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…

Examines the abilities of high school students (n=394) to reflect aspects of 36 cubes that were depicted in 2-dimensional perspective as upright and transparent. The reflections of points, edges, or corners was established through two-sided mirrors variously positioned within each cube. Analysis of the response errors reveals a tendency toward…

Methods developed by Newman and Casey for analyzing errors by children attempting verbal arithmetic problems are described. Emphasis is given to Newman's hierarchy of error causes. Data obtained by Newman, Casey, and Clements show a large proportion of errors by children are in categories…

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…

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)

The literature on proportional reasoning is reviewed. After methodology is discussed, strategies used to solve proportion problems, variables that influence performance, and training studies are each considered. (MNS)

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)