Monday, March 12, 2007

PUUPh ("puff") Give

Background: Tough Choices or Tough Times, the December 2006 report from the National Center on Education and the Economy (NCEE)'s Commission on the Skills of the American Workforce - these are the folks who brought you A Nation at Risk in 1983 and kicked off the standards movement; Taking Science to School, the 2006 report from the National Academy of Science's Committee on Science Learning, K-8; LiPing Ma, Knowing and Teaching Elementary Mathematics (1999).

Mainstream K-12 reform takes it pretty much as given that America's math and science teachers aren't good enough at math and science, and that this deficit is affecting our students' learning outcomes. For example, one of the key reforms advocated in Tough Choices or Tough Times is to move somehow from today's world, characterized as one in which most teachers come from the bottom fifth of college graduates, to a world of tomorrow in which most teachers come from the top fifth.

One of the key texts to have in the back of your mind in this discussion is LiPing Ma's must-read book, Knowing and Teaching Elementary Mathematics. Ma coined the term PUFM (pronounced "puff-em"), which stands for Profound Understanding of Fundamental Mathematics. If you have PUFM, then you probably know a slew of different algorithms for long division, half a dozen ways to explain why you need a common denominator to add fractions, and just why it is that dividing by a fraction is the same as multiplying by its reciprocal. The book argues that while elementary math teachers in China can do all this stuff, elementary math teachers in America are fuzzy on it - with consequences for student outcomes.

Sometimes I think that the standards people may have confused the need for teachers to have PUFM with the need for six-year-olds to have PUFM, but that's a post for another day. In the meantime, what seems to be clear is that you need PUFM to teach -FM.

Elementary math is not intellectually trivial stuff, by the way. The base-10 place value system is a towering achievement in human intellectual history - not to mention relatively recent in the scheme of things. According to my old copy of The World of Mathematics, the standard algorithm for long division dates from as recently as 1491!

Although the teacher-quality critique is pretty standard talk in K-12, I have often wondered at the apparent lack of any analogous concerns in the higher-ed setting. I guess one reason would be that it is academics who define what expertise is - and, being pretty satisfied with themselves, they have decided that expertise means a Ph.D. But of course, having a Ph.D. in physics mostly means that you spent an intense five or six years in a laboratory (or, for the theorists, in a cafe) pushing the frontiers of human knowledge or what have you. It would seem that this is poor training for teaching freshman physics.

Graduate students in physics nowadays take teaching seminars, but to order of magnitude, this activity amounts to roughly 1% of the integrated mental experience of a graduate program. 0%+1% is infinitely larger than 0%, and the results show it. But if you were serious about creating teachers of undergraduate physics, wouldn't you spend more like, say, 50% towards that end?

Why do the people who teach physics majors the core curriculum have to have research Ph.D.'s, anyway?

Or let me put it another way: Why are physics majors systematically denied the opportunity to learn physics from people with substantial training in the teaching and learning of physics?

Just brainstorming for a minute here, I am seeing two kinds of academic appointments in a higher-ed setting: an instructorship appointment, in which teaching craft and teaching effectiveness really matter, and a research appointment. To hold the research appointment, you have to do the usual Ph.D. To hold the teaching appointment, you have to do a teaching-intensive graduate program. Students majoring in physics would take courses from the instructors, but also take topic seminars with the researchers. In the topic seminars, researchers are allowed to do what they do best, which is to give inspirational and completely incomprehensible PowerPoint presentations.

Instructors will also, by the way, hold part-time research appointments to work in the research labs and contribute to frontier projects, though they won't lead these projects the way researchers do.

So, what do the instructors learn in graduate school? You guessed it: they learn PUUPh! (pronounced "puff"). Profound Understanding of Undergraduate Physics. The curriculum for this writes itself: intensive work on the force concept; common difficulties with the field concept; multiple ways of looking at the derivative [as a slope, as a rate, as a marginal return, as a functional] and the integral [as an area, as an accumulated change, as a functional]; dimensional analysis; lots of ways to explain line and surface integrals; intensive work on the conceptual foundations of stat mech and its relationship to phenomenological thermodynamics; linear algebra with special attention to vectors-vs.-components; special relativity with lots of discussion of the paradoxes; quantum theory with attention to identical particles, the meaning of the wavefunction; making arguments of a tensorial character; etc.

The vast majority of practicing physicists don't have PUUPh, any more than practicing mathematicians have PUFM. Unless you're invited to slow down and ponder the intricacies of some of these rich ideas, you get by perfectly well without doing so. I learned a lot about F=ma by writing a book about it, long after I'd become able to apply it to my professional work. And I leave aside the issue of pedagogical content knowledge - not just knowing what a flux integral is, but knowing five ways to explain it and a dozen excellent problems to assign for it.

In addition to doing a better job with the basic content for the physics major, with the right training instructors would also be able to do much more interesting things for non-majors. I'm thinking along the lines of the recommendations in the recent National Academy of Sciences report Taking Science to School, another worthwhile read. This report's recommendations are for K-8, but frankly even the colleges are utterly failing to do this work. Doing better here will require college science teachers to learn much more about the kinds of misconceptions and naive theories that 18-year-olds come to college with. A subject for another post....

P.S., a prize for whoever identifies the allusion in the title!


Anonymous said...

From a friend's email:

there are folk who have been working on these issues in algebra for the past few years and have expanded/refined some of the categories of knowledge and developed assessments that turn out to distinguish among teachers and where the scores have even turned out to corollate with student achievement scores.

Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.

Hill, H., Schilling, S., & Ball, D. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30.

Liping Ma was one of Deborah Ball's graduate students. The world is small.

JasonZimba said...

By the way, it's not clear that adding a role like this to the large university setting would cost any more money. Freeing researchers of their teaching duties would increase their research productivity, allowing you to have fewer of them if you want. Another effect, perhaps smaller, is that freeing them of teaching would allow the university to attract them at lower salaries. But I admit I don't have a great sense of the economics of the thing as a whole.