Investigating Links from Teacher Knowledge, to Classroom Practice, to Student Learning in the Instructional System of the Middle-School Mathematics Classroom

TLDR

Curriculum and other learning resources, such as technology and peer interactions, are key factors for student learning alongside teachers’ mathematical knowledge. The study calls for richer models of how teachers’ mathematical knowledge functions within complete instructional systems. Data from 125 seventh‑grade and 56 eighth‑grade Texas classrooms in the 2005–07 Scaling Up SimCalc project were used to examine relationships among teachers’ mathematics knowledge, classroom decision making, and student achievement on rate, proportionality, and linear function. Teachers’ mathematics knowledge correlated with student achievement in only one of three studies, showed no link to key instructional decisions, and appears to have a nonlinear, mediated effect that short‑term workshop gains may not sustain.

Abstract

Using data collected in 125 seventh-grade and 56 eighth-grade Texas classrooms in the context of the "Scaling Up SimCalc" research project in 2005–07, we examined relationships between teachers' mathematics knowledge, teachers' classroom decision making, and student achievement outcomes on topics of rate, proportionality, and linear function—three important and cognitively demanding prealgebra topics. We found that teachers' mathematical knowledge was correlated with student achievement in only one study out of three. We also found a lack of correlations between teachers' mathematical knowledge and critical aspects of instructional decision making. Curriculum and other learning resources (e.g., technology, student–student interactions) are clearly important factors for student learning in addition to, and in interaction with, teachers' mathematical knowledge. Our results suggest that mathematics knowledge for teaching may have a nonlinear relationship with student learning, that those effects may be heavily mediated by other instructional factors, and that short-term content knowledge gains in teacher workshops may not persist in classroom instruction. We discuss a need in the field for richer models of how "mathematical knowledge for teaching" works in the context of complete instructional systems.