Reflecting to learn mathematics: supporting pre-service teachers' pedagogical content knowledge with reflection on writing prompts in mathematics education

The use of and reflection on writing prompts in mathematics education can allow pre-service teachers to enhance their own mathematical knowledge and broaden their understanding of students' learning needs. In this paper, we share results from a study with secondary pre-service mathematics teachers who were asked to respond to writing prompts related to various mathematical concepts, reflect on their responses, and then give the same prompts to a group of college algebra students. Our analysis of the data shows that the prompts helped the pre-service teachers to reflect on their role as learners, student thinking and needs and classroom practices. We relate these findings to a framework for looking at pedagogical content knowledge and discuss the usefulness of writing prompts with pre-service mathematics teachers for expanding such knowledge.