This paper discusses findings from an ongoing study investigating mental mechanisms involved in the conceptualisation of linear transformations from the perspective of Action (A), Process (P), Object (O), and Schema (S) (APOS) theory. Data reported in this paper came from 44 first-year linear algebra students' responses on a task regarding the…

The number sequences describe a hierarchy of students' concepts of number. This research uses two defining cognitive structures of the number sequences--units coordination and the splitting operation--to model middle-grades students' abilities to write linear equations representing the multiplicative relationship between two unknowns. Results…

In an effort to examine the impact of the changes being made at San Jose State University (California) in the calculus curriculum, multiple measures were collected and analyzed. This study focuses on the relationship between performance on a pretest and the class grade. Through written responses on the pretest, a belief and knowledge profile for…

In this article, the meanings students construct and the conceptual advances they make as they deal with ratio and proportion problems are described. The study cites episodes with a second grader, two fifth graders, and three seventh graders. A critical factor in students' comprehension of and solution to ratio and proportion problems is their…

Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)

Structure of mathematical concept of multiplication and its integration into conceptual system, with respect to formal and informal aspects of understanding for 10 university students, are investigated through linear scale assessment of examples for prototypical effects and through follow-up interview which included direct explanations of…

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

Five- to six-year-old children estimated the size of Euclidian objects using an addition rule of Height plus Width, rather than a multiplying rule. Within the framework of information integration theory, tested whether intensive handling of objects would facilitate shift from addition rule to multiplication rule. Found that following handling,…