Tuesday, November 14, 2006

NY Times on Math Ed

Apparently not everyone agrees that mathematics education research is the gold standard. In the NY Times today, there was an article on parents and mathematics professors rebelling against "fuzzy" math.
“The Seattle level of concern about math may be unusual, but there’s now an enormous amount of discomfort about fuzzy math on the East Coast, in Maine, Massachusetts and Pennsylvania, and now New Jersey is starting to make noise,” said R. James Milgram, a math professor at Stanford University. “There’s increasing understanding that the math situation in the United States is a complete disaster.”

Who is James Milgram? What research has he conducted in how people learn? This leads me to their website, refuting several of the NCTM standards, by citing 3 peer-reviewed studies (and numerous other opinion articles). There are thousands of papers written in mathematics education, so three studies does not make a case. (In particular Klahr and Nigam.)

It seems so strange to me who is "allowed" to criticize education, teachers, curriculum, and standards. Does succeeding at math make you an expert on how people learn math, or how to best teach math? Anyone who has taken a university mathematics course surely can answer that question with a "no."

This is not to say that learning the "basics" is a meaningless endeavor or should not be part of the standards (though I can't tell you the last time I did long division, and I use problem solving strategies daily). I just think the research is ongoing, we don't know the answer yet, and anyone who claims differently has a limited view of what it is to have learned math.

One interesting point that this article does raise is a parent quoting a teacher who notes: "We don’t teach long division; it stifles their creativity." The disconnect between the intent of curriculum and the perceived intent by teachers is worrisome.

Monday, November 13, 2006

What do we know about mathematics curricula?

Thinking about where mathematics education is, what science education can learn from them, and how science differs from math, has been intriguing to me lately. I rely on certain core ideas in reasoning about new problems in science: energy, momentum, certain conservation laws, symmetries-- and it seems to me that there are some key "content" ideas that can help anchor your science thinking. I wonder if this is different from mathematics.

Schoenfeld, describing a mathematics course in problem solving that is not tied to a particular "content" topic but rather to problem solving heuristics, quotes a conversation with the department chair. He's trying to get credit towards the major for students who take the course, and argues that students in this class can outperform senior math majors on difficult math problems. The department chair replies: "I'm sure you're right, but we still can't give credit toward the major. You're not teaching them content-- you're just teaching them to think."

Schoenfeld goes on to say (p. 4):

The moral of this story and the reason that I tell it is that it demonstrates clearly that what counts as mathematical content depends on one's point of view. From Professor Y (the dept. chair)'s perspective, teh mathematical content of a course is teh sum total of the topics covered...

I would characterize the mathematics a person understands by describing what that person can do mathematically, rather than by an inventory of what a person "knows."... Note that this performance standard is the one that Professor Y lives by in his professional life, and the one that he uses to judge his colleagues.

This course he describes feels similar to a science course I've co-taught, where the students brought in questions and then reasoned through them. Topics included "will a human blow up in space (or freeze)" and "why is the sky blue." But in these courses I didn't just provide guidance on heuristics or scientific thinking, but also added a lot of content-- about how things lose heat, how prisms work, etc. And while some students might be well-prepared to reason scientifically at the end of the course, I doubt they could go toe-to-toe with a student with more content knowledge.

from Schoenfeld, A.H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55 - 80.

Wednesday, November 08, 2006

Towards an agreement on the goals of science instruction?

At a conference here at LessonLab on the use of video in teacher education, I was struck by the lack of consensus on what we should be teaching in science, what good instruction looks like, what we're asking teachers to do and why. I kept thinking that the findings of others' studies can scarcely inform my research because I'm interested in very different ways of speaking, talking, and doing science.

Mathematics education, I frequently hear, is much "farther along." And the few presentations and papers I've read from math ed convince me that this is true. But is science ed even having the necessary conversations to become "farther along"?

Reading Schoenfeld's "Purposes and Methods of Research in Mathematics Education" and "The Math Wars" now provides some interesting background on what mathematics education research is all about.

He notes that there are two main purposes, on pure and one applied:

- Pure (basic science): To understand the nature of mathematical thinking, teaching and learning;
- Applied (engineering): To use such understandings to imporve mathematics instruction.

Simply put, the most typical educational questions asked by mathematicians-- 'what works' and 'which approach is better?'-- tend to be unanswerable in principle. The reason is that what a person will think works will depend on what that person values... Just what do you want to achieve? What understandings, for what students, under what conditions, with what constraints?

The appropriate way to proceed was to look at the curriculum, identifying important topics and specifying what it means to have a conceptual understsanding of them. ... As a result of extended discussions, the NSF effort evolved from one that focused on documenting the effects of calculus reform to one that focused on developing a framework for looking at the effects of calculus instruction.

Looking at the evolution of the mathematics standards and the spirit behind this document, I wonder if science education was too quick to replicate math's success and create its own standards?

As Bruner said:
To instruct someone... is not a matter of getting him to commit results to mind. Rather, it is to teach him to participate in the process that makes possible the establishment of knowledge. We teach a subject not to produce little living libraries on that subject, but rather to get a student to think mathematically for himself, to consider matters as an historian does, to take part in the process of knowledge-getting. Knowing is a process not a product. (1966: 72)

How do the science standards support this view of instruction and knowing?