This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did…

Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children's transition to secondary school as both an opportunity and a problem, with reference to the Greek context. In discussions…

This document, in both English and French versions, is the Mathematics 33 Grade 12 Diploma Examination from Alberta Education. It is a 2.5 hour closed-book examination consisting of 37 multiple-choice and 12 numerical-response questions of equal value that are worth 70% of the examination, and 4 written-response questions of equal value worth 30%…

The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

Investigations into children's number learning have been a feature of recent mathematics education research in Australasia. This book is a compilation of the major results of this research with the aim of making them more accessible to researchers, teachers, and others who may be able to use the findings to improve classroom practice. The…

This paper describes a model of student attainment of mathematical concepts and its development. In this model three types of activities (developmental, connecting, and abstract) are considered as an overlay on the three ways of representing mathematical concepts (physical/visual, oral, and symbolic). Each activity type involves some means of…

Reports on two types of unsolvability in mathematics. One is an instance of impossibility and the second is a judgment of undecidability. Presents a number of examples of undecidable propositions. (GS)

The author argues that rote acquisition of "units of knowledge" such as "zero times anything is zero" or "differentiability implies continuity" is a valid aim of mathematics education. (SD)

A graphical method is proposed which allows one to visualize a real matrix and its inverse. In this scheme, various special properties of the matrix are easily recognized. Up to 5x5 matrices can be graphed on an average page if the range of values does not exceed two orders of magnitude. (Author/LS)

Three key predictions of Piaget's groupement model of middle childhood cognition were examined in the speed and time concept areas with a total of 93 children in grades 1, 2, and 3. (ED)