ABSTRACT
Over the last several years, many professional development projects have been implemented intending to help teachers build new ways of thinking about their mathematics teaching. The goal of these projects, generally speaking, is to help teachers move away from more traditional instructional approaches which emphasize memorization and the execution of rules and procedures, and move toward instructional practices, which provide students with the opportunity to build concepts and ideas as they are engaged in meaningful mathematical activities (NCTM, 1989, 2000). Moving away from teaching techniques that simply enable students to repeat, often without much understanding, various specific algorithms, rules, or procedures toward helping them develop deeper and more powerful understandings and abilities, is not an easy task. It “would require vast changes in what most teachers know and believe” (Cohen & Barnes, 1993, p. 246). “Teachers who take this path must have unusual knowledge and skills. They must be able to comprehend students’ thinking, their interpretations of problems, their mistakes they must have the capacity to probe thoughtfully and tactfully. These and other capacities would not be needed if teachers relied on texts and worksheets” (Cohen, 1988, p. 75).
