The Role of a Learning Community in Changing Preservice Teachers' Knowledge and Beliefs about Mathematics Education.

摘要: Commonly, preservice elementary teachers bring to their professional studies deeply rooted ideas about teaching and learning mathematics. These are embedded in the content knowledge, pedagogical experiences, epistemological orientation of prospective teachers. They view mathematics as a fixed body knowledge that is best learned by memorizing facts rules procedures for applying them textbook exercises. role teacher carrying out goals determined text material, providing demonstrations examples tasks be completed, checking assignments completeness accuracy. expect preparation program provide techniques make efficient effective. This conception education contrasts with nature creation discipline [Davis Hersh, 1981], it denies children's natural capacity interest understanding mathematical [Resnick, 1983; Riley, Greeno & Heller, Romberg Carpenter, 1986]. Further, conceives matter technical competence rather than reflection decision making based on what children coming know. The literature impact study teachers' beliefs points difficulty overcoming ingrained notions developed during previous school experiences [Ball, 1988; Feiman-Nemser, Tabachnick, Popkewitz Zeichner, 1979-80; Densmore, 1987]. If we cause rethink these beliefs, must create situations where faced reconsidered. demands powerful interventions challenge yet safe which students can take mathematical, emotional, intellectual risks. Creating community learners shared responsibility holds promise such an environment [National Council Teachers Mathematics, 1989a, 1989b; Schwab, 1976]. What building likely contribute teach mathematics? We have ample evidence isolation from interaction others result students' constructing worlds little fit accepted "truths" [e.g., Erlwanger, 1973]. One might extrapolate experience personal interactions others' exploring itself would lead equally impoverished views means Thus, one's private world exposed has potential learner's currently held construction more acceptable views. It through give one-to-one begins. Opening up oneself can, Schwab [1975] puts it, happen "in one only waythrough speech, talk" [p. 32]. He argues classrooms "rich occasions this symbolic exchange" " eans convey receive recognitions personality [,..]convey[...]the mutual support difficulty" "find sources help giving help" 2]. believe valid act receiving help, being nurtured, important. Of equal importance, especially teachers, help. However, herein lies traps-distinguishing between given telling, results dependent learners, questioning collaborating, empowered learners. Do insist telling how solve problem or do they ownership contributing prompts, questions, counterexamples wrong dir ctions, strategies thinking situatio ? former moves quickly but few truly encounter its solution. latter approach open shape who gives emphasis meaning key changing curr nt conceptions mathemat cs. I build schema use flexible way new situations, then develop disposition seek ways sense ideas. Establishing classroom arguments made conjectures, criterion makes working together, engender very different typical rule-and-procedure orientation. Alibert [1988] provides picture discourse supportive important mathemat-