Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

This paper argues that design fixation, in part, entails fixation at the level of meta-representation, the representation of the relation between a representation and its reference. In this paper, we present a mathematical model that mimics the idea of how fixation can occur at the meta-representation level. In this model, new abstract concepts…

A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)

The basic properties of a dynamic systems approach of development are illustrated by contrasting two simple equations. One equation is characteristic of dynamic systems models. The other refers to what, for the sake of simplicity, is referred to as the standard developmental approach. We give illustrations from cognitive, language and social…

This article presents a constructivist approach for teaching mathematics to prospective elementary school teachers in USA. This approach employs a model of a "mathematical situation," a set of physical operations and a physical language to reason about students' mathematical doings. One of the primary goals of this approach is to promote a…

Reports on year-long classroom teaching experiments in two predominantly Latino low-socioeconomic-status (SES) urban classrooms which sought to support first graders' thinking of 2-digit quantities as tens and ones. Presents a model of a developmental sequence of conceptual structures for 2-digit numbers to describe children's thinking.…