Sandy M. Spitzer

Prospective Teachers' Conceptions and Values about Learning from Teaching.

Although researchers and educators have suggested teaching prospective teachers (PTs) to investigate and learn from their own teaching over time, little research has investigated PTs’ beliefs about such an approach. This qualitative study examines prospective elementary teachers’ conceptions and values about systematically studying and improving their own teaching. Participants (N = 6) were students at a university in the USA enrolled in a semester-long mathematics methods course designed around one model for systematically improving teaching (learning-from-teaching [LFT], also known as lesson experiments). Interview results show that the PTs had a high level of procedural knowledge about the LFT skills and reported liking and intending to use all or part of the LFT model. However, results also reveal that four of the six PTs held multiple misconceptions and all six PTs placed less value on improving teaching than on other teaching goals. PTs’ conceptions and values about improving teaching may limit their ability to successfully learn from their own teaching, which has implications for how teacher educators teach PTs about lesson experiment skills such as writing learning goals or examining student learning.

Diagnosing Learning Goals: An Often-Overlooked Teaching Competency

We propose that an often overlooked competence for teaching is diagnosing learning goals. We propose further that this competence is an empirical process of hypothesis generation, testing, and revising. To understand our argument, diagnosis must be conceived as a process of analysis and mathematical decomposition, and learning goals must be treated as mathematical statements that can be decomposed into component parts or subgoals that must be mastered to achieve larger learning goals. By presenting several examples from our mathematics courses for prospective elementary teachers, we show how instructors can develop diagnostic competence by engaging in cycles of improvement. These cycles require diagnosing learning goals to create hypotheses about how to improve instruction, testing these hypotheses by gathering targeted data, and revising instruction based on relevant evidence. Conceived in this way, the diagnosis of learning goals is a competence teachers can develop as part of an evidence-based process for improving teaching.

Developing Prospective Teachers’ Ability to Diagnose Evidence of Student Thinking: Replicating a Classroom Intervention

In order for teachers to improve over time, they must be proficient at collecting and analyzing evidence of student thinking and learning (Hiebert, Morris, Berk, & Jansen, J Teacher Educ 58(1):47–60, 2007). This specific type of diagnostic competence, which focuses on diagnosing student learning with the specific goal of studying and improving teaching, can be improved through interventions in teacher education (see, e.g., Spitzer, Phelps, Beyers, Johnson, & Sieminski, JMTE 14(1):67–87, 2011). In this chapter, we discuss the findings of previous interventions aimed at helping prospective teachers (PTs) learn to analyze student thinking. Then, we present a replication study using a classroom intervention to teach prospective elementary teachers (N = 23) to identify and evaluate evidence of student understanding. Results of this study and previous work show that diagnostic competence is a skill that is teachable through interventions. After the intervention described in this chapter, participants performed better on a measure of diagnostic competence. In particular, they improved their ability to distinguish evidence of student thinking from nonevidence, such as a teacher’s lecture. They were also more likely to recognize that students’ procedural work cannot be used to diagnose conceptual understanding. Results will be used to suggest key features of interventions to improve diagnostic competence.

Using Mathematical Learning Goals to Analyze Teacher Noticing

Teacher noticing of student mathematical thinking is increasingly seen as an important construct, but challenges remain in operationalizing and assessing teachers’ analyses of their classrooms. In this chapter, we present a methodology for analyzing teachers’ professional noticing of student mathematical thinking based on its alignment to mathematical learning goals. This process entails first deconstructing a mathematical learning goal into its conceptually important pieces (known as subgoals). Then, researchers can look for references to these subgoals in teachers’ attending, interpreting, and deciding (the three skills of noticing). When teachers reference conceptual subgoals of a learning goal in their noticing, it indicates their attention to students’ reasoning about the important mathematical ideas of a lesson. This method of data analysis can be used across a variety of contexts and allows for greater precision in understanding teacher noticing by focusing on its mathematical content and attention to relevant student thinking. In this theoretical chapter, we describe this research methodology (and the process of deconstructing learning goals and using subgoals), justify its appropriateness as a measure of teacher noticing, and provide examples from our own and others’ work to illuminate its use.