Presented is an activity for teaching linear algebra to grade 7 or grade 8 students. The activity is taken from the "Victorian Secondary Reality in Maths Education" (RIME) Pack. The activity called "Backtracking" builds on intuitions and understandings that students already possess. (RH)

The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)

The role of sentential logic traditionally taught in high school geometry is challenged. A rationale for shifting that content to algebra and replacing it with inferential logic, which directly affects proof making, is given. (MNS)

Discusses common error-detecting identification codes using linear algebra terminology to provide an interesting application of algebra. Presents examples from the International Standard Book Number, the Universal Product Code, bank identification numbers, and the ZIP code bar code. (YP)

The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)

The creation of "false laws" of mathematics by many pupils as they attempt to rephrase new ideas and make them understandable and useful is discussed. The reasons for these mistakes and some ways teachers can help students adopt correct rules are reviewed. (MP)

This article develops an algorithm to find all solutions to the problem, making all sums of a hexagram's nine lines the same. It shows how to exploit the geometric structure of the hexagram and its group of automorphisms. (YP)

Describes a model for teaching early algebraic concepts using manipulative materials for elementary school students. Presents a rationale for the model. Provides activities for solving algebraic equations using envelopes and counters. (YP)

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

Discusses the importance of identifying and describing the pattern by students in algebra class. Provides some examples showing the usefulness of the method seeing the pattern from mathematical materials. (YP)

A proposal to replace plane geometry with computer programming in the standard high-school mathematics curriculum is presented. (MP)

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…

This article discusses the classroom use of discovery of number pattern. Provided are examples of a table of squares, multiplications of numbers, and algebraic expressions. (YP)