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…

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

This data snapshot highlights several differences in educational opportunities between males and females from prekindergarten through higher education. The information herein, gathered from a variety of education data sources, shows that--despite the enormous progress made in ensuring equal educational opportunities since the passage of Title IX…

The purpose of this study was to examine constructivist-based algebra lessons and a cooperative construct to address the achievement gap between White (non-Hispanic) and Mexican American 8th grade students at a southern California middle school. The lessons were designed to facilitate social interdependence which promoted peer-to-peer interaction…

This paper describes the effect of teacher comments, students' demographic information and learning management system utilisation on student final scores in algebra courses in a K-12 virtual learning environment. Students taking algebra courses in a state virtual school in the Midwestern US region during 2007-2008 participated in this study.…

This article describes Realistic Mathematics Education (RME), a design theory for mathematics education proposed by Hans Freudenthal and developed over 40 years of developmental research at the Freudenthal Institute for Science and Mathematics Education in the Netherlands. Activities from a unit to develop student understanding of logarithms are…

This paper reports findings of a post test experimental control group design conducted to investigate the role of modified Moore learning approach on improving students' mathematical understanding and proving abilities. Subjects of study were 56 undergraduate students of one state university in Bandung, who took advanced abstract algebra course.…