The purposes of this study were to assess the efficacy of remedial tutoring for 3rd graders with mathematics difficulty, to investigate whether tutoring is differentially efficacious depending on students' math difficulty status (mathematics difficulty alone vs. mathematics plus reading difficulty), to explore transfer from number combination (NC)…

Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…

Recent educational research has turned increasing attention to the structural development of young students' mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of mathematical structure is crucial to mathematical competence…

A quantitative observational study exploring the relationship of gender to mathematics self-efficacy and the frequency of back substitution in multiple-choice assessment sampled undergraduates at a western United States parochial university. Research questions addressed: to what extent are there gender differences in mathematics self-efficacy, as…

The Millennium Project is an international effort to improve the health, economic status, and environmental resources of the world's most vulnerable people. Using data associated with the Millennium Project, students use algebra to explore international development issues including poverty reduction and the relationship between health and economy.…

Within the project "Engaging mathematics for all learners", led and funded by the QCA, the mathematics team at the Royal Institution of Great Britain (Ri) looked into how mathematical tasks usually reserved for the "gifted and talented" can be used in the mainstream classroom with a wide range of learners to address core…

Since 2001, the authors have been working with groups of teachers to investigate students' early algebraic thinking--learning representations, connections, and generalizations in the elementary school grades. They began paying attention to students' explicit remarks about regularities in the number system or what students imply by their…

This collective case study reports on an investigation into the relationship between mathematics teachers' beliefs and their classroom practices, namely, how they organized their classroom activities, interacted with their students, and assessed their students' learning. Additionally, the study examined the pervasiveness of their beliefs in the…

This article describes how to make an origami paper box and explores the algebra, geometry, and other mathematics that unfolds. A set of origami steps that transforms the paper into an open box can hold mathematical surprises for both students and teachers. An origami lesson can engage students in an open-ended exploration of the relationship…

The attribute hierarchy method (AHM) is a psychometric procedure for classifying examinees' test item responses into a set of structured attribute patterns associated with different components from a cognitive model of task performance. Results from an AHM analysis yield information on examinees' cognitive strengths and weaknesses. Hence, the AHM…

The change from students learning all subjects together in a one-room schoolhouse to learning in classes separated by subject and grade resulted in distinct disciplines such as social studies, mathematics, science, and English. What was lost was the unified, holistic curriculum that a one-room setting required. Since students move from…

Thirteen years ago, Minnesota was a state with no academic standards in mathematics and science and what some observers said was a mixed record in grounding students in crucial academic content, such as number skills and algebra. Since then, the state has set clear guidelines for schools in both subjects, and it also appears to have tuned up what…

Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

The author responds to the recent work of Kaminski, Sloutsky, and Heckler (2008) and advances two major concerns about their research and its applicability to learning mathematics: a confounding variable that arises from the mathematical differences between the generic examples and concrete examples poses a threat to the construct validity of the…

In "Elementary School Mathematics Priorities," Wilson (2009 [this issue]) presents a list of five core concepts that students should master in elementary school so that they can succeed in algebra. As researchers in mathematics education, the authors enthusiastically endorse Wilson's recommendations. Learning algebra is key to further study of…