## Prospective Teachers’ Reasoning and Response to A Student’s Non-Traditional Strategy When Dividing Fractions

Source: *Journal of Mathematics Teacher Education, Volume 12, Number 4* / August 2009, p. 235-261.

Recognizing meaning in students’ mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined the reasoning and responses of prospective elementary and secondary teachers to a student’s non-traditional strategy for dividing fractions. The authors used a teaching-scenario task to explore the teachers' reasoning and responses.

Six categories of reasoning were constructed, making a distinction between deep and surface layers. The connections between the participants’ reasoning, their teaching response, and their beliefs about mathematics teaching were investigated.

The authors found that there were not only differences but also similarities between the prospective elementary and secondary teachers’ reasoning and responses. The authors also found that those who unpacked the mathematical underpinning of the student’s non-traditional strategy tended to use what the authors call “teacher-focused” responses, whereas those doing less analysis work tended to construct “student-focused” responses.

These results and their implications are discussed in relation to the influential factors the participants themselves identified to explain their approach to the given teaching-scenario task.