Mathematics Education

This article reports the authors' efforts to develop a practice-based theory of content knowledge for teaching built on Shulman's (1986) notion of pedagogical content knowledge. As the concept of pedagogical content knowledge caught on, it was in…

This study explored whether and how teachers mathematical knowledge for teaching contributes to gains in students mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders mathematical achievement…

The great Russian psychologist L. S. Vygotsky has long been recognized as a pioneer in developmental psychology. But somewhat ironically, his theory of development has never been well understood in the West. Mind in Society should correct much of…

Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady…

Constructivist theory has been prominent in recent research on mathematics learning and has provided a basis for recent mathematics education reform efforts. Although constructivism has the potential to inform changes in mathematics teaching, it…

This study documents how teachers who participated in a professional development program on understanding the development of students mathematical thinking continued to implement the principles of the program 4 years after it ended. Twenty-two…

Two different types of "understanding" are defined and discussed: knowing both what to do and why, and knowing rules without reasons. Advantages and disadvantages of each type of understanding are presented. (DT)

Widespread agreement exists that U.S. teachers need improved mathematics knowl- edge for teaching. Over the past decade, policymakers have funded a range of profes- sional development efforts designed to address this need. However, there has been…

The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept. This may not be globally coherent and may have aspects which are quite different from the formal concept definition. The…

In this paper, we have mentioned six ways in which a theory can contribute to research and we suggest that this list can be used as criteria for evaluating a theory. We have described how one such perspective, APOS Theory, is being used in an…

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students understanding of the rigorous definition of limit is influenced by the images of limit that the…

Abstract This article describes a study in which measures of mathematical knowledge for teaching developed in the United States were adapted to measure mathematical knowledge for teaching in Ireland. When adapting the measures it was not assumed…

This article examines the relationship between the mathematical knowledge of 438 K-8 California teachers and the demographics of the schools in which they work. To measure mathematical knowledge,we used a series of multiple- choice problems meant to…

Research literature (e.g., Thompson, 1992) suggests that teachers beliefs about the nature of mathematics provide a strong indicator of their future teaching practices.Moreover, current reformefforts (e.g., NCTM, 2000) ask teachers to lead mathe-…

In this paper the authors present three design principles they use to develop preservice teachers' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2)…

Research in the area of educational technology has often been critiqued for a lack of theoretical grounding. In this article we propose a conceptual framework for educational technology by building on Shulman's formulation of "pedagogical content…

In this article, the authors first indicate the range of purposes and the variety of settings in which design experiments have been con- ducted and then delineate five crosscutting features that collectively differentiate design experiments from…

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the…

When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods-to help children learn most effectively? This book offers…

Presents an overview of teacher preparation and concludes that the distinction between "knowledge" and "pedagogy" is a relatively recent development. Discusses different types of teacher knowledge ("content,""pedagogical content," and "strategic")…