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Cognitive and Affective Components o...

Satyam, Visala Rani.

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Cognitive and Affective Components of Undergraduate Students Learning How to Prove.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Cognitive and Affective Components of Undergraduate Students Learning How to Prove./
Author:	Satyam, Visala Rani.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	202 p.
Notes:	Source: Dissertation Abstracts International, Volume: 79-12(E), Section: A.
Contained By:	Dissertation Abstracts International79-12A(E).
Subject:	Mathematics education. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10930330
ISBN:	9780438292086

Cognitive and Affective Components of Undergraduate Students Learning How to Prove.
Satyam, Visala Rani.

Cognitive and Affective Components of Undergraduate Students Learning How to Prove. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 202 p.

Source: Dissertation Abstracts International, Volume: 79-12(E), Section: A.

Thesis (Ph.D.)--Michigan State University, 2018.

Students struggle with proving, a fundamental activity in upper-level undergraduate mathematics courses. Learning how to prove is a difficult transition for students, as they shift from largely computation-based to argument-based work. In response, mathematics departments have instituted courses, introduction or transition to proof, designed to help students learn how to prove. Existing research has extensively examined students' errors, struggles, and some of their strategies at a given point in time, but we know little about students' development over a longer period of time. There is a need for longitudinal work in this area, to follow students through the transition to proof.

ISBN: 9780438292086Subjects--Topical Terms:

641129
Mathematics education.

Cognitive and Affective Components of Undergraduate Students Learning How to Prove.
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245 1 0 $a Cognitive and Affective Components of Undergraduate Students Learning How to Prove.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 202 p.
500 $a Source: Dissertation Abstracts International, Volume: 79-12(E), Section: A.
500 $a Adviser: John P. Smith.
502 $a Thesis (Ph.D.)--Michigan State University, 2018.
520 $a Students struggle with proving, a fundamental activity in upper-level undergraduate mathematics courses. Learning how to prove is a difficult transition for students, as they shift from largely computation-based to argument-based work. In response, mathematics departments have instituted courses, introduction or transition to proof, designed to help students learn how to prove. Existing research has extensively examined students' errors, struggles, and some of their strategies at a given point in time, but we know little about students' development over a longer period of time. There is a need for longitudinal work in this area, to follow students through the transition to proof.
520 $a In addition, little is known about the affective side of proving (e.g., attitudes, beliefs, emotions). Affect plays a central role in mathematics learning, influencing students' cognitive processes while problem solving and their motivation to value and want to do mathematics. Understanding affective issues are important, as students consider their future participation in mathematical work and communities. Positive experiences at transitional junctions, such as learning how to prove, are crucial for retention of students through the STEM (Science, Technology, Engineering, and Mathematics) pipeline.
520 $a The purpose of this work was to explore the cognitive and affective factors involved in undergraduates' efforts to learn how to prove: how their proving developed during a transition to proof course and what kinds of satisfying moments, i.e. positive emotional reactions, they experienced. Four semi-structured interviews across a semester were conducted with eleven undergraduate students enrolled in a transition to proof course. The resulting data was analyzed using qualitative methods.
520 $a Findings indicate that students showed growth in fluency, strategy use, and monitoring and judgement over time. Four developments were frequently observed across the sample: (1) increased sophistication in students' rationales for choice of proof techniques, (2) awareness about how a solution attempt was going and managing that for their subsequent strategies, (3) intentional exploring and monitoring when unsure about what direction to pursue, and (4) checking examples in conjunction with other strategies as a way to become unstuck. The variety of developments---and the different ways in which they emerged---is significant, because it confirms that multiple developments occur in different ways, strongly suggesting that there is no one path that students take through the transition to proof.
520 $a Students' satisfying moments were largely about accomplishments both with and without struggle, understanding, external validation, as well as interacting with others. A theory for how satisfying moments are elicited was proposed. Expectations and a sense of mastery played large roles in mediating satisfying moments, but students' desire for understanding and sense-making was also prominent.
520 $a This work provides guidance for curriculum design of transition to proof courses, in considering how to support students' development in proving. In addition, examination of just what makes a satisfying moment satisfying is helpful in thinking about how to construct mathematical tasks with opportunities for positive experiences with math.
590 $a School code: 0128.
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650 4 $a Higher education. $3 641065
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