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What meanings are assessed in collegiate calculus in the United States?

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Abstract

This article presents the results of our analysis of a sample of 254 Calculus I final exams (collectively containing 4,167 individual items) administered at U.S. colleges and universities. We characterize the specific meanings of foundational concepts the exams assessed, identify features of exam items that assess productive meanings, distinguish categories of items for which students’ responses are not likely to reflect their understanding, and suggest associated modifications to these items that would assess students’ possession of more productive understandings. The article concludes with a discussion of what our findings indicate about the standards and expectations for students’ learning of calculus at institutions of higher education in the United States. We also discuss implications for calculus assessment design and suggest areas for further research.

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Notes

  1. Operations are reversible mental actions that can be applied to a generalized class of objects without regard to an initial state.

  2. College and university designations are based on the university classifications of U.S. News & World Report (www.usnews.com/education).

  3. A student who engages in static shape thinking makes associations between mathematical terms or inscriptions and visual properties of (or actions on) a graph as an object so that these perceptual associations constitute one’s meaning for such terms and inscriptions.

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Funding

This research was supported by National Science Foundation Grant DRL-0910240. Any recommendations or conclusions stated here are those of the authors and do not necessarily reflect official positions of the NSF.

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Authors and Affiliations

  1. Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078, USA

    Michael A. Tallman, Zackery Reed & Michael Oehrtman

  2. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA

    Marilyn P. Carlson

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  1. Michael A. Tallman
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  2. Zackery Reed
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  3. Michael Oehrtman
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  4. Marilyn P. Carlson
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Correspondence to Michael A. Tallman.

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Tallman, M.A., Reed, Z., Oehrtman, M. et al. What meanings are assessed in collegiate calculus in the United States?. ZDM Mathematics Education 53, 577–589 (2021). https://doi.org/10.1007/s11858-020-01212-3

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