The second volume of this proceedings contains the papers presented at the 21st annual meeting of the Mathematics Education Research Group of Australasia. Full papers include: (1) "Teachers Interpreting Algebra: Teachers' Views about the Nature of Algebra" (Brenda Menzel and David Clarke); (2) "Long Odds: Longitudinal Development of…

This profile is designed as a recording sheet for monitoring an individual student's progress throughout the school year. Sixth grade assessment materials and the "Strategies for Instruction in Mathematics" suggest tasks and questions that can be used for on-going and summative assessment. Directions for use and descriptions of levels of…

This profile is designed as a recording sheet for monitoring an individual student's progress throughout the school year. Eighth grade assessment materials and the "Strategies for Instruction in Mathematics" suggests tasks and questions that can be used for on-going and summative assessment. Directions for use and descriptions of levels of…

Presents a series of lessons that extend the concrete experiences many elementary students have had with attribute blocks to provide middle school students with informal opportunities to explore the concepts and properties of relations and functions. (DDR)

Argues that the vast majority of adults have no use for the specialized mathematics taught in high schools and required by colleges--algebra, geometry, or calculus. Suggests that colleges should accept applicants who have studied percents, formulas, logic, computer commands, and basic statistics. (TE)

Discussed are the use of spreadsheets for demonstrating and exploring with the whole class, basic and advanced spreadsheet operations, geometric progressions, and graphing. Teacher responses to these methods are described. (CW)

Discusses four activities focusing on communication about shapes and spatial relationships. The activities include requiring students to sketch patterns, and two-dimensional and three-dimensional visualizations. Provides several figures showing the geometric shapes. (YP)

Describes the Interactive Mathematics Program (IMP), a four-year program of problem-based mathematics that integrates algebra, geometry, and trigonometry with additional topics, such as probability and statistics, and uses calculator and computer technology to enhance student understanding. (MKR)

The game "Pythagoras" is an adaptation of the tangram puzzle. Describes the process of finding all the possible convex polygons with seven sides to prove that the solution to a given puzzle shape of seven sides difficult to find was not possible. (MDH)

An incident light ray parallel to the optical axis of a parabolic mirror will be reflected at the focal point and vice versa. Presents a mathematical proof that uses calculus, algebra, and geometry to prove this reflective property. (MDH)

Presents activities developed for teacher training courses for the middle school level that integrate mathematics history with the selected topics of number systems, fractions, and geometry. The activities seek to give relevance to history and to motivate and deepen students' understanding of the evolution of mathematical concepts. (MDH)

Presents guidelines for developing and evaluating games in mathematics, including a concrete example--coordinate geometry taught by the Rubber Bones game--and its evaluation using (n=52) seventh graders. Guidelines for development include analysis of the concepts and the learner, nature of learning, enjoyability, integration, and evaluation. (48…

Presented are six short articles on an application of an ellipse to carpentry, the area of an ellipse by stacking, using the isoperimetric quotient to solve a minimum problem, using an ill-posed trigonometry problem to encourage deeper exploration of concepts, the volume and centroid of the Step Pyramid of Zoser, and a unique telescoping series…

Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…

Beginning geometry students misunderstand the requirements of formal proof because of confusion between deductive reasoning and argumentation. Presented is a cognitive analysis of deductive organization versus argumentative organization of reasoning and the applications of this analysis to learning. Implications of a study analyzing students'…