Winning the Math Wars: No Teacher Left Behind

Introduction

3 Introduction A student remarked recently that high school geometry “was the most boring class I ever had in my life,” despite the fact that he was very interested in math and science. As he looked back on his high school math classes, he realized that what he had chosen to study in college and beyond had been seriously, and negatively, conditioned by this high school experience. Now graduated from college, the student wondered how different his future might have been if he had learned math in a different way. “We memorized formulas and proofs; if the teacher had taken me outside and shown me that I could find the distance to an unknown point just knowing an angle, I would have been much more engaged with the question and understood geometry as a discovery possibility.” This is not an isolated comment; no doubt everyone reading this book has heard similar things about math classes.Whether or not a student learns geometry well is a function of many things, not the least of which, of course, is the extent to which he or she is engaged in the subject and the extent of his or her overall aptitude for learning. It is important to point out, however, that the reasons for learning mathematics well often lie “outside” as well as “inside” the individual. Learning is related not only to the student’s own motivation and capability, but also to the nature of teaching, the curriculum in use, features of the learning environment, district policies that affect math offerings, and so on. One Introduction 4 could argue, for example (and it has been argued forcefully and repeatedly), that if the teacher were more interesting, the problem would be solved. But the same “inside/outside” dynamic applies. Whether or not the teacher is “more interesting ” is a function of the teacher’s own motivation as well as other factors: Is professional development relevant and timely? Do other math teachers regularly interact on lessons and about individual students? Do district policies ensure an adequate support system for mathematics instruction? Researchers, practitioners, educational leaders, parents, and policy makers all have suggestions about these and other factors and how they can be changed to positively impact student learning in math. Moreover, these individuals and groups can have very strident opinions that are often in conflict. Who is right and who is wrong? One of the main premises of this book, consonant with much previous research, is that the teacher’s role is critical. Teachers stand between the students, with their mixed readiness to learn, and the school system, which can be helpful or harmful to a teacher’s efforts to provide meaningful learning experiences in the classroom. We therefore want to note the elements of current and proposed educational reforms that have the potential to leave math teachers behind.We hope to underscore the need for supporting teachers to do their best in what they are called upon to do. Four Critical Insights Over the course of our research, we identified several factors that seem to affect the nature of math education reform and student academic achievement. Our insights are not necessarily new, but they do suggest new directions for resolving the debates about how to improve math teaching and learning. Introduction 5 1. Fidelity Reform efforts have not led to improved student outcomes because teachers have not been given the support necessary to change/align instruction with the standards-based system of education. Our research suggests that tests of mathematical achievement do not tell us much about the value of reform efforts because these reforms have not been implemented fully. Reform efforts may be unsuccessful because teachers are not given the support necessary to change the way they teach or even to understand the mathematical and pedagogical ideas at the center of the reformed curricula. The most sophisticated and wellconceived reform effort imaginable may fail because the means of carrying it out are not in place.This is a two-fold problem. First, fidelity to reform efforts usually requires change in the approach to teaching and learning. Faced with a lack of appropriate resources and information, school leaders and teaching staff may revert to what they have always done rather than grapple with the new expectations.The second problem relates to support: Is the reform effort comprehensive? Changing one part of a system may be helpful, but if the entire system is not changed and aligned with reform principles, the partial effort...