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,…

A model of qualities of mathematical activity was developed within a framework of learning goals. A clinical application of the model is described, in which ninth-grade students were given assignment projects. A hierarchy of effective guidance was established, permitting diagnostic evaluation and progressive development of mathematical activity.…

Diagnostic interviews were conducted with third graders to determine why they made mistakes on sixteen arithmetical tasks. A modified version of the Newman method of analyzing errors is discussed and applied to these interviews. (MP)

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)