| The question of subject matter knowledge of a good teacher of mathematics has been addressed over many years from the seventies to the present. Much has been written about what teachers ought to know, but there is very little documentation of what pre-service elementary teachers do know. My purpose was to document the mathematical subject matter knowledge of pre-service elementary teachers during the time they were taking their two semester required mathematics content sequence. My intention was to give a baseline so that instruction in content might be improved.; I conducted an intrinsic case study with two students, neither of whom intended to specialize in mathematics. Data collected included class observations both semesters, interviews, journals and mathematical autobiographies, as well as all homework, essays, quizzes and tests written during the second semester. Using Ball's (1988c) delineation into knowledge of mathematics and knowledge about mathematics, the data were categorized according to the five types of knowledge of Farnham-Diggory (1992): declarative, procedural, conceptual, analogical and logical. I also monitored their metacognitive skills. Prior studies have pointed out the importance of beliefs (Benbow, 1996; Kight, 1991; Pulver, 1996). I explored their beliefs about the nature of mathematics as well as their beliefs about learning and teaching mathematics.; The students differed in the knowledge they demonstrated not only by topics but also in how the five types of knowledge influenced each other. One student, who believed she would only teach small children and who saw mathematics as numbers and arithmetic operations, was very procedure oriented. Her algorithms influenced her conceptual knowledge. The other student, who believed she might teach any grade and whose beliefs about mathematics included patterns, logic and connections with other content areas, demonstrated that her conceptual and logical knowledge influenced her declarative and procedural knowledge.; Both students showed that their analogical knowledge effected the other types. This reliance on analogical knowledge suggests a way of improving teacher preparation by encouraging the growth of analogical knowledge. |
