Investigating Differences in EMSs' Provision of Opportunities to Justify

• In Event: The Work of Elementary Mathematics Specialists: Findings From the STEAM Project

Abstract

Purpose. In this poster I share results from an analysis of relationships between teacher characteristics (e.g. beliefs, knowledge), Elementary Mathematics Specialist (EMS) certification, teachers’ descriptions of classroom activities, and classroom observation data targeting students’ engagement in justification. This poster differs from others in the session in that it attends to the specific teaching practice of engaging students in mathematical justifications.

Theoretical Framework. I drew on a theoretical framework developed by Ernest (1989) and empirically tested by Wilkins (2008). Within this framework, teaching practice is modeled as an outcome of psychological factors such as teachers’ knowledge, attitudes and beliefs about mathematics teaching and learning, and background characteristics. In this study, the background characteristic of particular interest was EMS-certification. Although prior research has established connections between some of these characteristics and justification in elementary classrooms (e.g. Jansen et al., 2017; Stylianides et al., 2013), these characteristics have not been considered in concert with each other, or in the context of specialized training in mathematics teaching at the elementary level.

Methods. I utilized a mixed-methods sequential explanatory design (Ivankova et al., 2006). Exploratory factor analysis was used to analyze responses to survey items related to attitudes and beliefs about mathematics teaching and learning (Banilower et al., 2013; White et al., 2006) for 61 elementary teachers in grades 3, 4, and 5. Path analysis (Devlieger & Rosseel, 2017) incorporated these factors, scores on subtests of the Learning for Mathematics Teaching (LMT) instrument (Schilling et al., 2007), and an outcome variable related to students’ engagement in justification derived from classroom observations.

To explain the resulting path model, a single-case embedded design (Yin, 2014) was used to investigate how significant predictors of teaching practice were related to teachers’ descriptions of students’ opportunities to engage in justification. Eight EMS-certified elementary teachers with high scores on the Elementary School Number Concepts and Operations subtest of the LMT (Schilling et al., 2007), and who represented a full range of observation scores, participated in task-based interviews (Ginsburg, 1997). All teachers were presented with a set of tasks taken from an elementary textbook, and the semi-structured interview incorporated questions designed to elicit teachers’ descriptions of their own instructional practice, expectations for students’ roles in the justification process, and criteria for sufficient or valid justifications from students.

Results. Path analysis revealed that teachers’ knowledge had only an indirect effect on justificationobservation scores, while EMS-certification status and a subset of beliefs and attitudes factors had direct effects. Teachers’ descriptions of classroom activities included general and justification-specific features of the classroom environment that corresponded to higher observation scores. Consistent with their self-reported beliefs, teachers with higher justificationobservation scores described ongoing efforts to establish classroom norms for discussion. Teachers with the highest scores further elucidated their role in facilitating discussions, and also described specific classroom activities designed to acclimate students to the practice of justification. In summary, students were more engaged in justification in classrooms where teachers’ pedagogical practices were consistent with self-reported beliefs that situated the students as active participants in mathematical discussions.

Author

• Christopher A Austin, University of Southern Maine