TY - JOUR

T1 - Classroom engagement towards using definitions for developing mathematical objects

T2 - the case of function

AU - Tabach, Michal

AU - Nachlieli, Talli

N1 - Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - For mathematicians, definitions are the ultimate tool for reaching agreement about the nature and properties of mathematical objects. As research in school mathematics has revealed, however, mathematics learners are often reluctant, perhaps even unable, to help themselves with definitions while categorizing mathematical objects. In the research from which we take the data presented in this article, we have been following a group of prospective mathematics teachers studying functions. In the course of learning, the students gradually accepted the definition as the ultimate criterion to identify examples of function. And yet, this use was hindered by the difficulty the students experienced while trying to understand the logical structure of the definition. Our close analysis has shown that the determiners “for every” and “unique” constituted the main source of the difficulty. We propose that a brief introduction to logic and, in particular, to parsing complex mathematical sentences, may be a useful addition to mathematics curriculum.

AB - For mathematicians, definitions are the ultimate tool for reaching agreement about the nature and properties of mathematical objects. As research in school mathematics has revealed, however, mathematics learners are often reluctant, perhaps even unable, to help themselves with definitions while categorizing mathematical objects. In the research from which we take the data presented in this article, we have been following a group of prospective mathematics teachers studying functions. In the course of learning, the students gradually accepted the definition as the ultimate criterion to identify examples of function. And yet, this use was hindered by the difficulty the students experienced while trying to understand the logical structure of the definition. Our close analysis has shown that the determiners “for every” and “unique” constituted the main source of the difficulty. We propose that a brief introduction to logic and, in particular, to parsing complex mathematical sentences, may be a useful addition to mathematics curriculum.

KW - Commognitive conflict

KW - Discourse analysis

KW - Learning processes

KW - Mathematics definitions

KW - Sociocultural approach

UR - http://www.scopus.com/inward/record.url?scp=85032068426&partnerID=8YFLogxK

U2 - 10.1007/s10649-015-9624-0

DO - 10.1007/s10649-015-9624-0

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AN - SCOPUS:85032068426

SN - 0013-1954

VL - 90

SP - 163

EP - 187

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

IS - 2

ER -