Designing Mathematics Teacher Preparation That Matters: Results and Lessons Learned From a 15-Year Effort

• In Event: 41.046 - How Can a Teacher Preparation System Be Improved? Lessons Learned From Purposeful Intervention and Research

Abstract

Objective. This presentation describes empirical findings and lessons learned from a 15-year effort to improve mathematics teacher preparation.

Perspectives. The four-year, K-8 certification program under study graduates about 130 students annually. Prospective teachers (PSTs) complete three mathematics content courses and one mathematics methods course. Improvement efforts focused on preparing PSTs to teach mathematics for conceptual understanding. We hypothesized this requires mathematics-knowledge-for-teaching (Ball et al., 2008), and knowledge of two key pedagogical principles shown to support students’ conceptual understanding – making key mathematical ideas explicit and having students grapple with these ideas (Hiebert & Grouws, 2007). For each course, we developed a shared curriculum designed to enact the two key principles and support MKT development. Applying principles from design research (Gravemeijer et al., 2009) and improvement science (Bryk et al., 2015), we engaged in cycles of curriculum planning, implementation, analysis, and revision. Empirical data indicated successive cohorts of PSTs achieved the learning goals at increasing rates (e.g., Authors, 2009).

Methods. To investigate whether PSTs retained and applied knowledge developed in the program, we conducted a longitudinal study following them from graduation into their first three years of teaching. We employed a design in which graduates served as their own controls. Graduates were assessed on four mathematics topics. Three targeted topics were well-developed in the program; the fourth topic was not addressed and thus served as a control.
To investigate how preparation might affect teaching, we used a proxy measure shown to predict quality of mathematics teaching and students’ learning (Kersting et al., 2010, 2012). Teachers view a video clip of mathematics instruction and are asked, “Discuss how the teacher and students interact around the mathematical content.” Each year, all participants completed four such tasks, one for each topic. Two researchers scored responses using a modification of Kersting’s rubric, with inter-rater reliability of 88%.
To assess teaching directly, we observed a subset of graduates teach two lessons each year – one targeted topic and one control topic lesson. For each topic, participants were asked to plan and teach a lesson for conceptual understanding. A coding scheme was designed to capture the extent to which instruction exhibited the two key principles of teaching for conceptual understanding. For each principle, each lesson was categorized as Strong, Moderate, or Weak. A team of researchers coded the data and resolved disagreements.

Findings. Two-way repeated measures ANOVAs conducted on the video task responses indicated significant differences between the control and targeted topics each year, in each case favoring the targeted topic. Moreover, participants’ instruction consistently exhibited greater attention to making key ideas explicit during targeted topic lessons than during control topic lessons. However, we found no differences in terms of providing students with opportunities to grapple with key ideas. Rather, participants who were inclined (or not) to provide such opportunities tended to do so (or not) during both targeted and control topic lessons.

Significance. Results indicate significant effects of mathematics teacher preparation. Shared learning goals and curricula, and consistent modeling of the two key principles, were crucial program features.

Author

• Dawn M. Berk, University of Delaware