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Sameness of Representation of Mathematical Entities.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Sameness of Representation of Mathematical Entities./
Author:	Mirin, Alison.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	222 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
Subject:	Mathematics education. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28549387
ISBN:	9798535544052

Sameness of Representation of Mathematical Entities.
Mirin, Alison.

Sameness of Representation of Mathematical Entities. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 222 p.

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--Arizona State University, 2021.

This item must not be sold to any third party vendors.

This dissertation is on the topic of sameness of representation of mathematical entities from a mathematics education perspective. In mathematics, people frequently work with different representations of the same thing. This is especially evident when considering the prevalence of the equals sign (=). I am adopting the three-paper dissertation model. Each paper reports on a study that investigates understandings of the identity relation. The first study directly addresses function identity: how students conceptualize, work with, and assess sameness of representation of function. It uses both qualitative and quantitative methods to examine how students understand function sameness in calculus contexts. The second study is on the topic of implicit differentiation and student understanding of the legitimacy of it as a procedure. This relates to sameness insofar as differentiating an equation is a valid inference when the equation expresses function identity. The third study directly addresses usage of the equals sign ("="). In particular, I focus on the notion of symmetry; equality is a symmetric relation (truth-functionally), and mathematicians understand it as such. However, results of my study show that usage is not symmetric. This is small qualitative study and incorporates ideas from the field of linguistics.Each study is at a different point in the journey of becoming a self-contained journal article. Portions of the first study have been published in two separate conference proceedings (Mirin, 2018, 2020b). The second dissertation study is already published in a journal (Mirin & Zazkis, 2020). Copyright of the journal paper is held by For the Learning of Mathematics Publishing Association (https://flm-journal.org/). The third study is earliest in this process; no empirical aspects of it have been published in any proceedings or journals. However, preliminary results were presented at the Northeastern RUME (Research in Undergraduate Mathematics Education) conference (Mirin & Dawkins, 2020), and theoretical contributions are reported in Mirin (2019) and Mirin (2020a).

ISBN: 9798535544052Subjects--Topical Terms:

641129
Mathematics education.
Subjects--Index Terms:

Calculus

Sameness of Representation of Mathematical Entities.
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500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
500 $a Advisor: Zazkis, Dov.
502 $a Thesis (Ph.D.)--Arizona State University, 2021.
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520 $a This dissertation is on the topic of sameness of representation of mathematical entities from a mathematics education perspective. In mathematics, people frequently work with different representations of the same thing. This is especially evident when considering the prevalence of the equals sign (=). I am adopting the three-paper dissertation model. Each paper reports on a study that investigates understandings of the identity relation. The first study directly addresses function identity: how students conceptualize, work with, and assess sameness of representation of function. It uses both qualitative and quantitative methods to examine how students understand function sameness in calculus contexts. The second study is on the topic of implicit differentiation and student understanding of the legitimacy of it as a procedure. This relates to sameness insofar as differentiating an equation is a valid inference when the equation expresses function identity. The third study directly addresses usage of the equals sign ("="). In particular, I focus on the notion of symmetry; equality is a symmetric relation (truth-functionally), and mathematicians understand it as such. However, results of my study show that usage is not symmetric. This is small qualitative study and incorporates ideas from the field of linguistics.Each study is at a different point in the journey of becoming a self-contained journal article. Portions of the first study have been published in two separate conference proceedings (Mirin, 2018, 2020b). The second dissertation study is already published in a journal (Mirin & Zazkis, 2020). Copyright of the journal paper is held by For the Learning of Mathematics Publishing Association (https://flm-journal.org/). The third study is earliest in this process; no empirical aspects of it have been published in any proceedings or journals. However, preliminary results were presented at the Northeastern RUME (Research in Undergraduate Mathematics Education) conference (Mirin & Dawkins, 2020), and theoretical contributions are reported in Mirin (2019) and Mirin (2020a).
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