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Toward a description of how engineering students think mathematically
Czocher, Jennifer A

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.

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Czocher, J. (2013). Toward a description of how engineering students think mathematically. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Czocher, Jennifer. "Toward a description of how engineering students think mathematically." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 19 Nov 2018.

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Czocher, Jennifer "Toward a description of how engineering students think mathematically." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

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