Not for Hitting.”
By January, three children who were violent had been moved to more-structured environments; seven other first graders moved away or withdrew, reducing the class size to 50.
Interspersed with all this, however, are the following gushes of enthusiasm:
All this was the early stages of an audacious public education experiment taking place in Crown Heights, Brooklyn, one that its founder hopes will revolutionize both how students learn and how teachers are trained... The founder, Shimon Waronker, developed the idea with several other graduate students at Harvard. It draws its inspiration, he said, from Phillips Exeter Academy, an elite boarding high school in New Hampshire where students in small classes work collaboratively and hold discussions around tables.
But Mr. Waronker decided to try out the model in one of the nation’s toughest learning environments, a high poverty elementary school in which 20 percent of the children have been found to have emotional, physical or learning disabilities. The idea, he said, was to prove that his method could help any child, and should be widely used elsewhere. “I didn’t want to create an environment that wasn’t real for everyone else and then say, look at my success,” he said.


“This is messy work — this is the front lines.”


At its heart is the idea that the teachers, not to mention the students, will collaborate and learn from one another, rather than being isolated in separate classrooms.


The intensive collaboration, [Waronker] believes, is what will cause his model, while admittedly still in a “trial-and-error” phase, to ultimately surpass others.


Indeed, by this month, there were significant improvements. Children appeared more focused during lessons. Jahmeer decided to play with pencils rather than do his counting work sheet, but he stayed in his seat, and another child asked if he needed help. One boy started crying, but not because someone pushed him; he wanted to have a turn writing his answer on the board.
Indeed, given that the audacious, Harvard-educated Mr Waronker has set out "to prove that his method could help any child," and that this school "stresses student independence over teacher-led lessons, scientific inquiry over rote memorization and freedom and self-expression over strict structure and discipline," how could it possibly not succeed--at least in its portrayal by the media. 

Monday, January 10, 2011

The stereotype of rote learning in East Asian classes, III

Two paired articles in this weekend's Wall Street Journal, I predict, will entrench this stereotype even further. 

First we have Amy Chua explaining how she and other "Chinese mothers" extract straight A's and award-winning musical performances from their children by forbidding play dates, restricting extra curriculars to piano and violin lessons, and forcing their kids, through harsh shaming and credible threats, to spend nearly all their after-school hours studying and practicing their instruments.

Then we have Jiang Xueqin, also quoted in the New York time and here, berating China for its "demanding parents, ambitious students, and test-obsessed culture" and Chinese schools for their "rote-memorization system" that produces "mid-level accountants, computer programmers and technocrats" who lack imagination, curiosity, passion, and social skills, rather than the "entrepreneurs and innovators needed to run a 21st century global economy." China's "most promising students," Jiang claims, must "still must go abroad to develop their managerial drive and creativity, and there they have to unlearn the test-centric approach to knowledge that was drilled into them."

Whatever conclusions Chinese parents and educators will draw from these articles, I worry that their American counterparts will find plenty of reasons not to emulate what the Chinese are doing well: educating their children in math and other core academic subjects. Here are some things to keep in mind:

1. Hard work does not equal rote learning, even if you are being forced to work hard by someone else. 
2. The fact that the techniques some people use to get kids to work hard are morally revolting doesn't mean that there are no reasonable, ethical ways to encourage hard work.
3. Test preparation does not equal rote learning, especially if the test is a good one like the PISA.
4. As I noted earlier, Jiang provides no examples of rote learning in Chinese classrooms. Math instruction in China involves rigor, but rigor does not equal rote, and much of what we see in Chinese k12 classrooms is higher-level mathematical problem solving in the truest sense of "higher level" and "mathematical".
5. As I also noted earlier, to the extent that China fails to produce entrepreneurs, innovators, and team players, there are alternative explanations that have nothing to do, in particular, with Chinese classrooms. 
6. Indeed, to the extent that Chua's descriptions of Chinese parents, and Jiang's description of Chinese students and graduates, are accurate, "Chinese parents," not Chinese  classrooms, may be the prime culprit in rearing kids who lack imagination, initiative, and social skills.
7. Embracing a Chinese--or Singaporean, or Japanese--model for math instruction does not mean embracing Amy Chua's model for child rearing.

Saturday, January 8, 2011

Defanging the evil machine

Following on the heels of the New York Times article on math instruction in Shanghai classrooms is this one from NPR on stress reduction in American classrooms. Entitled "What's New In High School? Stress Reduction 101," it is as enthusiastic as the Times piece was skeptical:
There's enormous pressure on kids these days. But it turns out that getting schools, parents — and even kids — to ratchet it down is easier said than done.
Beaver Country Day School in Chestnut Hill, Mass., outside Boston, is one of a small but growing number of prep schools determined to buck the trend for kids on the college track.

One of the biggest changes the school has made is on display in its calculus class, which used to be an Advanced Placement course.

Senior Sophie Deitz is dancing in front of a dry-erase board, improving math-themed lyrics to Christmas carols. Instead of poring over those fat old textbooks, and working on piles of AP practice tests, she and her classmates are learning complicated concepts like integration by parts by making videos about them.

"I want the calculus to be like a scary monster and then, we being like superheroes!" she exclaims.

It's exactly the kind of high-energy, low-stress kind of learning that Beaver administrators were hoping for when they decided a few years ago to eliminate their AP classes.

"I think that pressure to make sure that you had that trophy on your transcript was something that we felt wasn't necessarily that healthy for kids," says Peter Gow, director of college counseling and special programs at Beaver. "It didn't seem appropriate to be playing into that."
One might wonder whether replacing AP calculus with math-themed Christmas carols and super hero videos might make the college application process, ultimately, more stressful, but:
Gow insists the bold move has not hurt Beaver's students' chances of getting into the most competitive colleges.
To its credit, NPR acknowledges that there might be other ways to ameliorate high school stress:
Instead of trying to eliminate stress, many schools have put their focus on teaching kids to better handle it. Schools are experimenting with everything from yoga classes and breathing exercises to therapy dogs. They are also giving students more time to vent.
If Beaver students are still gaining admission to the "most competitive" colleges, one wonders how their stress levels are affected by competition from classmates who learned integration by parts from fat old textbooks. On the other hand, one might also wonder about the stress levels experienced by those whose high schools took time out of academics for yoga and breathing exercises.

With this in mind, here's my modest proposal for stress reduction. Instead of reducing the time spent preparing students academically for college, why not use tried and true teaching methods that neither hold them back nor expect too much of them, but meet them exactly where they are and push them gently ahead. Along the way, eliminate all homework before 4th grade, eliminate all busy work, increase unstructured recess, eliminate all developmentally inappropriate, organizationally demanding projects, and stop requiring students share their personal feelings and work in groups instead of independently, at their own rates.

As far as NPR is concerned, however, the final word goes to Peter Gow at Beaver Day:
"The whole system is like an evil machine that's consuming kids," he says. "Our school has defanged it, but only as much as any one school can."
In some sense I agree with Gow. But I see a different, much more encompassing system at work than he does. With the many credulous, enthusiastic pieces like this one on "cooperative," "creative," "discovery-based" classrooms (read: watered down academics), along with the many others that criticize traditional classrooms and East Asian "rote learning," the all-powerful media appears to be in cahoots with the all-powerful education establishment (which, in turn, spans everything from teaching certification programs to boards of education to curriculum developers and their funders at the National Science Foundation). 

Meanwhile, dissenting teachers, who, for example, try to sneak some traditional teaching into their classrooms, risk retaliation by administrators; and principals, Home and School Associations and PTAs have grown quite effective at squelching protests by parents. Who's left? One might hope for some help from mathematicians and scientists, but, as I've discussed earlier (e.g., here) and will revisit in another post, even some of these people are toeing the party line--and all it takes is a few. After all, who does the media pay more attention to: a mathematician who thinks that students learn integration by parts more effectively by making super hero videos, or one who thinks that a better option is "those fat old textbooks"?

Thursday, January 6, 2011

Math problems of the week: 4th grade Pennsylvania vs. Singapore assessment questions

Fractions word problems: 

I. From a sample test from the Pennsylvania PSSA Assessment Anchors Grade 4 ("fully aligned to the most up to date Assessment Anchors"):

II. From the Singapore Math 4a Placement Test, intended to measure skills learned in the first half of 4th grade:

III. Extra credit
Is it bad for 4th grade teachers to teach to either of these tests?

Tuesday, January 4, 2011

The stereotype of rote learning in East Asian classes, II

There were so many excellent comments of '10 to post that I was able to take quite the extended vacation from blogging. Now that it's time to start posting my own stuff again, I'll begin by catching up on the latest news about math education, starting with a December 30th New York Times article on--what else?--math in Shanghai:

In Li Zhen’s ninth-grade mathematics class here last week, the morning drill was geometry. Students at the middle school affiliated with Jing’An Teachers’ College were asked to explain the relative size of geometric shapes by using Euclid’s theorem of parallelograms.

“Who in this class can tell me how to demonstrate two lines are parallel without using a proportional segment?” Ms. Li called out to about 40 students seated in a cramped classroom.

One by one, a series of students at this medium-size public school raised their hands. When Ms. Li called on them, they each stood politely by their desks and usually answered correctly. They returned to their seats only when she told them to sit down.

Educators say this disciplined approach helps explain the announcement this month that 5,100 15-year-olds in Shanghai outperformed students from about 65 countries on an international standardized test that measured math, science and reading competency.

The Shanghai students performed well, experts say, for the same reason students from other parts of Asia — including South Korea, Singapore and Hong Kong — do: Their education systems are steeped in discipline, rote learning and obsessive test preparation.
But many educators say China’s strength in education is also a weakness. The nation’s education system is too test-oriented, schools here stifle creativity and parental pressures often deprive children of the joys of childhood, they say.
Ah, yes, and how well all this fits our self-serving stereotypes of East Asian students and East Asian countries. Subtext: they may have memorized more meaningless facts and procedures than non-Asian Americans do, but how good are they at higher-level thinking, creativity, and risk-taking?  

Consider the classroom profiled above. Discipline, yes; the children are, by American standards, extraordinarily well-behaved. Obsessive test preparation? Maybe. But does test preparation detract from meaningful learning? That depends on what sort of test the students are preparing for. What if the test involves conceptually challenging problems and higher-level thinking?

Rote? Drill? We usually associated these with mindless trivia; here the students are being asked "how to demonstrate two lines are parallel without using a proportional segment." By this reasoning, I myself was "drilled" repeatedly on the proof of the Rank Nullity Theorem when I took linear algebra in an American college. Each time I was "drilled" on it, I understood it better--and, though it would take some serious reviewing to get back up to speed on it today, I suspect I'm closer to understanding it now than if I would be if I hadn't once seen it repeatedly proved and been repeatedly asked to prove it.

Even some Chinese educators--at least the ones that get quoted by the New York Times--are buying into the idea that the Chinese schools stifle creativity:
“These are two sides of the same coin: Chinese schools are very good at preparing their students for standardized tests,” Jiang Xueqin, a deputy principal at Peking University High School in Beijing, wrote in an opinion article published in The Wall Street Journal shortly after the test results were announced. “For that reason, they fail to prepare them for higher education and the knowledge economy.”

In an interview, Mr. Jiang said Chinese schools emphasized testing too much, and produced students who lacked curiosity and the ability to think critically or independently.

“It creates very narrow-minded students,” he said. “But what China needs now is entrepreneurs and innovators.”
This is a common complaint in China. Educators say an emphasis on standardized tests is partly to blame for the shortage of innovative start-ups in China. And executives at global companies operating here say they have difficulty finding middle managers who can think creatively and solve problems.
From what I know about middle management, I suspect that the shortage of "middle managers who can think creatively and solve problems" isn't specific to China. As for Chinese managers in particular, the New York Times itself acknowledges the existence of cultural forces that extend beyond Chinese schools:
In many ways, the system is a reflection of China’s Confucianist past. Children are expected to honor and respect their parents and teachers.
As for the shortage of innovative startups, is isn't too difficult to think of possible impediments to starting up a business in mainland China that have nothing to do with how much Chinese schools focus on test preparation.

Because this East Asian stereotype--minds drilled with facts and procedures but incapable of creativity--is so popular among k12 educators these days, I've taken to asking people I know who work with graduate level East Asian students whether these students lack creativity in comparison with their American counterparts. So far that's not what I'm hearing. 

But it's a tough stereotype to bust, partly, I think, because it's reinforced by another entrenched bias: the right-brain bias against left-brain kids. Too many of us fail to see how a narrow focus can deepen rather than rigidify thinking, and how discipline and knowledge can enhance rather than stifle creativity. And, failing to imagine what might lie behind the quiet deference that comes from politeness or introversion, we forget how deeply still waters can run.

Monday, January 3, 2011

Favorite comments of '10, *Final Installment!!!*: Knowledge Based Science, Anonymous, Anonymous, & Anonymous on parental involvement in schools

Knowledge Based Science (Hainish)

This really confirms my impression that parental involvement pendulum has swung way way WAY up in recent years (maybe the last decade? earlier?).

The thing is, parental involvement isn't just a consequence of those edu-fads you mention. Parental involvement is an edu-fad in and of itself.

I think it started with the findings that greater parental involvement, parents reading to children, etc., correlated with student success.

And yes, they did. But correlation is not causation. Schools were trying to tap into that causal relationship to get better results for their students. It's a way of improving educational outcomes without actually improving education.

(BTW, when studies find that teacher quality is correlated with student success, that is called "blaming the teacher.")


In this economy, companies are trying to get more work out of fewer employees, which will make it really hard for many parents to take time off. Stay-at-home mothers often have younger children at home and may have no one to turn to for childcare while they do volunteer work. 

As for teaching at home, that has become a necessity. When I went to school, I rarely needed help with my homework because I understood what had been taught during the school day. Many kids today have no idea what to do without their parents helping to figure it out. The percentage of grade schoolers who can read independently by 4th grade would plummet if parents (yes, mostly mothers) didn't step in and do so much reading instruction. Unfortunately, I don't see that changing anytime soon. We have to fund the schools with our taxes and do the teaching too.


This is why we decided to forgo my half-day unpaid volunteer efforts and go for full-day, all-inclusive homeschooling.

At least I don't have to attend a bunch of useless meetings to get that job done.


I teach at an inner city high school and we really don't have the parental involvement of which you speak, so the demands upon teachers are very great. It is wearing. 

Students and teachers alike are short changed and it seems like in education there is simply so much change for change sake, rather than truly measured outcomes.

We are so busy meeting the needs of the individual that serious concepts which can and should be taught as "whole group instruction" are neglected (multiplication tables, etc.) and reinforced at an individual level. It does seem to have become backwards, ineffective and burdensome on students, parents and teachers. So much for education reform. I agree with Hainish regarding blaming the teacher. If this trend continues, and it has been on going on for a number of years, I really feel that fewer people will enter or remain in the teaching field.

Favorite comments of '10: Anonymous on "real world" math


Really, I don't think there is any such thing as math at the K-12 level that isn't "real world." What teachers and others mean when they say it isn't "real world" is either that it focuses on the concept/practice level instead of the applicaiton level, OR that it involves applications that they personally don't find engaging.

Sunday, January 2, 2011

Favorite comments of '10: Deirdre Mundy on 4th grade Investigations

Deirdre Mundy

As an experiment, I tried a few "people, spiders and bunnies" problems on my 6 year old (saxon math first grade book educated) daughter.

If a first grader can do these in her head (adding rather than multiplying, but still...) then they are WAY to easy for a fourth grader, IMO....

Favorite comments of '10: Liz Ditz and Anonymous on why there are so many ieps

Liz Ditz

The more I work with kids who struggle, the more I think the big culprits are:

1. Developmentally inappropriate expectations beginning in kindergarten
2. Failing to teach handwriting to mastery in k-3
3. Failing to use evidence-based instruction in reading and mathematics.

Some of this may be classified as "dysteachia" but you cannot teach what you do not know -- our teacher preparation programs are deeply at fault.


I got a 504 for one of my child because 
1. she is bright
2. she can't handle the endless repetition in mixed ability classroom
3. She will cause trouble if she has no work to do in class.

I would have gotten a 504 for my older child if I had known about them early enough. 

I have an IEP for my youngest. 

They likely have no learning disabilities aside from dysteachia. However, the only tools I had to use to get appropriate schooling was a 504/IEP. When all you have is a hammer, everything becomes a nail.

If I could have gotten my kids into a homogenous class, I/they woud not have needed a diagnosis.

Favorite comments of '10: gasstationwithoutpumps, Knowledge Based Science and Set on relevant science projects


It isn't just teachers but science fair judges who have raised application on a pedestal. A very good pure math project will lose to a mediocre math project that pretends to be applicable to traffic patterns or to the environment. In the past three years, the best way to get awards at the state level in California was to claim your project was related to health or the environment. Quality was definitely second to application area. (Disclaimer: I was a judge at the California State Science Fair one year and I saw this bias among my fellow judges, but I did not do a rigorous statistical test to determine if what I was seeing was more than expected by chance.)
November 10, 2010 11:30 AM

Knowledge Based Science

It's not just teachers and science fair judges, though. This is the position advocated by the largest professional organization for science teachers, the NSTA. 

From today's NSTA email update (yes, I am a member):

The NSTA Board of Directors voted recently to adopt a newly revised position statement advocating for K–16 science instruction to be provided within the context of personal and societal issues. The statement recognizes the influence that science and technology have on our lives, and how these issues provide a rich and motivating context in which students can learn the principles and practices of science and technology. The draft statement gives recommendations on what students should know and be able to do and how science instruction should occur within the context of societal and personal issues.

It's in the water. I'm not sure what can be done about it, other than better organize those teachers with differing views, or maybe change the selection process in schools of education.

...The link to the actual position statement... includes the following gem:

The purpose of understanding science and technology is not solely for the sake of learning, but rather to enable and motivate citizens to contribute to and engage in society.

So...I guess that answers your question. Learning for the sake of learning? That's _so_ last century.



Sounds like excellent training for grant applications :)

Favorite comments of '10: gasstationwithoutpumps and FedUpMom on extra time and labeling

(The Lake Wobegon effect, with a twist: where no child is neurotypical)


I had noticed the tendency at a private school my son had gone to offer almost all kids "extra time" on tests. They even provided a "diagnosis" for my kid (by someone who had never even met him) to give him extra time, though he was always the first one done on tests and usually needed to have a book with him to keep from getting bored on test days. This bogus definition of learning disability resulted in over a third of the students at the school being "diagnosed". Probably only about 1-5% had LDs, as elsewhere.

I haven't seen the problem much at the university, though---only about 4% of students there register with the disabilities resource center.


"Executive dysfunction", don't get me started. My older dd got a "strike" against her in math class because she forgot to get my signature on her quiz. She did all her homework and had an A on the quiz, but now she feels discouraged because she forgot one stupid piece of paperwork? How does that make sense?

I had a conversation with the math teacher and he doesn't require my signature anymore. 

We are getting to the point where the requirements schools place on kids are wildly inappropriate for most kids. It's time to change the requirements. Inventing new labels doesn't help.

I don't even get the IEP business. When older dd was in public school, she had an IEP, because of her "gifted" label (and that's another discussion.) I'm not at all sure that any of her teachers actually read this document, and I don't see how it influenced anything they did. Public school is all about marching kids through the day lockstep. What difference does an IEP make?

Favorite comments of '10: Alexis Francis on explaining your answer

(Math problems of the week: 4th grade Investigations vs. Singapore Math)

Alex Francis

Wow. If the people who created the first assignment really believe that being able to answer it says anything about knowing how to do math, then they have completely confused declarative knowledge with procedural knowledge. By that reasoning, being able to explain "First sit on the seat. Then push off, put your feet on the pedals, balance, pedal and steer at the same time" means you know how to ride a bicycle...

Saturday, January 1, 2011

Favorite comments of '10: Hainish on writing about your feelings

(Autism diaries XXIII: Writing what you feel)


Others may disagree, but what I see again and again is that it all comes down to the personality type(s) selected for in the teaching profession.

If these people find it wonderful to write about their feelings, then of course they will ask their students to do so. And they will think that they are doing their students a favor.

My guess is that most new English teachers have less interest in grammar and linguistics than in the past, and are much more about self-expression and "creativity." It goes right back to the selection criteria used by schools of education.

Favorite comments of '10: Amy P and Joanne Jacobs on East Asians and creativity

(Skewing college admissions)

Amy P

"...they virtually eliminated the admissions edge enjoyed by some ethnic groups."

I think this is what it's really all about. He's afraid of having a campus with too many quiet, introverted East Asians, so they want to put a finger on the scale to keep their numbers down.

Joanne Jacobs

If writing a "creative" story based on a goofy prompt becomes part of college admissions, then super-striving, high-achieving Asian-American students will learn how to write "creative" stories based on goofy prompts.

Favorite comments of '10: Niels Henrik Abel, Anonymous, Anonymous, ChemProf on science museums and science entertainment

Niels Henrik Abel 

Reminds me of the hands-on "discovery" science museums where kids race from station to station, madly pushing buttons and scarcely waiting for the interactive exhibit to do its thing before running off to the next one. They're not discovering anything; it's all about noisy, flashy exhibits that amuse and entertain rather than educate.

"Science songs"? You've got to be kidding...


Niels comment is right on-I was at the Exploritorium in San Fran and the children did not stop to ponder the significance of what the interactive display was about-but just mindlessly went about each display as fast as possible. 
Your comment about the rigor and hard work of science is so true. Even scientists do not model this hard work when around students. They do the wow! factor too much. I teach Physics and my students ask to watch Bill Nye. I refuse to because as I tell them, he portrays scientists as goofs, and geeks and that science isn't always fun and games. I tell them the story of the medical research who spent 17 years working on a cancer treatment and found out after all the results came back, that it didn't work. What seemed possible initially didn't work when it came to human trials. 
Then, to my amazement, we watch a twenty minute video of Richard Feynman and they asked to see more when it was over! And he didn't mince words! 
DO not be afraid the challenge the kids with hard work!


Children do need exposure to science in order to develop the intention (and the persistence) to pursue it. But over-emphasis on the entertainment approach is a mistake. It's been called "science appreciation," and that's an apt term. What children really need is judicious exposure to the different science disciplines, plus a really solid math grounding, since there is no scientific discipline any more that doesn't depend on advanced math skills.
October 10, 2010 2:54 PM


Plus too much focus on science appreciation can leave even science majors with a strange idea of what scientists do. I have had so many students who, as sophomores or juniors, describe what they want to do, and it is to be a docent. Which is a wonderful thing, but as a volunteer, not a job.

Favorite comments of '10: Tor Hershman on Chess

(How about a friendly game of chess?)

Tor Hershman

"Who is to say that an intellectual, or collaborative, or competitive exchange is any less meaningful than the more emotional ways in which more typical people connect?"

Who? An insipid arse, moi supposes.