TY - JOUR

T1 - A conceptual model of mathematical reasoning for school mathematics

AU - Jeannotte, Doris

AU - Kieran, Carolyn

N1 - Funding Information:
The authors express their appreciation to the Social Sciences and Humanities Research Council of Canada for its financial support of this research and to the reviewers for their helpful comments. In addition, the first author wishes to thank the members of her doctoral research committee for their academic support and encouragement during the years of this project.
Publisher Copyright:
© 2017, Springer Science+Business Media Dordrecht.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - The development of students’ mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR, this research project aimed to qualify it from a theoretical perspective, with an elaboration that would not only indicate its ways of being thought about and espoused but also serve as a tool for reflection and thereby contribute to the further evolution of the cultures of the teaching and research communities in mathematics education. To achieve such an elaboration, a literature search based on anasynthesis (Legendre, 2005) was undertaken. From the analysis of the mathematics education research literature on MR and taking a commognitive perspective (Sfard, 2008), the synthesis that was carried out led to conceptualizing a model of mathematical reasoning. This model, which is herein described, is constituted of two main aspects: a structural aspect and a process aspect, both of which are needed to capture the central characteristics of MR.

AB - The development of students’ mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR, this research project aimed to qualify it from a theoretical perspective, with an elaboration that would not only indicate its ways of being thought about and espoused but also serve as a tool for reflection and thereby contribute to the further evolution of the cultures of the teaching and research communities in mathematics education. To achieve such an elaboration, a literature search based on anasynthesis (Legendre, 2005) was undertaken. From the analysis of the mathematics education research literature on MR and taking a commognitive perspective (Sfard, 2008), the synthesis that was carried out led to conceptualizing a model of mathematical reasoning. This model, which is herein described, is constituted of two main aspects: a structural aspect and a process aspect, both of which are needed to capture the central characteristics of MR.

KW - Anasynthesis

KW - Commognition

KW - Mathematical reasoning

KW - Process aspect of mathematical reasoning

KW - School mathematics

KW - Structural aspect of mathematical reasoning

KW - Theoretical model

UR - http://www.scopus.com/inward/record.url?scp=85019103144&partnerID=8YFLogxK

U2 - 10.1007/s10649-017-9761-8

DO - 10.1007/s10649-017-9761-8

M3 - Article

AN - SCOPUS:85019103144

VL - 96

SP - 1

EP - 16

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

SN - 0013-1954

IS - 1

ER -