kitchen table math, the sequel: Why we can't trust math professors...

Sunday, January 16, 2011

Why we can't trust math professors...

At least on k12 math education...

(Cross-posted at Out In Left Field

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.


Anonymous said...

Thank you, Katherine. What these sorts of math professors also forget is that for almost all K-12 students (including many headed for STEM occupations), being an innovator in math is not the goal. The goal is to be able to use mathematical tools to do something else, ranging from altering a recipe to reading a statistical table to doing basic engineering tasks. Sensible academics in other fields (and sensible math professors) realize that there are a variety of types of students and K-12 curricula should serve all of them, not just the most extremely talented.

ChemProf said...

I'd argue that for K-12 math, it is also important not to give mathematicians priority over faculty in other STEM fields, in terms of what students need to know. The mathematicians I know work in knot theory and topology. Their research involves developing proofs. My research, on the other hand, involves lots of more basic math -- graphing, algebra, basic calculus -- and so my sense of "what students need" can be very different than that of a mathematician.

Crimson Wife said...

The full professors at a place like Stanford don't teach freshmen. That chore is left to graduate students. I took a whole year's worth of calculus and a quarter of statistics at Stanford and never saw a full professor.

The only undergraduates full professors encounter are upperclassmen majoring in the subject.

Dr. Devlin should mosey over from the "Human-Sciences and Technologies Advanced Research Institute" to the Science & Engineering Quad for a conversation with some of the engineering profs. Perhaps he'd stop worrying so much about the so-called "achievement gap" and start worrying more about the dismal math performance among American students of all demographic groups.

bky said...

The Moore method is usually used in topology and number theory classes. It may very well be a good way to develop talented and motivated math students -- the kind who want to be mathematicians (e.g. anyone doing math-related research, physicists, mathematicians, etc) It would not be wise to nay-say it because of one's frustrations with constructivist teaching in k-12; nor would it be wise to say, gee, this works well for senior level and graduate topology courses, so it will do wonders for kids learning arithmetic.

Barry Garelick said...

It would not be wise to nay-say it because of one's frustrations with constructivist teaching in k-12;

Well, R. L. Moore himself said that his method (which he used for grad students in topology) was not appropriate for freshman calculus. Domain knowledge is key here. The trend toward inquiry-based classes in college is growing and from what I've seen of "reform calculus" classes using the method, the frustrations from constructivist teaching in K-12 are not out of place. One generally has wider latitude with inquiry-based approaches, the larger the domain knowledge. Scaffolding is still important and knowing the depth of the steps and the leaps students are able to make is key.

OrangeMath said...

As a note to Crimson Wife. I took the same courses you did and always had a professor. The only grad student teacher I had at Stanford was in my first and only CS class. This was a quality that set Stanford apart from other elite schools. I'm greatly disappointed that your experience was different from mine.

Crimson Wife said...

I wouldn't have had a problem with grad students teaching my math classes had they spoken English well. But they were all foreigners with thick accents and I had an awful time trying to understand their lectures.

All my science classes, by contrast, were taught by actual professors.

Lisa Jenifer said...

Yes, all mathematicians I know work in knot theory and topology. Their research must contain developing proofs. My research, on the other hand, involves lots of more basic math -- graphing, algebra, basic calculus, and so my sense of "what students need" can be very different than that of a mathematician. I have found this website helpful to learn math Fun Math Worksheets.