Rachael Kenney

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.

POETIC: Interactive solutions to alleviate the reversal error in student-professor type problems

The reversal error-reversing the relationship between two variables in a mathematical word problem-is a long-standing issue in mathematics education, despite its apparent simplicity. In this paper, we describe and study POETIC, an interactive web-based environment we developed to teach users to avoid the reversal error. POETIC uses two types of novel interactive visualization, called the Test-Case and Room-Metaphor approaches. To verify the effectiveness of these approaches, we conducted crowdsourcing-based comparison studies with 200 participants and found that both approaches significantly decreased the frequency of reversal errors for certain types of word problems. Our results show that interactive visualization of equations can reduce the occurrence of the reversal error.