PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Insights into Students’ Images of a Geometric Object and its Formula from a Covariational Reasoning Perspective
Page: 997
In covariational reasoning, when a student conceives of a situation as composed of measurable attributes that vary in tandem, discussing the relationship between quantities represented in a formula requires an interplay between a students’ image of the situation and their conception of a formula. In this study, I categorize four pre-service teachers’ images of both the situation and the formula as they describe the relationship between a given triangle’s height and area. The results indicate how students’ images of the situation and conceptions of a formula influence reasoning about the relationship between two quantities, specifically the role of numerical values and the development of a sophisticated dynamic image of the situation from which the student is able to draw conclusions.