Coordinating Co-Occurrence and Same Extent When Modeling Proportional Relationships

• In Event: Investigations in Middle School Algebra

Abstract

We designed tasks that encourage reasoning about proportional relationships between two co-varying quantities from the novel variable-parts perspective. We then investigated how 10 future middle grades mathematics teachers generated equations to relate quantities in the task situations. Our analysis revealed the importance of coordinating two perspectives on equations as models of problem situations which we term the co-occurrence and same extent perspectives. We argue that past research on school algebra has overlooked as important the distinction between the two perspectives. We then present results demonstrating that ways in which the future teachers did or did not coordinate the two perspectives played a consequential role in their generating normatively correct and normatively incorrect drawings and equations.

Authors

• Andrew G. Izsak, Tufts University

• Sybilla Beckmann, University of Georgia