A Study of Prospective Elementary Teachers' Perceptions and Reflections while Investigating Children's Thinking in a Mathematics for Teaching Course

摘要

Teacher educators use children's thinking activities as a means to prepare prospective teachers to teach mathematics. Research in methods courses and student teaching practica has shown these types of activities help prospective teachers deepen their own mathematical knowledge as well as better understand how children think. This study investigates prospective teachers' perceptions in a mathematics for teaching course when using children's thinking activities. Specifically, this study documents how four case study students perceived of the activities, their own and children's mathematical thinking, and the role of language in mathematics teaching and learning.Observations, interviews, and written class work were analyzed through the generation of themes within and across cases. It was found that all of the participants perceived the children's thinking activities as beneficial to providing insight into how children think mathematically. In contrast, two of the four participants did not perceive the activities as supportive of their own mathematical learning. However, the participants' reflections, both on children's mathematical thinking and their own, showed that all participants grappled with important mathematical concepts. Specifically, through consideration of their own thinking, children's strategies, and children's understanding, participants discussed the fractional whole, the meaning of operations, and connections among strategies, among other topics. This difference between how the participants perceived the use of children's thinking activities and what was evidenced through their reflections suggests that participants might have felt a stigma in studying elementary mathematics.While the participants did not often reflect on the role of language in teaching and learning mathematics, they did articulate various ideas regarding language and mathematics, in particular regarding the instruction of English Language Learners (ELLs). They discussed ways to help ELLs acquire mathematical language, which three participants saw as more than just vocabulary. All participants also thought it was important for children to express their mathematical understanding. However, two participants seemed to conceive of a unique way to express that understanding. This finding suggests that prospective teachers need to be critically exposed to literature regarding mathematics instruction of language-minority children.