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Proof and Proving in School and University Mathematics Education Research: A Systematic Review

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Title: Proof and Proving in School and University Mathematics Education Research: A Systematic Review
Language: English
Authors: Gabriel J. Stylianides (ORCID 0000-0003-1770-8753), Andreas J. Stylianides (ORCID 0000-0002-3526-0342), Andreas Moutsios-Rentzos (ORCID 0000-0002-9614-2825)
Source: ZDM: Mathematics Education. 2024 56(1):47-59.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 13
Publication Date: 2024
Document Type: Journal Articles
Information Analyses
Education Level: Elementary Secondary Education
Postsecondary Education
Descriptors: Mathematics Education, Validity, Mathematical Logic, Educational Research, Elementary Secondary Education, Postsecondary Education
DOI: 10.1007/s11858-023-01518-y
ISSN: 1863-9690
1863-9704
Abstract: This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on "proof" and "proving" in both school and university mathematics. As an organizing framework, we used Cohen et al.'s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the "Teacher" and "Students") and the "Content" around which the actors' work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students' engagement with proof and proving. About a quarter of the papers fell in the Student-Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student--Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards 'breaking ground' through making an explicit theoretical and/or methodological contribution (Student-Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on 'building ground' through elaborating or employing existing methodological and/or theoretical approaches.
Abstractor: As Provided
Entry Date: 2024
Accession Number: EJ1407838
Database: ERIC
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  Data: <searchLink fieldCode="AR" term="%22Gabriel+J%2E+Stylianides%22">Gabriel J. Stylianides</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0003-1770-8753">0000-0003-1770-8753</externalLink>)<br /><searchLink fieldCode="AR" term="%22Andreas+J%2E+Stylianides%22">Andreas J. Stylianides</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-3526-0342">0000-0002-3526-0342</externalLink>)<br /><searchLink fieldCode="AR" term="%22Andreas+Moutsios-Rentzos%22">Andreas Moutsios-Rentzos</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-9614-2825">0000-0002-9614-2825</externalLink>)
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  Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
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  Data: This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on "proof" and "proving" in both school and university mathematics. As an organizing framework, we used Cohen et al.'s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the "Teacher" and "Students") and the "Content" around which the actors' work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students' engagement with proof and proving. About a quarter of the papers fell in the Student-Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student--Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards 'breaking ground' through making an explicit theoretical and/or methodological contribution (Student-Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on 'building ground' through elaborating or employing existing methodological and/or theoretical approaches.
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