Argues that the challenge for teachers of algebra in Australia is to find ways of making the structural aspects of algebra accessible to a greater percentage of students. Uses the zero product principle to provide an example of a common student error grounded in the difficulty of understanding the structure of algebra. (DDR)

Underlines the common points in F. Uhlig's approach published in an earlier issue of this journal about the question of proof in linear algebra. Describes some of his ideas in a new light and gives perspective for a further didactical development of Uhlig's first experiments. (Author/KHR)

Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…

Presents evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale, and angle. Participants responded to a simple but non-standard task concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches termed…

Sixth- and seventh-grade students (n=68) with learning disabilities in mathematics received either concrete-to-representational-to-abstract (CRA) or traditional instruction in algebraic transformation equations. Students receiving the CRA instruction outperformed peers receiving traditional instruction on both post-instruction and follow-up tests…

Demonstrates the transformations that are possible to construct a variety of magic squares, including modifications to challenge students from elementary grades through algebra. Presents an example of using magic squares with students who have special needs. (YDS)

Identifies big ideas for the informal study of algebra-related topics in the middle grades including notation, variable, function, and properties of number. Suggests meaningful ways to accomplish them. (YDS)

Describes a lesson plan in which students apply their mathematical intuition to determine win-loss possibilities of teams in a sports league and develop a formula for calculating the magic number for clinching first place. (YDS)

Presents the "Food for Thought" problem and discusses different approaches used by Algebra 1 students to solve the problem. (YDS)

Outlines a lesson on the Fibonacci and Lucas sequences that captures student interest by presenting the opportunity for computation practice, mental mathematics, and proof for algebra students. Discusses an extension for solving simultaneous equations. (YDS)

Describes how student thinking about geometric patterns can be used to develop algebraic reasoning and to make sense of mathematical notation and symbols. (Contains 11 references.) (YDS)

Investigates how mathematics is used in various careers. Students explore number sense and operations, logical reasoning, data analysis, and algebra. (Author/NB)

Shows how the phenomenon of instability in the solution of a system of linear equations can be analyzed both algebraically and geometrically. (KHR)

Describes a lesson taught in primary school based on the use of linking cubes. Shows how meaningful mathematics can be made accessible to children and how fundamental issues of variant and invariant properties might be developed. (KHR)

Describes how the cubic formula can be presented easily at the precalculus level, shows how to verify that the formula is correct, and identifies when it is profitable to use. (KHR)