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
SN - 1098-6065
VL - 16
SP - 285
EP - 311
JO - Mathematical Thinking and Learning
JF - Mathematical Thinking and Learning
IS - 4
ER -