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.