On May 21 I gave the following presentation at a meeting of the Prince William County Virginia School Board concerning mathematics textbooks and programs.
May 21, 2008
Dear Board Members:
During my tenure on the National Mathematics Panel, I heard testimony from many sources including parents, teachers, textbook publishers, college presidents, mathematicians, technology specialists, and a host of researchers. I also listened to and learned from the other panel members even though at times we had varying opinions on many topics.
One item that we all seemed to agree on from the start was the need for a focused coherent K-8 mathematics curriculum leading up to algebra. We were tasked with determining the critical foundations for success in an authentic algebra course. Skip Fennell, NCTM president at the time headed up the Conceptual Knowledge and Skills task group. He along with mathematicians and researchers on the panel suggested a list of algebra topics and the critical foundations necessary for learning those topics. As a practicing middle school mathematics teacher of thirty-five years my input was valued heavily by Skip Fennell’s task group.
After two years of peering over many reams of research, the panel reached conclusions that I had always assumed were no brainers. For instance, students need to learn and use the standard algorithms in order to succeed in grasping the critical foundations leading up to and including the topics of algebra. If one cannot make use of the division algorithm, it is highly unlikely that they will be able to understand and perform division of polynomials nor will they be able to solve higher level equations .Your mathematics program should require fluency with the standard algorithms for addition, subtraction, multiplication, and division. Fluent use of the algorithms not only depends on the automatic recall of number facts but also reinforces it. Your mathematics program should also require that students have proficiency with whole numbers, fractions, and particular aspects of geometry and measurement. Our student’s proficiency with fractions seems to be presently lacking in many classrooms.
Your task is to select mathematics curricula that will allow your teachers to teach the critical foundations of algebra so that students will be prepared for an authentic algebra course, not just in name only. You need to adopt focused coherent textbooks that students, parents, and teachers all understand and at the very minimum, I suggest that you allow your individual school faculties and their students a choice in textbooks and teaching methods.
I served on the Instructional Practices Task Group and one of our main findings was that all – encompassing recommendations that instruction should be entirely “student centered” or “teacher directed” are not supported by research. If such recommendations exist, they should be rescinded. If they are being considered, they should be avoided. High quality research does not support the exclusive use of either approach. I suggest that you offer mathematics programs and textbooks that will not force teachers to exclusively use one type of instruction.
During my thirty-five year teaching career, I have always had the following minimum expectation for even an average textbook: I would assign myself a topic to learn. I would find that topic in the textbook and pretend that I was a student or a teacher who had a weak background on that particular topic. Was the presentation of the topic in the textbook focused and coherent enough for me to adequately learn the material? Were there clearly written non-infested examples? Were there enough practice problems of varying levels and were they actually related to the topic?
At a minimum, a mathematics textbook should possess the above traits and should also cover the critical foundations found in the National Math Panel Report.
Sincerely,
Vern Williams
