What Are and What Are Not Extrema Points? Examining Definitions and Examples

This paper reports on five secondary school mathematics prospective teachers’ conceptions of extreme point. The analysis of the data addressed students’ definitions, examples, and evaluation of given examples, with special attention to the related domain. Written assignments and individual interviews uncover salient, erroneous concept images regarding what is and what is not an extreme point. Participants viewed extrema points as points that necessarily satisfy f′ = 0 or as points that are always at a “change in monoticity” of the function. The topic “extreme points” is both an aim and a mean to address broader issues related to mathematical definitions, examples, and nonexamples. We conclude with possible next-step ideas.