Teachers' Mathematical Knowledge for Teaching, Instructional Quality, and Their Students' Achievement: Evidence From Quantile Mediation

• In Event: 66.051 - Tracing the Production Function: Connecting Teacher Preparation, Knowledge, Beliefs, and Instruction to Student Achievement

Abstract

We investigate the extent to which teachers’ Mathematical Quality of Instruction (MQI) mediated the relationship between teachers’ Mathematical Knowledge for Teaching (MKT, Hill et al., 2008) and their students’ mathematical achievement. To more fully understand these relationships, our analyses consider (a) multiple outcomes, (b) multiple dimensions of instructional quality, and (c) the persistence of the individual and total mediational effects across the distribution of student achievement.

In the area of mathematics, there is a lack of detailed understanding of both the types of knowledge teachers need to hold to be effective, and how this knowledge informs instruction in ways that lead to improved student achievement gains. This lack of detail leaves critical gaps in our understanding of how teachers' knowledge impacts their instruction in ways that promote increased student achievement (Hill et al., 2008). For this reason, recent research has called for more systematic and concurrent studies of knowledge, instruction, and achievement to illuminate theories of knowledge (e.g., how knowledge informs practice) and instruction (e.g., how instruction influences student achievement) within mediational frameworks (Desimone, 2009).

In this study, we contribute to this line of inquiry by closely considering how three aspects of effect heterogeneity may provide a more comprehensive understanding of mediation in this context, using data from the overarching main study. First, because prior literature has noted the sensitivity of teacher effects to the choice of outcomes (Lockwood et al., 2007), we examine how teachers' knowledge, their instruction, and their students' achievement were related using state standardized tests as well as a researcher developed test. Second, we investigate the extent to which multiple dimensions of instruction concurrently mediated the relationship between teachers' knowledge and their students' achievement using a multiple mediator framework (Preacher & Hayes, 2008). Prior research has suggested that instruction is multidimensional and that the magnitude and direction of mediation effects may vary across dimensions of instruction (Hill et al., 2008; Kersting et al., 2012; MET, 2013). Third, we investigate the persistence of aforementioned relationships across the distribution of students' achievement using a quantile mediation framework. Prior research has suggested that the magnitude and direction of such relationships may differ across the distribution of achievement gains (e.g., Corey et al., 2012).

To assess the extent to which dimensions of instructional quality (differentially) mediated the relationship between teachers' knowledge and their students' achievement, we use quantile mediation methods (Imai, Keele, & Tingley, 2010). We are careful to note that our investigation only examines correlational relationships and makes no claims about causation.

We find that the mediation effects suggested considerable heterogeneity across outcomes, instructional dimensions, and quantiles of achievement. As the mediation effects varied considerably across instructional dimensions and outcomes and their distribution, it is apparent that researchers should approach studies of mediation with a view toward representing the complexities and variability inherent in mathematics instruction.

Author

• Benjamin Kelcey, University of Cincinnati