TY - JOUR

T1 - A Teacher’s Conception of Definition and Use of Examples When Doing and Teaching Mathematics

AU - Johnson, Heather Lynn

AU - Blume, Glendon W.

AU - Shimizu, Jeanne K.

AU - Graysay, Duane

AU - Konnova, Svetlana

N1 - Funding Information:
The research reported in this article was supported in part by Grant No. ESI-0426253 from the National Science Foundation for the Mid-Atlantic Center for Mathematics Teaching and Learning (MAC-MTL) at The Pennsylvania State University. Any opinions, findings, or conclusions and recommendations expressed herein are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Publisher Copyright:
© , Copyright © Taylor & Francis Group, LLC.

PY - 2014/10/25

Y1 - 2014/10/25

N2 - To contribute to an understanding of the nature of teachers’ mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher’s conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical knowledge, the authors give an account of the case of Lily, a prospective, then beginning, teacher who conceived of mathematical definition as an object with particular form and function and engaged in purposeful, specialized use of examples when doing and teaching mathematics. Lily’s case illustrates how a teacher’s interpretation of examples (as exemplifications or single instances) and conception of the form and function of definitions can influence her doing and teaching mathematics. An implication is that teacher preparation should foster teachers’ abilities to use examples purposefully to provide students with rich opportunities to engage in mathematical processes such as defining.

AB - To contribute to an understanding of the nature of teachers’ mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher’s conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical knowledge, the authors give an account of the case of Lily, a prospective, then beginning, teacher who conceived of mathematical definition as an object with particular form and function and engaged in purposeful, specialized use of examples when doing and teaching mathematics. Lily’s case illustrates how a teacher’s interpretation of examples (as exemplifications or single instances) and conception of the form and function of definitions can influence her doing and teaching mathematics. An implication is that teacher preparation should foster teachers’ abilities to use examples purposefully to provide students with rich opportunities to engage in mathematical processes such as defining.

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U2 - 10.1080/10986065.2014.953018

DO - 10.1080/10986065.2014.953018

M3 - Article

AN - SCOPUS:84908067805

VL - 16

SP - 285

EP - 311

JO - Mathematical Thinking and Learning

JF - Mathematical Thinking and Learning

SN - 1098-6065

IS - 4

ER -