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Conceptualizations of Slope: A Review of State Standards

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Abstract

Since slope is a fundamental topic that is embedded throughout the U.S. secondary school curriculum, this study examined standards documents for all 50 states to determine how they address the concept of slope. The study used eleven conceptualizations of slope as categories to classify the material in the documents. The findings indicate that all of the slope conceptualization categories were evidenced in the standards documents with the vast majority of state documents addressing five or more of the eleven conceptualizations. Results are reported on the most and least commonly documented conceptualizations of slope. The findings provide evidence that there tends to be consensus among the states as to the conceptualizations of slope that should be addressed. Suggestions are made for future work both to consider the initial conceptualizations of slope that students hold or most readily form when introduced to the concept as well as to consider if (or how) slope instruction takes into account students' initial conceptualizations of slope.

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