How Do Students Know What They Learn in Middle School Mathematics Is True?

摘要

This article presents ways in which students ascertain that what they have learned in mathematics is true. Students in the middle school (and a few from other grades) were interviewed by prospective and in-service teachers. Students were asked what they had learned recently in mathematics and how they knew it was true. The answers were grouped by the author according to the justification schemes used by the students in their explanations. Students interviewed used three kinds of justification schemes: externally based, empirical, and analytic. For each kind, examples are provided of students' justifications. Additional insights are included from the reflections of the interviewers. Some suggestions are offered regarding how teachers can help increase their students' ability to give convincing arguments in mathematics.