Analysis of content-specific pedagogy in programs that grant mathematics single-subject credentials in California.

摘要

As many national and international studies have indicated, student performance in mathematics in the United States in general and in California, specifically, is less than satisfactory. While there are clearly numerous reasons for this low level of performance, many national bodies such as the NCTM have proposed that we need to seriously consider substantial changes both in the mathematics curriculum and in how teachers deliver instruction.;For purposes of this study, a new pedagogical model was developed. This study proposes that Shulman's ideas on pedagogical content knowledge be extended to include the structure of mathematics as proposed by Hierbert and Lefevre. When Shulman's theory is combined with Hiebert & Lefevre, a potentially effective model for conceptually describing the pedagogical tools that mathematics teachers need specifically emerges. This new model is named Secondary Mathematics Pedagogy (SMP). The purpose of this study was to determine to what extent SMP is a component of teacher training programs in California.;This study used a descriptive study design to gain understanding of the status of preservice secondary mathematics programs in the state of California with respect to SMP. Two main data sources were used: interviews with preservice mathematics teacher method course instructors, and a syllabi of mathematics methods courses were content analyzed.;There was a clear divide between instructors and how they viewed mathematical training. Some made decisions based on the number of undergraduate mathematics units a student would take. Others made the case eloquently that students with lots of mathematical courses did not necessarily work out to be good mathematical thinkers. Not surprisingly, it was the later group of methods instructors who tended to put a heavy emphasis on SMP within their methods courses. This study provides important initial evidence which indicates the SMP model is a critical factor in the training of today's high school mathematics teachers and that it appears that some preservice candidates are getting great exposure while others are left bereft.