Preparing Teachers to Notice Student Thinking Through a Task-based Interview Module

Supplementary Materials for AMTE Standards

Student-centered instruction requires that teachers not only attend to and interpret student thinking, but also respond to student thinking in a way that uses students’ current understandings and methods as a basis for instruction (NCTM, 2014). To support pre-service teachers (PSTs) in developing these professional noticing skills (Jacobs, Lamb, & Phillip, 2010) we designed and implemented a task-based Interview Module in secondary methods courses (Krupa, Huey, Lesseig, Casey, & Monson, 2017; Lesseig, Casey, Monson, Krupa & Huey, 2016). The original Interview Module consisted of a pre-post video assessment of PSTs’ noticing, readings and discussion to support PSTs in eliciting student thinking through focusing questions, as well as a detailed protocol for conducting and analyzing the task-based interview. Our initial research, conducted with 32 PSTs across three institutions, showed that completion of the module improved secondary PSTs’ abilities to attend to and interpret student thinking, but was insufficient in terms of improving PSTs’ ability to effectively respond to student thinking.

Based on this research we created additional assignments within the module to specifically foster PSTs’ ability to respond to students’ mathematical thinking (Casey, Lesseig, Monson, & Krupa, in press). These additions included providing PSTs with background research on student thinking related to the mathematical content in the task-based interview, a set of four characteristics of a good response derived from the literature (e.g., Jacobs, Lamb, Philipp, & Schappelle, 2011), and opportunities for PSTs to collectively, and individually, construct responses to student work that met these four criteria. The student work samples were generated from previous interview assignments we had collected. The four criteria of a good response—(1) works towards the student learning objectives, (2) draws on and is consistent with the student thinking presented, (3) draws on and is consistent with research on students' mathematical development, and (4) proposed interaction leaves space for student's future thinking, not just the teacher's thinking—align with targeted SPTM indicators discussed in the next section.

The four authors have implemented the complete Interview Module in secondary methods courses at our respective universities since 2016. The materials presented reflect our collaborative learning through this process and include all student materials as well as three documents intended to support other MTEs in effectively implementing the Interview Module and assessing PSTs progress along the way.

Standards and Indicators these Materials Target

The Interview Module is designed to support pre-service secondary teachers’ abilities to notice student thinking. Thus, it primarily addresses standard C.3: Students as Mathematics Learners. However, given the clear overlap between attending to students’ mathematical thinking, interpreting that thinking in relation to core mathematical ideas, and responding to that thinking in a productive manner, the Interview Module necessarily addresses aspects of each of the other three standards. Below we outline specific connections to key indicators within each of the four standards.

  • C.1.5. Analyze Mathematical Thinking. The initial activity in the module has PSTs interview a high school student and analyze the student’s mathematical thinking on a task that involves solving linear equations using multiple representations. After the interview, PSTs write a reflection paper in which they detail what the student seemed to understand mathematically, what the student still needs to understand, and what they would do as a classroom teacher to move this student from where they appear to be to a more robust understanding of the interview topic.
  • C.2.3. Implement Effective Instruction. Along with eliciting and using evidence of student thinking, the Interview Module as a whole provides opportunities for PSTs to work on the effective instructional practices of posing purposeful questions to assess and advance student thinking and building procedural fluency from conceptual understanding (NCTM, 2014).
  • C.3.1 Anticipate and Attend to Students’ Thinking About Mathematics Content. Two additional aspects of the reflection paper focus PSTs’ attention on students’ thinking about the specific mathematics content in the task. First, PSTs use a rubric to rate the student’s versatility and adaptability in relation to the Rule of Four Model of Multiple Representations (Huntley, Marcus, Kahan & Miller, 2007). Second, PSTs are asked to identify and analyze a surprising or interesting interchange from the interview transcript that “provides evidence of what the student understands about the math in the task.”
  • C.4.3. Draw on Students’ Mathematical Strengths. The responding portion of the module demands that PSTs attend and respond to student’s current understandings. In our study, we found that when responding to student thinking, PSTs tended to focus on student errors and often described their instructional responses in terms of “fixing” student mistakes by telling them what they did wrong (Krupa et al., 2017; Lesseig et al., 2016). The responding assignment seeks to confront this deficit thinking and scaffolds PSTs’ ability to respond by providing structured opportunities for them to identify the mathematical strengths evidenced in typical student solutions, which often vary from their own ways of thinking. The four criteria of a good response provides a research-based tool through which PSTs can then evaluate their planned response to student thinking.

About the Authors

Kristin Lesseig - Washington State University Vancouver
Stephanie Casey - Eastern Michigan University
Erin Krupa - North Carolina State University
Debbie Monson - University of St. Thomas