Erin R. Ottmar

Mathematical Knowledge for Teaching, Standards-Based Mathematics Teaching Practices, and Student Achievement in the Context of the Responsive Classroom Approach

This study investigates the effectiveness of the Responsive Classroom (RC) approach, a social and emotional learning intervention, on changing the relations between mathematics teacher and classroom inputs (mathematical knowledge for teaching [MKT] and standards-based mathematics teaching practices) and student mathematics achievement. Work was conducted in the context of a randomized controlled trial. Participants were 88 third-grade teachers and their 1,533 students. A multigroup path analysis accounting for fidelity of implementation revealed no direct or indirect effects linking MKT to student achievement in the RC or control condition. The same analysis revealed different findings for the RC versus control teachers. In the RC group only: (a) Teachers trained in RC who used more RC practices showed higher use of standards-based mathematics teaching practices, and (b) higher use of standards-based mathematics teaching practices related to greater improvements in math achievement. No comparable findings were evident in the control condition. Results demonstrate the importance of building social and emotional capacity in teachers by helping create a supportive classroom that helps teachers provide stronger mathematics teaching practices that lead to improved student learning.

Categories of Large Numbers in Line Estimation.

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words-thousand, million, billion-to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and response time are expected near the boundaries between categories. In contrast to previous work (Landy, Silbert, & Goldin, 2013) that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers.