Working on her dissertation in the mid-1990s, Sheryl Stump (now the Department Chairperson and a Professor of Mathematical Sciences at Ball State University) did some of the best work to date about how we define and conceive of slope. We believe that a better way to settle this would be to consult the published work of experts on slope. Rather, Karim argued, slope should be defined as “a rate that describes how two variables change in relation to one another.” Sal promptly responded, saying Karim was incorrect, and that “slope actually is defined as change in y over change in x (or rise over run).” To bolster his case Sal referenced Wolfram Mathworld, and he encouraged Valerie Strauss to “seek out an impartial math professor” to help settle the debate. As an example, he pointed to the video on “slope.” Specifically, Karim claimed Sal’s definition of slope as “rise over run” was a way to calculate slope, but wasn’t, itself, a definition of slope. While Karim’s initial post focused mainly on Sal Khan’s pedagogical approach, Karim also took issue with the accuracy of Khan Academy videos. The Answer Sheet has recently been the focus of a lively debate pitting teacher and guest blogger Karim Kai Ani against the Khan Academy’s Salman Khan. Raymond blogs about math education and policy at and Fred shares his research and curriculum at. Raymond and Fred each have six years of experience teaching Algebra 1 and are engaged in research on how students understand slope and linear functions. students in mathematics education at the University of Colorado at Boulder and the Freudenthal Institute US. This was written Raymond Johnson and Frederick Peck, Ph.D.
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