PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Generating Equations for Proportional Relationships Using Magnitude and Substance Conceptions
Page: 1215
We discuss a magnitude conception and a substance conception of fractions and variables that future middle-grades and secondary teachers used when developing and explaining equations for proportional relationships by reasoning about quantities. We conjecture that both conceptions are important for developing equations. The substance conception is useful when a fraction or variable functions as a multiplicand, but not when it functions as a multiplier. The magnitude conception is useful when a fraction or variable functions as a multiplier, but may not be essential when it functions as a multiplicand. Expertise may involve recognizing that the conceptions are distinct and developing a sense of when each conception is useful.