[Rescued from my old blog.]
From Time magazine, June 18, 1956:
“[M]athematics has the dubious honor of being the least popular subject in the curriculum… Future teachers pass through the elementary schools learning to detest mathematics… They return to the elementary school to teach a new generation to detest it.”
Quoted by George Polya in How to Solve It. I finally got my very own copy of this excellent book, so I can quit pestering the librarian to let me order it from library loan again…
Blogger Rudbeckia Hirta teaches math to pre-service teachers, and it seems that not much has changed since 1956. Hirta says the test answers shown were representative of her class — for instance, 25% of her students missed the juice problem. Too bad these students never read Polya’s book, in which he discusses a four-step method for solving problems. Step four is to look back and ask yourself whether the answer makes sense. Good advice!
What Is PUFM?
Mistakes like these demonstrate how important — and apparently rare — it is that teachers truly understand mathematics. We need to work at developing a profound understanding of fundamental mathematics (PUFM). This phrase was coined by Liping Ma in her landmark book, Knowing and Teaching Elementary Mathematics, to describe the deep, broad, and thorough understanding exhibited by several of the Chinese teachers she interviewed.
PUFM builds gradually over a lifetime of learning and teaching math. Homeschoolers may have an advantage in this, because we follow our older students from one grade level to the next, and then we go back and follow the same sequence with the younger ones, allowing us to see how math concepts build on each other through the years.
PUFM also grows as we discuss math with fellow teachers. The Chinese teachers that Liping Ma studied met weekly in teaching research groups to benefit from each other’s experience, to find multiple ways to solve problems, and to broaden their mathematical understanding. In America, most of us don’t have groups like that — although at least one school has tried something similar, with good results (unfortunately, the article I linked to here no longer exists online) — but we do have blogs.
On Let’s play math! blog, I hope to create a reservoir of articles that will help you understand the “why” behind the math topics you teach, as well as the “how” of communicating them to your students. I want to help you see the connections between mathematical concepts and build up your own PUFM. So if you have questions about learning or teaching math — if there’s anything about math that stumps you, or has never made sense, or you’re simply curious about — I’d love to hear from you!