Teacher Knowledge and Student Learning: Bringing Together Two Different Conceptualizations of Teacher Knowledge

• In Event: Teacher Quality, Teaching Quality, and Student Outcomes in Mathematics: Putting the Puzzle Together

Abstract

Recent research findings provide empirical support connecting what teachers know to what students learn (Author, 2005; Baumert et al., 2010; Kersting et al., 2012; Rockoff et al. 2011). Despite the progress made on this front, especially during the past decade, scholars seem to have largely focused on single conceptualizations of teacher knowledge—either on teachers’ basic mathematical knowledge or on their knowledge for teaching mathematics. Missing from scholarly discussions are questions examining whether these constructs are really distinct or form a unidimensional construct; absent are also investigations of the contribution of such constructs to student learning. Addressing such issues can have significant implications for teacher preparation and certification, given that the question as to whether teachers need to have strong mathematical knowledge or strong knowledge for teaching the subject remains open (National Mathematics Advisory Panel, 2008).

Attending to these two types of teacher knowledge, which have for long been considered in parallel, in this paper, we ask:
1. Is teacher knowledge of the content and its teaching multidimensional, as advanced by different theoretical frameworks (e.g., Shulman, 1986)—or does it comprise a single construct?
2. If teacher knowledge consists of multiple dimensions, which is more predictive of student outcomes? If these are not multidimensional, do they predict student outcomes?
To address these questions, we developed teacher surveys that included items measuring teacher content knowledge drawn from two sources: released items of the Massachusetts Test for Educator Licensure; and items tapping into teachers’ mathematical knowledge for teaching drawn from the work of the Learning Mathematics for Teaching project. The surveys were administered to about 300 teachers over a three-year period. The students of those teachers also completed state tests and tests developed at the National Center of Teacher Effectiveness (NCTE), which enabled studying student learning during this period.

Using confirmatory factor analyses, we compared the fit of the data to a model including a single factor, a second-order factor model comprising two first-order factors (content knowledge and knowledge for teaching), and a bifactor model (cf. Chen, Hayes, Carver, Laurenceau, & Zhang, 2012) including a general teacher-knowledge factor and two specific knowledge factors corresponding to content knowledge and knowledge for teaching. For all years under consideration, the analyses converged in showing that a single factor solution had a better fit to the data, suggesting that, contrary to expectations and to other similar findings (Baumert et al., 2010), a single factor could better capture the data structure. Using this single factor in a multilevel analysis and two value-added measures of student learning based on either the state test or the NCTE test, we found that teacher knowledge had effect sizes in the range of 0.04- 0.05 (p<.05) on student performance, net of other student/classroom background factors. Although small, these effect sizes are comparable to those reported in other teacher-knowledge studies (cf. Hattie, 2009), thus, supporting the importance of attending to both basic mathematics knowledge and knowledge for teaching when trying to understand what contributes to student learning.

Authors

• Charalambos Y. Charalambous, University of Cyprus

• Heather C. Hill, Harvard Graduate School of Education

• Daniel McGinn, Harvard University