Professional Development for Teachers of Mathematics

In the initial preparation of teachers at both the elementary and secondary level it is imperative that the Curriculum and Evaluation Standards for School Mathematics written by the National Council of Teachers of Mathematics (1989) be used as the mainstay of the mathematics methods course presented in the teacher preparation program. Future teachers must become acquainted with the framework of the Standards to meet the challenges they will find within their classrooms. The goals of the Standards can be the guide for these teachers in developing their philosophy of teaching mathematics. In many mathematics methods courses, the Standards are required reading at all levels of preparation for future teachers of mathematics. In these courses, each section of the Standards is discussed and analyzed and appropriate modeling of teaching strategies are incorporated to emphasize the major strands of the Standards. With an exposure to this research-based instruction, future elementary, middle, and secondary school teachers can develop a perspective to better understand what is required of their students to function competently in mathematics. Students in the methods courses see the Standards modeled in class presentations. Lessons are presented by the instructor focusing on the use of concept development with manipulatives, problem solving as a content area as well as a methodology, and cooperative learning techniques with emphasis on the teacher's role as facilitator. Communication skills are stressed and the use of a journal is encouraged. Students in the methods courses are required to keep a journal to reflect on presentations made in class and also to reflect on the observations made during their fieldwork experiences. The future teachers are required to make lesson presentations in class which reflect the spirit of the Standards. Teaching strategies include the use of manipulatives, visual aids, grouping techniques, and integration of technology. New mathematical topics to focus on include estimating, writing and communicating, connecting mathematics to real life, and using a variety of problem solving strategies. The remainder of this article will focus on methods used in training teachers of mathematics at the elementary, middle, and high school level to reflect the strategies suggested in Standards. The discussion focuses on the components of mathematics teaching recommended in the companion document Professional Standards for Teaching Mathematics (1991)--tasks, discourse, environment, and analysis. Tasks An excellent mathematical task to use in training future teachers is to use the journal as a means of communicating observations about mathematics and the teaching of mathematics. Pre-service teachers use the journal or log to keep a written account of the on-going development of their depth of reflection on teaching. Entries can include reflections on a lesson just presented, an observation jotted down concerning a pedagogical technique discussed during class or, perhaps, a summary of the past week's fieldwork visitation. Ball and Schroeder (1992) define tasks as the projects, problems, constructions, applications, and exercises in which students engage to develop competence in mathematics. The journal is an excellent project to reflect one's competency level in mathematics teaching. The following passages are excerpts from journals to illustrate the reflective process. The first passage is written by a pre-service teacher"who was concerned about classroom timing, student involvement, and closure of the lesson. "I thought my lesson went very well. I did not realize the lesson would take a full 50 minutes but it did not seem that long. This was a lesson I created solely around a worksheet I found while doing my calculator paper. I was glad I made use of the overhead projector but I should have gotten more students involved. . .I liked the way I wrapped up the lesson with the use of the journal. …