This paper reports on students' conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as well as erroneous "mis-out examples" that mistakenly regard examples as non-examples and "mis-in examples" that mistakenly grant non-examples the status of examples. We used Tall and…

This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times "something" (i.e., "2i" is an even number),…

Inequalities are one of the foundational subjects in high school math curricula, but there is a lack of academic research into how students learn certain types of inequalities. This article fills part of the research gap by presenting the findings of a study that examined high school students' methods of approaching absolute value inequalities,…

Previous research has shown that--due to the extensive attention spent to proportional reasoning in mathematics education--many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the "illusion of linearity". For example, in…

Describes observations, written samples, and interviews of (n=24) high school teachers learning concepts of group, subgroup, coset, normality, and quotient group in an Abstract Algebra course. General observations are made about the role of errors and misconceptions in light of an action-process-schema framework. (32 references) (MKR)