|Jinfa Cai (USA)||email@example.com|
Pedagogical representations are the representations that teachers and
students use in their classroom as both carriers of knowledge and thinking
tools to explain a concept, a relationship, a connection, or a problem-solving
process. Although there is no universal agreement about what constitutes
"good pedagogical representation" in mathematics teaching, no
one questions the idea that the construction of desirable pedagogical
representations is influenced by teachers' beliefs, conceptions, and knowledge
of mathematics. This paper will present results from a study investigating
12 experienced and 12 inexperienced math teachers' conceptions and construction
in their teaching of arithmetic average. This study used interviews and
analyses of lessons to examine teachers' conceptions and constructions
of pedagogical representations. The interviews and analyses of lessons
weave together pedagogical representations in mathematics teaching from
three aspects: knowing students' representations and strategies in problem
solving, evaluating students' representations and solution strategies,
and generating pedagogical representations for classroom instruction.
Any representation will express some, but not all, of the information;
it will stress some aspects and hide others. Hopefully, the results of
this study will not only help us understand desirable pedagogical representations
for teaching arithmetic average, but also help us establish a balanced
view of using various representations in mathematics instruction.
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