In this paper we analyze the meanings of the "equal" sign as generated by sense production of the methods of substitution and comparison for solving problems and systems of equations of two unknowns. These methods are usually introduced through an extension process of the syntax and meanings recently learned by students in order to solve…

The purpose of this study was to investigate the effects of the Casio 9850 and the TI-85 graphing calculators on college students' procedural skills and conceptual understanding in two different developmental mathematics courses. The courses used in this study were Elementary Algebra and Intermediate Algebra. Both the non-graphing calculator group…

This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…

Presented are a series of word problems which give students the opportunity to use or develop problem solving skills. The problems are open-ended, with possible answers included. (JP)

Several brief articles are included in this section. "Purple Puzzlers" are challenging problems for algebra students. "Linear Invaders" is a game to reinforce concepts of graphing lines. "The Diagonal Method" is used to prove that the real and natural numbers cannot be put into one-to-one correspondence. (MNS)

Teaching ideas related to the instruction of decimal division as the opposite of multiplication, an approach to approximating logarithms that help reveal their properties, and the simple creation of algebraic equations with radical expressions for use as exercises and test questions are presented. (MP)

Ideas are presented regarding: (1) unique learning activities for students who have difficulty with operations with signed numbers; (2) a mathematical inspection of a unique card trick that can be expressed as an equation; and (3) sketching of graphs of composite trigonometric functions. (MP)

Geometry is revealed as one of the most universal and useful tools in all parts of mathematics, with the idea of a "pure" geometry divorced from algebra an historically recent idea. (MP)

The use of a 25-pin lattice geoboard in a six-week course in middle school geometry is presented, with sample activity cards and test items. Two other ideas discuss the use of algebra in solving verbal problems and teaching negative exponents. (MP)

Three problem-solving strategies--working backward from the unknown, forward from the given, and mixed--were applied to interrelated algebra equations. The mixed strategy was most popular and most efficient with grouped variables. Memory load or information-processing load differences among the strategies were evident. (CP)

Reports on an experiment in which Algebra I students (N=181) learned to translate word problems with two unknowns from the prose representation to symbolic representation using two variables when first solving word problems with two unknowns. Concludes that students who had learned to solve equations with the new method scored higher than those…

Presents two games that provide practice with equivalent fractions, that were produced at three levels of difficulty, Level 1 being the simplest. Also describes another game for practice in solving simple linear equations. Appendices contain examples of materials used in the games. (ASK)

Compared tutoring episodes where tutoring did and did not cause learning in university physics students to inform design of intelligent tutoring systems. Found that when students were not at an impasse, learning was uncommon regardless of the tutorial explanations employed. When students were at an impasse, tutorial explanations were sometimes…

Uses the notion of focusing phenomena to explain how a teacher's actions were connected to her students' interpretations of a linear equation. Conducts interviews and analyzes a high-school classroom that emphasized dependency relationships in real-world situations. Describes how the teacher directed attention away from functional relationships…