Developing teachers’ knowledge of students as learners of mathematics through structured interviews

Abstract

A structured interview process is proffered as an effective means to advance prospective teachers’ understandings of students as learners of mathematics, a key component of pedagogical content knowledge. The interview process is carried out in three phases with the primary objective of developing listening skills for accessing students’ mathematical thinking. The interviews adhere to clinical interview procedures for discovering cognitive activities and, accordingly, are initiated by presenting an open-ended mathematics task. Three rounds of interviews were completed by undergraduates enrolled in a middle school mathematics methods course. Anecdotal data generated by their interview reports suggest that the structured interview process engenders an interpretive orientation to listening to students and furthers awareness of how students make sense of mathematics. Features of the interview process that may limit its potential benefits are discussed; recommendations for further study are proposed.

Appendices

Appendix A: Student interview report

Name: _______________________________________ Date: __________________

Problem/Task: ________________________________________________________________

Part I (To be completed prior to the interviews):

• 1. Identify responses you might expect from middle grades students engaging this problem or task taking into account (a) anticipated strengths and misconceptions and (b) characteristics attributable to middle grades students.

• 2. Create a simpler problem to use should students initially struggle with the original task. What anticipated misconceptions are overcome by the “simpler” problem?

Part II (To be completed during the interviews):

The “interviewer” conducts the interview adhering to established guidelines. The “recorder” observes how students’ reason through the task and takes notes. Attach students’ work and the interview notes to this report.

Part III (To be completed after the interviews):

• 1. Analyze the interview data (students’ work samples and the interview notes). What can you conclude about the students’ knowledge of mathematics content relevant to the task? What misconceptions did they bring to the task? How did they reason through the task? What problem-solving strategies did they employ? How well did they communicate mathematical ideas? What connections did they make among mathematical ideas and to contexts outside of mathematics? How did they use mathematical representations to interpret (or model) the task and solve problems?

• 2. What insights have you gained from these interviews with respect to middle grades students’ thinking about mathematics – in particular, how they think about the mathematics concepts underlying the interview tasks? Your response should be grounded in the preceding analysis of interview data and informed by applicable learning theories and mathematics education research.

• 3. Compare your findings and/or methodology to those reported in a related published article (when available).

Appendix B

See Table 1.

Table 1 Scoring rubric for student interview report