Suggests a few alternative approaches to teaching algebra that allow students to construct and reflect upon meanings for expressions and equations. The three lessons, which require extended discussion and reflection, are "Representing Algebraic Expressions,""Evaluating Algebraic Statements," and "Generating Equations." (WRM)

Investigates the conceptual structures of Year 9 students in Korea and Australia while constructing various geometrical terms. Reports that two samples of students exhibited major differences in definition-ranking preferences on angle and in semantic profiles for some geometrical concepts due to the differences in nature of Korean and English.…

Describes a hands-on, guided-learning activity that forges vertical connections among grade levels and relies on physical models in the investigation of algebraic concepts. This lesson helps students discover that a given value can have multiple representations. Includes a sample student activity log. (AIM)

Describes how various projects helped middle school students build mathematical conclusions through algebraic thinking as they used number patterns and verbal rules to explore the interrelationships of representations. Suggests some topics for projects. (AIM)

Presents science investigations that involve some challenging mathematics related to proportional reasoning. Can be embedded in thematic, interdisciplinary units to reinforce understanding of specific proportions, provide practice in proportional thinking, or assess abilities in solving problems that involve proportions. (JRH)

Three experiments tested whether it is possible to teach college students who are not trained investigators to comprehend information regarding knowledge of conservation problems and mathematical equivalence conveyed through children's hand gestures. Findings suggest that instructing adults to attend to gesture enhances their assessment of…

Children from grades 2, 3, 4, 6, and 8 made speeded, bimanual parity (odd/even) judgments of numerals. Response times indicated that from fourth grade on, parity information was retrieved directly from memory. By grade 3, children represented magnitude information as a left-to-right number line which was accessed obligatorily and, by grades 6 and…

This article describes TI-73 calculator activities appropriate for middle school students. It was found that the use of the calculator allowed for higher-level thinking and a richer exploration of mathematical ideas by students. [Included with this article are "Dice Roll Worksheet" and "Transforming Tree Worksheet".] (Contains 9 figures.)

This article illustrates students' efforts to resolve an apparent discrepancy between their self-generated solutions and the answer obtained using the division algorithm for fractions. (Contains 5 figures.)

This article details a variety of activities that can be used with middle school students to investigate the size of the number 1,000,000. The activities focus on real-life applications of mathematical proportions and helps students to understand the magnitude of large numbers. (Contains 8 figures.)

Many students have traditionally found the processes of algebraic manipulation, especially factorisation, difficult to learn. This study investigated the value of introducing students to a Vedic method of multiplication of arithmetic numbers to algebra that is very visual in its application. This research considered a possible role of the…

In this study, we investigated the development of basic effects that have been found in single-digit multiplication arithmetic: the problem size, five, and tie effects. Participants (9-,10-, and 11-year-olds and adults) performed a production task on simple multiplication. The procedure replicated Campbell and Graham's (1985) study ["Canadian…

The use of reform-based curricula is one possible avenue for the widespread implementation of mathematics education reform. In this article, we present two urban elementary teachers' "models of curriculum use" that describe how each teacher used a reform-oriented mathematics curriculum. In particular, we examine when and how the teachers made…

In this article, Laura Grandau traces a self-study research project focused on teaching algebra to fourth-grade students. Facing a new curriculum and a new grade level, Grandau considers what good instruction and "good habits of practice" may be. Through journaling, videos, observations, analysis of students' verbal and written responses, and…

We describe a project for calculus and differential equations students involving trajectories of a spacecraft whose propulsion system depends solely on muting gravitational effects of heavenly bodies. In particular, we consider the spacecraft imagined by H. G. Wells, and focus on getting his spacecraft from the Moon to the Earth. Cavorite, angular…