Sunday, March 14, 2010

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.

3 comments:

Anonymous said...

Mathematicians and social skills are inversely correlated - ask any college student and they will surely agree that most mathematicians are aloof, dress slovenly and have little to no social skills.

Amy P said...

"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."

Definitely. I suspect the social skills are specific to the area of interest, and may not generalize.

"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."

Right. There's a big difference between two mathematicians or two philosophers who are on fire for their subject talking about a problem that they have chosen to work on, and two elementary school students talking about a problem that somebody else has chosen for them.

"Mathematicians and social skills are inversely correlated - ask any college student and they will surely agree that most mathematicians are aloof, dress slovenly and have little to no social skills."

Do you know the joke about what the difference is between a normal mathematician and an extroverted mathematician--the extroverted mathematician looks at the other guy's shoes.

Seth said...

I've heard that joke for computer programmers as well. Whenever there are one-too-many meetings at work, I "joke" that one of the reasons I got into computers was so that I wouldn't have to talk to people.

It would be interesting to consider the working independently/in groups
question for programmers as well. I suspect for the vast majority of programmers, there are some core design issues for which it's good to talk it over with others, but for a lot of the work, it has to be done individually. I've been in lots of conversations that end "Let me figure it out and I'll get back to you."

Somewhat related, I've often wondered what would happen if some of the undergraduate or graduate computer science curriculum was taught to 3rd or 4th graders. I don't see why it couldn't be done. Is there any sense in which regular expressions or push-down automata are harder than long division? ie, not computers, but computer science.

(sorry, haven't read your book, so don't know if I'm repeating or contradicting you or whatever.)