This study investigates student teachers' conceptions of even numbers and the relationship between proof types and conceptions of even numbers. 22 student teachers in the course of mathematical teaching for young children participated in this study. All participants were asked to finish three research tasks. Task 1 was designed to provide information of student teachers' concept of even numbers. Task 2 and 3 asked the participants to reply what is even number and then to judge the statement true or false and give proofs for their argumentations. All the data were analyzed based on two frameworks. One is the category of even numbers and the other one is proof style. After the classifications, we checked the thinking path from conceptions to the proofs. The results are: student teachers' conceptions of even numbers could be identified into three kinds, including numerical conception, procedural conception and abstract conception. When they proved the proposition that the sum of two even numbers is always even, they used two more conceptions of even numbers. But when they proved that if you want to make a judgment whether 14, 17, 23, 28 are even numbers or not respectively, you could find the results depending on the units digit only, their representations of even numbers are back to the original situation. In addition, two research conjectures are proposed: the need of solution will excite one's multiple representations of concept, and these multiple representations of concept will catalyze the connection between conceptions and proofs.
Analiza Liezl Perez-Amurao, Mahidol University, Thailand
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