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Tague_Dissertation_Defense_Revise.pdf (138.1 MB)

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Conceptions of Rate of Change: A Cross Analysis of Modes of Knowing and Usage Among Middle, High School, and Undergraduate Students

Tague, Jenna
http://rave.ohiolink.edu/etdc/view?acc_num=osu1437141987

Abstract Details

2015, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
The purpose of the current study was to examine conceptions of rate of change across learners enrolled in middle school, high school, undergraduate calculus and differential equations. The participants were chosen deliberately so to examine how intuitive understandings of rate of change may transform as learners move through the grade levels. Data sources consisted of a large sample of written work (called problem sets) and a small set of in-depth, task-based interviews. The problem sets were collected from 4th through 8th graders across the states of Ohio and Michigan. The interview participants included a total of 8 middle school, high school, undergraduate calculus, and undergraduate differential equations. The tasks used in the study were designed to align with rate-related standards from the Common Core State Standards in Mathematics (CCSSM) (National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010). Both data sets were instigated using conceptual analysis (Thompson, 2008) and Zandieh’s (2000) framework for students’ conceptions of the derivative. Participants showed a strong preference for additive and discrete modes of reasoning about rate of change across many contexts in ways that have not been previously documented. Zandieh’s (2000) framework was extended to include indicators for conceptions of rate of change in context occurring in earlier grade levels. The dynamic technology seemed to shift participants to a more covariational conception of rate of change, but need additional scaffolding for helping students coordinate amongst the physical and graphical representations.
Azita Manouchehri (Advisor)
Patricia Brosnan (Committee Member)
Greg Baker (Committee Member)
356 p.
Mathematics Education

Recommended Citations

Citations

  • Tague, J. (2015). Conceptions of Rate of Change: A Cross Analysis of Modes of Knowing and Usage Among Middle, High School, and Undergraduate Students [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437141987

    APA Style (7th edition)

  • Tague, Jenna. Conceptions of Rate of Change: A Cross Analysis of Modes of Knowing and Usage Among Middle, High School, and Undergraduate Students. 2015. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1437141987.

    MLA Style (8th edition)

  • Tague, Jenna. "Conceptions of Rate of Change: A Cross Analysis of Modes of Knowing and Usage Among Middle, High School, and Undergraduate Students." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437141987

    Chicago Manual of Style (17th edition)

osu1437141987
287
© 2015, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.
Release 3.2.12