id: 06468443
dt: j
an: 2015e.00446
au: Johnson, Heather Lynn; Blume, Glendon W.; Shimizu, Jeanne K.; Graysay,
Duane; Konnova, Svetlana
ti: A teacher’s conception of definition and use of examples when doing and
teaching mathematics.
so: Math. Think. Learn. 16, No. 4, 285-311 (2014).
py: 2014
pu: Taylor \& Francis (Routledge), Philadelphia, PA
la: EN
cc: E49 C49 C39 D30 D40
ut: definition; use of examples; teachers’s mathematical knowledge;
teachers’ conception of definition
ci:
li: doi:10.1080/10986065.2014.953018
ab: Summary: 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.
rv: