Teachers' Formative Assessment Practices for Early Addition and Subtraction: Is Teachers' Awareness of a Learning Trajectory Related to How They Respond to Students?

Abstract

This dissertation is an investigation into the nature of teachers’ formative assessment responses to students as they learn addition and subtraction. Teachers’ background experiences, including classroom experience and professional learning opportunities, were considered as factors which could play a role in accounting for that variation, both when teachers responded to individual students’ thinking and when they determined goals for group discussion based on students’ thinking. In particular, this study investigates whether the responses from teachers who had been trained in a learning trajectory for early addition and subtraction reflected a quality that had the potential to extend student learning opportunities. Data for the study came in the form of practicing elementary teachers’ responses to a multimedia scenario-based survey. In a series of classroom scenarios, participant teachers were shown instances of students solving problems of early addition and subtraction. Those teachers were asked to describe those instances of student thinking, indicate how they would respond to the student, and what learning goal they would set forth for the student. After seeing two individual students’ solutions, the teachers were also asked to choose a problem and set an instructional goal for a discussion of the problem with a group of students that included the two just observed. Twenty-two teachers teaching at the time in elementary schools in a Midwestern state participated; some of those teachers had previously participated in professional development related to a learning trajectory for early addition and subtraction. The results of the study indicate that teachers’ classroom and professional learning experiences were associated with higher rates of teachers interpreting student thinking. In addition to this, those teachers who taught in an early elementary classroom and had training in a learning trajectory were more likely to describe responses to student thinking that showed a potential to extend learning opportunities. Some differences were found among the instructional goals set for the group discussion of addition and subtraction word problems: Some early elementary teachers were open to students’ use of multiple methods, and a small number of early elementary teachers who had been trained in the learning trajectory discussed those multiple methods by connecting them in discussion in ways that attended to the mathematical sophistication of those methods. The findings suggest that when supporting or studying teachers’ formative assessment practices, a content-specific lens may be useful for informing and analyzing those practices. In addition, the findings may provide insight into teachers’ mathematical knowledge for teaching and the measures used to determine quality of teaching responses.