Precalculus and calculus are considered gatekeeper courses because of their academic challenge and status as requirements for STEM (science, technology, engineering, and mathematics) and non-STEM majors alike. Despite college mathematics often being seen as a neutral space, the field has identified ways that expectations, interactions, and…

Equivalence is mostly associated with the strand of Number and Algebra and is fundamental in both of the substrands. Equivalence is considered a key and foundational concept of algebra, and whereas an assumption might be made that equivalence is a relatively "easy" concept; studies have shown that when asked to balance an equation such…

Many current policy initiatives focus on teacher qualifications and high-stakes assessments for students as a means to improve mathematics education in the United States, but this approach ignores the actual practice of teaching through which students have opportunities to learn mathematics. The present study is an effort to answer scholars'…

This study drew on data from a large, randomized trial of Cognitive Tutor Algebra (CTA) in high-poverty settings to investigate how mathematics curricula and classroom achievement related to teacher reports of time spent on inquiry-based and lecture-based mathematics activities. We found that teachers using the CTA curriculum reported more time on…

More important than infusing courses and curricula with modern content is to give students the tools to use and understand mathematics--including some that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what users and makers of mathematics do and what they say. These cross-journal articles are…

Building coherence in the development of mathematical ideas across the grades is key to improving students' mathematical learning in the United States. Knowing the mathematical experiences, understanding, skills, and habits of mind that students bring to a grade level and what the expectations are for the following grades can help teachers bridge…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

Mental skills developed through the study of mathematics are identified, and ways in which this information can shape the role of teachers of algebra are suggested. (MNS)

There is a significant gap between theories of general psychological functions on one hand (e.g., memory) and theories of mathematical content knowledge on the other (e.g., content of algebra). To better guide the design of ground breaking and demonstrably better mathematics instruction, we need instructional principles and associated design…

The investigation reported is primarily a description of how college students solve or fail to solve algebra equations. Protocols were collected from two groups of college students; one group was expected to be good solvers, the other group contained many poor solvers. The investigators sought to identify and classify the difficulties students…

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

Knowledge about the structure of arithmetic expressions enables people to reason effectively about such expressions, including an ability to judge equivalence under transformations. This paper reports an empirical study of six middle-school children who judged the equivalence of three sets of three-term arithmetic expressions with an addition and…

This document contains 53 plenary and contributed papers presented at the eighth Psychology of Mathematics Education (PME) meeting. Two plenary addresses focused on mathematics research in Australia and Japan, and problem solving and symbolism. Contributed papers were classified under 13 headings including: teaching and learning theory; cognition;…

This volume contains the proceedings of the International Conference on Technology in Mathematics Education (TIME 2000). It includes papers, posters, and short oral reports. Research papers include: (1) "Implications of the Shift from Isolated Expensive Technology to Connected, Inexpensive, Ubiquitous and Diverse Technologies" (Jim…

Major revision in the U.S. mathematics curriculum since the 1960s have led to significant differences between the mathematics curriculum of the United States and those of many other countries. This study explored how eight Chinese immigrant students, with different cultural backgrounds, mathematics knowledge, and learning styles, learned in an…