Prospective Teachers' Subject Matter Knowledge of Similarity

Abstract

Teachers' knowledge of the subject matter needed for teaching is seen as diverse, multidimensional, and vital to a teachers' knowledge base for teaching (Ball, Lubienski, & Mewborn, 2001; Cooney & Wilson, 1995; Even, 1993; Grossman, Wilson, & Shulman, 1989; Ma, 1999; Shulman, 1986; Thompson, 1992; Wilson, Shulman, & Richert, 1987). Understandings of subject matter knowledge become important when researching students' conceptual understandings because teachers' knowledge of organization, connections among ideas, ways of proof and inquiry, and knowledge growth within discipline are important factors needed to teach the subject.

Some research has been done on secondary mathematics teachers' subject matter knowledge (e.g., Cooney, Shealy, & Arvold, 1998; Cooney & Wilson, 1995; Even, 1993; Leinhardt, 1989; Leinhardt & Smith, 1985), however, today抯 studies tend to report more on elementary prospective and inservice teachers' subject matter knowledge rather than the knowledge of middle grades and high school prospective and inservice teachers.

Therefore, the focus of the research is in reaction to researchers' statements about research and teachers' subject matter knowledge (e.g. Ball et al., 2001, Borko & Putnam, 1996; Schoenfeld, 1999) and is driven by two interrelated questions: (1) What is the nature of the subject matter knowledge that prospective teachers rely on when planning a lesson to introduce the concept of similarity, and (2) What growth in the subject matter knowledge of similarity is revealed as prospective teachers plan a lesson to introduce the topic.

To analyze the subject matter knowledge of similarity that prospective teachers rely on when planning a lesson to introduce the topic of similarity, the transcripts of the interviews, the group presentation, and the written artifacts from the final individual lessons were coded using Even抯 (1990) seven aspects of subject matter knowledge and Shulman抯 (1986) three forms of teacher knowledge. The growth in subject matter knowledge of similarity was assessed within the Berenson, Cavey, Clark and Staley(2001) adaptation of the Pirie-Kieren (1994) model noting instances of folding back, collecting, and thickening. Within each level of the Berenson et al. model, Even抯 (1990) aspects of subject matter knowledge were looked at for potential growth in the context of what and how to teach.

Results from the study show that the prospective teachers' ideas of what and how to teach focused on procedural generalizations conveying meanings. In some instances the prospective teachers used one or two examples of procedures and expected students to make generalizations from these examples. Another result from the study was that the prospective teachers' images of what and how to teach had to contend with their belief structures about teaching and learning. The prospective teachers in the lesson plan study relied heavily on their belief structures about teaching and learning and changed them minimally. Another result from the study is that the prospective teachers' starting place for growth in the subject matter knowledge is determined by their existing knowledge. The implications of this conjecture are that teacher education programs need to find ways to benefit from the vast knowledge and backgrounds of all their prospective students. Lastly, prospective teachers were limited in their substantive and syntactic knowledge of the concept of similarity. The prospective teachers seemed to fixate on particular aspects of similarity; however, the connections between these facts and the proof they established in their lessons were in need of reinforcement.