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Toward a description of how engineering students think mathematically

Czocher, Jennifer A
http://rave.ohiolink.edu/etdc/view?acc_num=osu1371873286

Abstract Details

2013, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
The purpose of this study was to build a descriptive model for how individuals add mathematical structure to a problem setting. Blum and Leiß’s (2007) mathemat- ical modeling cycle was adopted as a research framework. Data was collected using task-based clinical interviews with four engineering students enrolled in differential equations. Analysis led to the creation of three theoretical constructs which together describe the process of structurally enriching (Schwarzkopf, 2007) a nonmathematical context: mathematical framing, the pseudo-empirical setting, and intertwining. The students in this study made sense of the modeling tasks by assuming that the solution had a certain mathematical structure (the mathematical framing) and then verifying that choice by making sure all the necessary information was present (comparing the information in the task to the pseudo-empirical setting). This process of matching up the variables and operations in the mathematical framing with the quantities and re- lationships in the pseudo-empirical setting was called intertwining. To move forward in the modeling task, the students then externalized a mathematical representation and analyzed it. Validating activity was observed throughout this process and analysis confirmed five distinct types of validating activity: (i) to check alignment of the mathematical representation with the individual’s interpretation of the context (checking mathe- matical representation against the real model); (ii) confirming alignment between the mathematical framing and the individual’s interpretation of the context (checking the mathematical representation against the situation model); (iii) to check alignment be- tween the results of analysis and the individual’s interpretation of the context (check- ing the real results against the real model); (iv) to check the analysis itself (checking mathematical results against the mathematical representation); (v) to check agree- ment between the results of the analysis and the information available from the real world (checking real results against the situation model). These findings were used to build a theoretical model of the mathematical mod- eling process which deviates from previous theoretical and research frameworks used to study mathematical modeling.
Azita Manouchehri (Advisor)
Gregory Baker (Committee Member)
Michael Battista (Committee Member)
409 p.
Mathematics Education
mathematics education; mathematical modeling; post-secondary education; engineering students

Recommended Citations

Citations

  • Czocher, J. A. (2013). Toward a description of how engineering students think mathematically [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1371873286

    APA Style (7th edition)

  • Czocher, Jennifer. Toward a description of how engineering students think mathematically. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1371873286.

    MLA Style (8th edition)

  • Czocher, Jennifer. "Toward a description of how engineering students think mathematically." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1371873286

    Chicago Manual of Style (17th edition)

osu1371873286
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© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.