Opportunities for reasoning-and-proving in mathematical tasks: a discursive perspective

Merav Weingarden; Orly Buchbinder; Jinqing Liu

Opportunities for reasoning-and-proving in mathematical tasks: a discursive perspective

Merav Weingarden, Orly Buchbinder, Jinqing Liu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the curricular-based mathematical discourse and as participation in the meta-discourse about proof, which is focused on the aspects of deductive reasoning. By cluster analysis performed on 106 tasks designed by prospective secondary teachers, we identify four types of tasks corresponding to four types of ORP: limited ORP, curricular-based reasoning ORP, logic related ORP, and fully integrated ORP. We discuss these ORP and the contribution of this framework in light of preparing beginning teachers to integrate reasoning and proving in secondary mathematics classrooms.

Original language	English
Title of host publication	Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
Editors	Alyson E. Lischka, Elizabeth B. Dyer, Ryan Seth Jones, Jennifer Lovett, Jeremy Strayer, Samantha Drown
Pages	857-866
State	Published - 2022
Externally published	Yes
Event	The 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education - Middle Tennessee State University, Nashville, United States Duration: 17 Nov 2022 → 20 Nov 2022

Conference

Conference	The 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
Abbreviated title	PME-NA
Country/Territory	United States
City	Nashville
Period	17/11/22 → 20/11/22

Keywords

Beginning teachers
Classroom Discourse
Cluster analysis (Statistics)
Curriculum
Instructional Activities and Practices
Mathematics education
Preservice Teacher Education
Reasoning
Reasoning and Proof

Cite this

Weingarden, M., Buchbinder, O., & Liu, J. (2022). Opportunities for reasoning-and-proving in mathematical tasks: a discursive perspective. In A. E. Lischka, E. B. Dyer, R. S. Jones, J. Lovett, J. Strayer, & S. Drown (Eds.), Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 857-866)

Weingarden, Merav ; Buchbinder, Orly ; Liu, Jinqing. / Opportunities for reasoning-and-proving in mathematical tasks : a discursive perspective. Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. editor / Alyson E. Lischka ; Elizabeth B. Dyer ; Ryan Seth Jones ; Jennifer Lovett ; Jeremy Strayer ; Samantha Drown. 2022. pp. 857-866

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title = "Opportunities for reasoning-and-proving in mathematical tasks: a discursive perspective",

abstract = "In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the curricular-based mathematical discourse and as participation in the meta-discourse about proof, which is focused on the aspects of deductive reasoning. By cluster analysis performed on 106 tasks designed by prospective secondary teachers, we identify four types of tasks corresponding to four types of ORP: limited ORP, curricular-based reasoning ORP, logic related ORP, and fully integrated ORP. We discuss these ORP and the contribution of this framework in light of preparing beginning teachers to integrate reasoning and proving in secondary mathematics classrooms.",

keywords = "Beginning teachers, Classroom Discourse, Cluster analysis (Statistics), Curriculum, Instructional Activities and Practices, Mathematics education, Preservice Teacher Education, Reasoning, Reasoning and Proof",

author = "Merav Weingarden and Orly Buchbinder and Jinqing Liu",

year = "2022",

language = "الإنجليزيّة",

isbn = "9781734805710",

pages = "857--866",

editor = "Lischka, {Alyson E.} and Dyer, {Elizabeth B.} and Jones, {Ryan Seth} and Jennifer Lovett and Jeremy Strayer and Samantha Drown",

booktitle = "Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education",

note = "The 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education ; Conference date: 17-11-2022 Through 20-11-2022",

}

Weingarden, M, Buchbinder, O & Liu, J 2022, Opportunities for reasoning-and-proving in mathematical tasks: a discursive perspective. in AE Lischka, EB Dyer, RS Jones, J Lovett, J Strayer & S Drown (eds), Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. pp. 857-866, The 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Nashville, United States, 17/11/22.

Opportunities for reasoning-and-proving in mathematical tasks: a discursive perspective. / Weingarden, Merav; Buchbinder, Orly; Liu, Jinqing.
Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. ed. / Alyson E. Lischka; Elizabeth B. Dyer; Ryan Seth Jones; Jennifer Lovett; Jeremy Strayer; Samantha Drown. 2022. p. 857-866.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T2 - The 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education

AU - Weingarden, Merav

AU - Buchbinder, Orly

AU - Liu, Jinqing

PY - 2022

Y1 - 2022

N2 - In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the curricular-based mathematical discourse and as participation in the meta-discourse about proof, which is focused on the aspects of deductive reasoning. By cluster analysis performed on 106 tasks designed by prospective secondary teachers, we identify four types of tasks corresponding to four types of ORP: limited ORP, curricular-based reasoning ORP, logic related ORP, and fully integrated ORP. We discuss these ORP and the contribution of this framework in light of preparing beginning teachers to integrate reasoning and proving in secondary mathematics classrooms.

AB - In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the curricular-based mathematical discourse and as participation in the meta-discourse about proof, which is focused on the aspects of deductive reasoning. By cluster analysis performed on 106 tasks designed by prospective secondary teachers, we identify four types of tasks corresponding to four types of ORP: limited ORP, curricular-based reasoning ORP, logic related ORP, and fully integrated ORP. We discuss these ORP and the contribution of this framework in light of preparing beginning teachers to integrate reasoning and proving in secondary mathematics classrooms.

KW - Beginning teachers

KW - Classroom Discourse

KW - Cluster analysis (Statistics)

KW - Curriculum

KW - Instructional Activities and Practices

KW - Mathematics education

KW - Preservice Teacher Education

KW - Reasoning

KW - Reasoning and Proof

M3 - منشور من مؤتمر

SN - 9781734805710

SP - 857

EP - 866

BT - Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education

A2 - Lischka, Alyson E.

A2 - Dyer, Elizabeth B.

A2 - Jones, Ryan Seth

A2 - Lovett, Jennifer

A2 - Strayer, Jeremy

A2 - Drown, Samantha

Y2 - 17 November 2022 through 20 November 2022

ER -

Opportunities for reasoning-and-proving in mathematical tasks: a discursive perspective

Abstract

Conference

Keywords

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Cite this