This study examined and compared the intended mathematics curricula according to topic coverage, focus, coherence, and learning progression in grades 1-12 within China and the province of Ontario, Canada. The findings show that the overall topics in the two curricula are similar: Chinese curriculum covers 78 topics out of 79 while the Ontario…

Presents a study to determine students' concept of slope carried out in three classes of the second form before introducing the notion of derivative. Discusses the meaning of conceptual framework and reviews literature on slope. Analyzes student responses to a questionnaire for mathematical content and expression and interprets the results. (MDH)

This paper focuses on some main distinctions that are necessary to analyze mathematical knowledge from a learning point of view and explain how many students come up against difficulties at each level of the curriculum. From a learning point of view, visualization cannot be used as an immediate and obvious support for understanding, even though it…

Investigated the upper limits of (n=22) seventh-grade students' informal processes in solving first degree equations in one unknown prior to instruction. Results indicated the existence of a cognitive gap between arithmetic and algebra characterized as the students' inability to operate spontaneously with or on the unknown. (37 references)…

This handbook has been structured to provide teachers (K-2) with the most recent research on problem solving. It contains information and practical applications which deal with the key concepts of problem solving in mathematics. The handbook consists of four sections. The first section establishes the background and gives the purposes of the…

This paper begins with a summary and analysis of Robert Glaser's arguments, presented in his paper "Education and Thinking: The Role of Knowledge," which contend there are strong interactions between structures of knowledge and cognitive processes, and that problem solving and reasoning are taught best in the context of the acquisition…

To be numerate is to be able to function mathematically in one's daily life. The kinds of mathematics skills and understandings necessary to function effectively in daily life are changing. Despite an awareness in Australia of new skills necessary for the information age and calls that the schools should be instrumental in preparing students with…