Middle school mathematics teachers' subject matter knowledge and pedagogical content knowledge of probability: Its relationship to probability instruction.

摘要

As a result of the calls for reform in mathematics education and the ever-changing nature of mathematics, today's teachers face the challenge of teaching unfamiliar content in ways that are equally unfamiliar. In view of this challenge, the purpose of this study was to investigate middle school teachers' subject matter and pedagogical content knowledge of probability and its relationship to the teaching of probability. The study also explored the nature of the instructional tasks and classroom discourse during probability instruction.;The results of this study indicate the teachers generally (a) lacked an explicit and connected knowledge of probability content, (b) held traditional views about mathematics and the learning and teaching of mathematics, (c) lacked an understanding of the "big ideas" to be emphasized in probability instruction, (d) lacked knowledge of students' possible conceptions and misconceptions, (e) lacked the knowledge and skills needed to orchestrate discourse in ways that promoted students' higher level learning, and (f) lacked an integrated understanding of the nature of the reform.;One teacher captured the essence of the reform effort in her probability instruction; the other 3 teachers generally fell short of the goal despite their efforts to implement aspects of the reform. Although students were actively involved in exploring probability content through the use of games, simulations, and other hands-on instructional tasks, the cognitive level of the tasks and discourse was limited by the nature of instruction.;The findings of this study have implications for mathematics education reform, preservice teacher preparation, staff development, and curriculum development.;Case study methodology was used to examine the knowledge and practice of 4 middle school teachers. A pre-observation interview assessed the teachers' subject matter knowledge of probability. The teachers were then observed as they taught probability. Post-observation interviews further explored teacher knowledge and its relationship to teaching practice. Data sources included interview transcripts, observational field notes, video and audiotapes of classroom instruction, and written instructional documents. Individual case studies were written describing the teachers' background and probability instruction. Cross-case analyses compared and contrasted the cases in response to the research questions.