College Students’ Understanding of Linear Functions: Slope is Slippery


A common obstacle for students in the transition from arithmetic to algebra is developing a conceptual understanding of equations representing functions. Two experiments manipulated isomorphic problems in terms of their solution requirements (computation vs. interpretation) and format to test for understanding of linear functions. Experiment 1 provided problems in a story context, and found that performance on slope comparison problems was low, especially when problems were presented with equations. Experiment 2 tested whether performance on slope comparison problems improves when problem prompts include explicit mathematical terminology rather than just natural language consistent with the problem story. Results suggest that many undergraduate students fail to access the mathematical concept of slope when problem prompts are presented with natural language. Overall, the results suggest that even undergraduate students lack understanding of the slope concept and equations of linear functions, both which are foundational for advanced algebraic thinking.

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