Reducing problem complexity by isolating elements has been shown to be an effective instructional strategy. Novices, in particular, benefit from learning from worked examples that contain partially interacting elements rather than worked examples that provide full interacting elements. This study investigated whether the isolating-elements…

In a series of two "in vivo" experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly…

This study investigated factors promoting the use of self-constructed diagrams by examining students' perceptions and daily class activities, and comparing Japanese (n = 291) and New Zealand (n = 323) students. Algebra word problems and a questionnaire were administered. The results revealed that the New Zealand students used diagrams more often…

In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular nature of mathematical knowledge and the neurobiological bases of mathematical cognition. In the empirical study that is reported in this article, we investigated ninth graders'…

This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to…