The Development of Teaching Knowledge in Elementary Mathematics

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

Abstract

Objective. This study examined factors associated with elementary teaching candidates’ mathematical knowledge for teaching (MKT).

Theoretical Framework. Our study is grounded in cultural historical activity theory (CHAT; Sannino, Daniels, & Gutierrez, 2009). CHAT views learning as a collective activity that occurs through social interaction in particular settings and is mediated both by individual and institutional histories and by conceptual and material tools (Engeström, 1999; Wenger, 1998). With its emphasis on activity settings, CHAT is useful in understanding the process of knowledge development as it is shaped by university courses and elementary classrooms.
Our study examined how elementary candidates’ opportunities to learn (OTL) in mathematics methods courses and student teaching placements shaped their development of MKT. Consistent with CHAT, we see teachers’ characteristics as dynamic and changing over time as candidates move through and engage in a range of experiences and contexts. Moreover, we view subject matter as a key factor for understanding this engagement (Hill, Rowan, & Ball, 2005; Spillane & Hopkins, 2013).

Data Sources and Methods. In 2015-16, we invited all 455 elementary teaching candidates at four large research universities who were in their final year of their programs to participate in the study; 287 (63.1%) of these candidates completed surveys for the project. The surveys included a teaching candidate survey that featured items about OTL in mathematics and student teaching and a measure of MKT in number and operations (Hill et al., 2005).
We used multiple regression to study the main outcome as a function of several independent variables (including individual teacher characteristics and OTL in methods courses and student teaching) and interactions among these variables. Our primary outcome was teaching candidates’ MKT.

Findings. Our findings indicate that elementary candidates’ exposure to decompositions of practice in elementary mathematics (i.e., opportunities to learn different ways students solve math problems, theoretical concepts and ideas underlying math procedures, and misconceptions students have in math) and their opportunities to engage in approximations of practice were associated with their MKT levels. Further, the extent to which they had full instructional responsibility for teaching mathematics during student teaching was associated with significantly higher levels of MKT.

Significance. Teacher education must be a key facet of efforts to identify and reward effective elementary teachers. This study enhances our understanding of how teacher education programs help prepare elementary candidates acquire content-specific teaching knowledge. Such cross-institutional work, with data collected from a relatively large number of candidates, enables us to identify effective strategies, including indicators of coursework and field experiences, for preparing novices.
The knowledge of elementary teachers, given the long tail of their potential effects (Chetty et al., 2011), is an important lever for improving student outcomes. Elementary teachers are also key in understanding the role of content in learning to teach. They teach multiple subjects, but often have divergent experiences both in learning to teach and in teaching different subjects. By studying how those experiences and outcomes vary across the same sample of candidates, we can better understand how content mediates the effects of preparation.

Authors

• Peter A. Youngs, University of Virginia

• Julie Jackson Cohen, University of Virginia

• Corey Drake, Michigan State University

• Dorothea M. Anagnostopoulos, The University of Connecticut

• Tutita M. Casa, University of Connecticut