By now you may well have read an op-ed piece called “How to Fix Our Math Education” in the August 25 edition of the New York Times. The authors, Sol Garfunkel and David Mumford, argue for replacing the current typical high school curriculum with one “focused on real-life problems.” The article has already generated some interesting discussion in the readers’ comments section, and as I type it’s number one on the “most emailed” list. I appreciate the emphasis on the concepts of quantitative literacy and mathematical modeling; the more these terms enter the public discourse, the better.
However, I have several concerns about the article, and find the reasoning, well, sloppy. First, there’s that title. Something like “How to Improve Our Math Curricula” would more accurately describe their thesis. If we want to “fix” math education, we need to pay attention to much more than the curriculum. Even if we restrict ourselves to in-school factors (though family income, parents’ educational backgrounds, and geography play huge roles), teachers are more important than curriculum.
Second, the authors assume that all high school math classes ignore real-life problems. This is not true at the public school my sons attended (see this, for example) or the one where my students and I observed classes, and it’s not what I hear from my students. To find out what’s actually happening in schools, one needs to do much more than look at standards or curricula (which are not the same thing, by the way).
Third, the article mentions the Common Core standards (available here) without noting that the Common Core includes “Standards for Mathematical Practice,” which state (among other things) that “(m)athematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize… and the ability to contextualize.” There’s also a standard called “Model with Mathematics.” One has to wonder if Garfunkel and Mumford bothered to read the document they criticize.
I could go on…if the point is to apply math in other areas, why not push for math across the curriculum as has been done with writing? Have you ever tried to teach “how computers are programmed” to someone with weak algebra skills? (I have; it’s painful.) Doesn’t public education have a higher purpose than simply preparing students for “21st century careers”? Fundamentally, though, I’m annoyed that two mathematicians (of all people) would propose a single silver bullet for a very complex problem without closely examining their own assumptions.