Outside-In-Inside-Out:
Seventh Grade Students' Mathematical Thought Processes
Abstract: In this paper, Dr. Lillie Albert, Associate Professor of Mathematics Education at Boston College, investigates the relationship between students' oral thought processes and written thought processes in mathematics. Expanding upon Vygotsky's research involving the role of social exchanges and the zone of proximal development (ZPD) in student learning, Albert argues that the practice of writing in mathematics can be used to aid students in reaching a new zone of learning: the zone of proximal practice (ZPP) in which students are able to self-direct and self-regulate their own thought processes regarding mathematics concepts and ideas. To support this argument, the researchers conducted a case study of seventh grade students engaged in collaborative mathematics problem-solving activities. Questioning was used to facilitate learning processes and to co-construct problem-solving strategies, which was effective in improving students’ understanding of the process as well as the mathematical concepts involved. Interview protocols and writing samples were used to describe students' strategies for solving problems and to record students' oral and written thought processes. Results indicate that the writing process can be an effective tool for deepening conceptual understanding and advancing the learner from the ZPD to the ZPP.
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