Understanding the Math Wars, Implications for Science

In the American Journal of Physics-- a journal for which most of the publications are physics professors sharing interesting problems/labs/ideas, but also some interesting physics education research-- the following editorial was published this month:

School math books, nonsense, and the National Science Foundation


The editorial itself isn't too surprising; it's the kind of editorial that shows up in newspapers and websites when mathematics education reform curriculum is introduced. And it's from a vocal critic of those reforms. What is surprising is that the AJP decided to publish it, with all of its ranting rhetoric.

Some history on the Math Wars is necessary for understanding how to interpret Klein's editorial.

I think science education has different concerns: for one, most parents have less expectations about what students should learn in science than they do for math, are less likely to think they use traditional science content every day, and so are less likely to be vocal opponents to reform curricula. Also, people have an image of scientist as a doer of experiments; a mathematician (perhaps?) they think of as a knower of math. (Actually, I wonder what most people think that mathematics professors do all day?) So science-as-activity is easier to pull off.

But it is concerning that this shows up in the AJP. I composed an editorial in response. (Tried attaching it to no avail. I'll try again later.) We'll see if it gets published.

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.

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.