A Design for Development:

 The Legacy of Robbie Case
 
October 6 and 7, 2000
 
Croft Chapter House & Rm.179
University College
University of Toronto

 Joan Moss


 Outline of Talk


The Theory of Central Conceptual Structure and the Use of Spatial Metaphors in the Teaching of Mathematics: The Special Case of Rational Number

Robbie's theory of central conceptual structures has led to the creation of a series of successful instructional programs in different mathematical domains. A principal feature that is common to each of these programs is the use of spatial metaphors as a key integrating device in instruction. In the rational number curriculum we use linear measurement of continuous quantity and percent as the central context. Our goal here is to foster the integration of students' schema for visual proportional evaluation and their numerical schema of splitting and doubling --two schemas that we have proposed as central to the development of rational number understanding. Initial props such as drainage pipes, venting tubes, and cylindrical beakers filled with water allow students to make ratio and proportional judgements of fullness using the language of percents. In my talk, I will discuss the curriculum and illustrate the kinds of reasoning that the students acquired as a result of their participation.

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