Here’s another sign that the “math wars” have intensified to a new level: a judge in Seattle sides with a parent, a retired math teacher and a professor at the University of Washington by rejecting a decision by the Seattle School Board to adopt the Discovering Mathematics textbooks by Key Curriculum Press. You can read more about it in this Seattle PI article and response from Key Curriculum Press.
The criticisms for the Discovering Mathematics series seem to line up with criticisms of “reform mathematics” in general. There are lots of people out there who believe that one should learn computational skills before concepts, that learning through inquiry or discovery is flawed, that an emphasis on concepts automatically means a shunning on . “Back to basics” is a common battle cry that is heard, and people often quote statistics or anecdotes about how poorly students are doing in mathematics “these days.” However, we frequently neglect to take a longer view of things. As Suzanne Wilson points out in her book “California Dreaming: Reforming Mathematics Education,” one can retrace the movement of the math curriculum pendulum in our country from “reform” to “traditional” and back again as early as 1830. This is nothing new, folks. Can’t we figure out how to stop having the same tired argument over and over again?
Though my school has not adopted the Discovering Mathematics textbooks, I’ve been a fan for a long time. I love the Discovering Geometry textbook in particular–I have been supplementing our geometry textbook with activities from this textbook. So, I am clearly biased on this matter.
Nevertheless, I feel I have some credibility in this matter as a university professor, as a current high school teacher, and as one who successfully learned mathematics in the “traditional” manner. Clearly, teaching mathematics in the traditional manner works–I am an example of that. However, I strongly believe that this manner of teaching mathematics generally favors the students who are already good at mathematics. I am the type of student who will try to figure out the logic behind a procedure if I can’t see why it works, but most of the students in my classes are not trained (yet) to think in this way. For these students, it is important that I try to help them learn concepts and procedures and to develop the habit of mind that leads one to ask “Why?”
Here’s a more concrete example. I could easily teach my students a three-step procedure for solving any linear equation of the form ax+b=cx+d. They would probably be able to follow the procedure pretty quickly. It is much more difficult to help them develop an understanding of what the equals sign means, why one can add or subtract something to both sides of the equals sign, and an intuition for what steps to take to isolate x by itself on one side of the equation. My experience has been that this constructivist approach has helped some students develop a much richer understanding of what it means to solve an equation. This week, a few students could explain to me, without me telling them, why any value for x is a solution to the equation 7(x+3)=7x+21. Of course, getting to this point required lots of practice on solving equations.
I believe that most of the sentiments espoused by folks on the “traditional” side of the math wars boils down to a discomfort with what is new or unfamiliar. Many of the people in this camp are parents, teachers and professors who don’t like it that current reform math education looks different from the mathematics of their youth. It seems to me presumptuous that one parent, one retired math teacher, one professor of atmospheric sciences and one judge would know more about teaching mathematics than the school board.
This decision also scares me in that it sets a dangerous precedent–does this mean that more and more curricular decisions are going to be made through our courts?
Finally, I’d like to close this blog post with a call for more calm. I wish people would stop fighting about textbooks and curricula. By itself, the choice of a math textbook cannot be a panacea or poison that will fix or ruin student achievement. This year I have witnessed first-hand that textbooks matter very little. There are so many other factors that affect my students’ mathematical performance: attitudes towards mathematics and education, life situation, self-confidence, language skills, parental support, teacher’s skill, teacher’s content knowledge, classroom environment, etc. The choice of textbook seems almost insignificant when you think about all of these things. In the language of asymptotic expansions, students and teachers have an O(1) effect on learning, schools have an O(epsilon) effect and textbooks are an O(epsilon2) effect. And even if the perfect textbook were written, it cannot teach itself; teachers would need training on how to use this miracle textbook and would want to use it. Teachers like to teach the way they were taught, teachers like to reuse things that they have used before, and teachers are under lots of other pressures to “cover” material that circumvent the recommendations of their textbook.
So, can we please stop arguing so much about textbooks now?