In my mathematics courses designed for prospective teachers, a primary goal is to have each student begin to develop an advance perspective on the mathematics that they will teach. There are varied opinions about what it means for a teacher to have an advance perspective, and with these opinions the related views of what mathematics teachers need to know to teach well. Yet there is general agreement that high quality teaching at the K-12 level requires a deep understanding of school mathematics, or a “Profound Understanding of Fundamental Mathematics” (Liping Ma’s, Knowing and Teaching Elementary Mathematics). If teachers at all levels are to teach mathematics as a coherent, reasoned activity while communicating an appreciation of the elegance and power of the discipline, then math courses designed for prospective teachers must foster the development of a deep understanding of the mathematics that they teach.
On this web site I have included selected activities that I have found promote such development. Most of the activities come without explanation for their use, so please take ideas from these pages at your own risk.
If you are relatively new to mathematics teacher education, the following may be helpful:
1. For background on what it means for teachers to have a “deep understanding” of school mathematics, I suggest Liping Ma’s book, Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Mahwah, N.J.: Lawrence Erlbaum Associates, 1999. (ISBN 0-8058-2909-1).
2. For a general vision of the kinds of courses that prospective teachers (elementary, middle, and secondary) should take, see the Conference Board of Mathematical Sciences (CBMS) publication http://www.maa.org/cbms/MET_Document/index.htm on the mathematical preparation of teachers. The full report and a brief executive version are currently available through the American Mathematical Society.
3. For a description of school mathematics, the new Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics is on-line at http://www.standards.nctm.org There are no-doubt State standards where you work that are worth reading. I suggest that you look up your state department of education on the web and locate the mathematics content standards in your state.
4. For professional development in mathematics teacher education, I highly recommend the Association for Mathematics Teacher Educators – a professional organization devoted to just this topic. For more information, see http://www.amte.net