Mathematical Thinking and the Process of Specializing.

摘要

This study used qualitative research methods to investigate students' perceptions of mathematical thinking and how the explicit instruction of the strategies related to specializing (L. Burton, 1984) impacted student approaches to problems. This research was conducted at a rural community college in the Midwest. The data were comprised of student-generated definitions of mathematical thinking, student work, classroom observations, and student exit interviews. Through the analysis of student definitions of mathematical thinking, along with the analysis of student work, this research provided insight into student views of mathematical thinking and strategies that mathematics teachers can employ to develop the skill of mathematical thinking in their students. The students expressed a view of mathematical thinking that was largely at odds with the description by the National Council of Teachers of Mathematics. While a number of different strategies related to specializing were modeled for the students, the method of systematic guess and check was the one used most often by students. Results among students and among tasks varied, although the majority of students demonstrated mild improvement in their level of specializing after only a short period of instruction.