Friday, January 19, 2007

Math Education: An Inconvenient Truth

A little over two years ago, in a posting comparing schools here in the Seattle suburbs with those in the Gainesville, Florida area, I wrote, "... Northshore uses the Everyday Math textbooks, while Alachua uses Harcourt Math. Both series are, in our opinion, excellent." That was from my wife's and my points of view as parents of a second-grader, with whom we work outside of school on supplementary math and other subjects. As the YouTube video linked from the subject line above indicates, our assessment probably isn't reflective of the full K-8 experience of most families.

First off, go right now and watch the video; it's excellent. Seriously, watch it.

My opinion of Everyday Math was based on two of its aspects:

  1. Because of its spiral approach, it introduces algebraic concepts very early and at a level that seemed appropriate for those children.
  2. It has some very interesting ways of teaching concepts such a addition and subtraction that seem, to me, to make their relationship as inverse operations intuitively obvious. Again, a more advanced concept introduced in what seemed an age-appropriate manner.
It is important to keep in mind that this was coming from a parent of a child who was far ahead of her grade level in math (not to brag, but as a fourth-grader, she is doing seventh-grade math) and who did extra work at home. The YouTube video points out some matters that have become much clearer as time has passed and my children have worked with math textbooks in higher grades.
  • There's not much practice in the textbook. This is offset by extra materials used by teachers in our school here (such as Mad Minute), and by our own use of the Singapore Math books.
  • There's all sorts of irrelevant materials in the textbook. A chapter on patterns has a page on Native American crafts, but that page says nothing about the patterns in those crafts. It's basically a generic, too-brief overview of such crafts. Certainly, there is a strong connection between weaving and patterns, but nothing is said about that there. We fix this ourselves by talking about such issues.
  • Exercises at the end of sections are a mish-mash of all sorts of problems. On the one hand, review is good. But why have the first problems in a section of a late elementary or early middle school textbook be a series of very simple addition or subtraction problems? It distracts the child from the topic just learned, and makes her wonder if maybe there isn't some sort of trick involved and those problems aren't as easy they seem. It could have made her less secure about her math ability! (Actually, by this point, our older daughter is quite cynical about these "baby problems" and isn't bothered by them.)
  • It has all sorts of bizarre approaches, such as those detailed in the YouTube video (did I mention that you should really watch it?). Stuff which leaves me wondering if the authors were on peyote when they wrote that section. For our daughters, these are just random and interesting things, and they rightly dismiss them as inefficient and confusing. They ask their teachers if they have to do it that way, and do so for the few problems where it's required, reverting back the much more efficient, standard algorithms they are familiar with.
As a Computer Science professor, my observation is that I can see the effect of this approach to education. At the end of my third week teaching freshman calculus (I plan to blog about that shortly), I have noted that the de-emphasis of topics such as division of fractions impacts college-level math. Unfortunately, we're on the quarter system here, and so there's not much leeway to address these issues in class. However, I am making a mental note for myself to discuss this with our Quantitative Skills Center folks; maybe a review of K-12 textbook content would provide some ideas for remediation. In the final analysis, that is what these textbooks have done: pushed topics they think too time-consuming into university education time.

Additional Links: Reviews of UCSMP Everyday Mathematics, Where's the Math?, Donald Simanek's documents and links on education.

Topics: , .

No comments:

Post a Comment