東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

Sameness of Representation of Mathematical Entities.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Sameness of Representation of Mathematical Entities./
作者:	Mirin, Alison.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	222 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
標題:	Mathematics education. -
電子資源:	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.
LDR:03292nmm a2200397 4500 001 2345156
005 20220531132452.5
008 241004s2021 ||||||||||||||||| ||eng d
020 $a 9798535544052
035 $a (MiAaPQ)AAI28549387
035 $a AAI28549387
040 $a MiAaPQ $c MiAaPQ
100 1 $a Mirin, Alison. $3 3684044
245 1 0 $a Sameness of Representation of Mathematical Entities.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 222 p.
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.
506 $a This item must not be sold to any third party vendors.
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).
590 $a School code: 0010.
650 4 $a Mathematics education. $3 641129
650 4 $a Mathematics. $3 515831
650 4 $a Cognitive psychology. $3 523881
650 4 $a Names. $3 3680861
650 4 $a Students. $3 756581
650 4 $a Investigations. $3 3561159
650 4 $a Equality. $3 520285
650 4 $a Ebola virus. $3 3684045
650 4 $a Algebra. $3 516203
650 4 $a Literature reviews. $3 3559998
650 4 $a Set theory. $3 520081
650 4 $a Mathematicians. $3 514781
650 4 $a 19th century. $3 1972810
650 4 $a Philosophy. $3 516511
650 4 $a Philosophers. $3 558041
653 $a Calculus
653 $a Equals sign
653 $a Functions
653 $a Multiple representations
653 $a Sameness
653 $a Systemic functional linguistics
690 $a 0280
690 $a 0405
690 $a 0633
690 $a 0422
710 2 $a Arizona State University. $b Mathematics. $3 3433211
773 0 $t Dissertations Abstracts International $g 83-02B.
790 $a 0010
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28549387