The aim of this research is to characterize profiles of the teaching competence "noticing students' mathematical thinking" in the context of the pattern generalization. Prospective primary teachers were asked to describe and interpret the answers of three primary students to three linear pattern generalization problems. Five profiles for…

In many mathematics classrooms, the teacher provides "worked examples" to demonstrate how students should perform certain algorithms or processes. Some students find it difficult to generalize from the examples that teachers provide and cannot apply what they have learned in new situations (Watson and Mason 2002). Instead, teachers might…

This article focuses on the ways in which four eighth-grade girls, each with varying levels of algebraic understanding, share ideas, debate, and gradually move toward generalizations inherent in the "Painted Cube" problem. The intent of this article is to examine how students move to progressive formalization and to provide insights into the ways…

Based on the results of a generalizability study (G study) of measures of teacher knowledge for teaching mathematics developed at The National Center for Research, on Evaluation, Standards, and Student Testing (CRESST) at the University of California, Los Angeles, this report provides evidence that teachers are better at drawing reasonable…

Although this article is reprinted from a 1978 issue of "Arithmetic Teacher," its content is relevant to today's conversations about the roles of conceptual understanding and procedural fluency in the teaching of mathematics. This article attempts to advance and demonstrate the proposition that moves in teaching mathematics can serve as a basis…

Many students with disabilities continue to struggle with understanding what mathematics means. They memorize basic facts or step-by-step mathematical procedures without understanding the underlying concepts related to the problems. Thus, instruction designed to help students understand the meaning of the mathematics that they are learning in…

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…