Using the results of diagnostic testing to promote mathematical pedagogical knowledge

Teachers require a range of knowledge bases, including both content knowledge and pedagogical knowledge (Shulman, 1986). In recent times there have been calls from a variety of sources for teacher preparation courses to improve the mathematical knowledge of teachers, particularly primary teachers. These calls have been underlined by the recent formation of bodies such as the Institutes of Teachers in Victoria and NSW, as well as the development of teaching standards by professional bodies including the Australian Association of Mathematics Teachers. Rather than simply adopt a "back-to-basics" approach, work is required that uses the results of educational research to design courses that help pre-service students to understand how and why errors are made (by themselves and by children in their own classrooms). Diagnostic testing of preservice students is the first step in the process. However, it is not enough to simply test students and to remediate their misconceptions. Instead, the aim is to use the results of the testing to improve students' pedagogical knowledge as well as their subject content knowledge. This paper outlines one approach to the use of diagnostic testing with pre-service students and how the results can be used to assist in the development of pedagogical knowledge.