Assessing the Structure of Knowledge in Teaching Mathematics

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Understanding how elementary teachers' mathematical knowledge for teaching develops and how it influences instruction and student learning has been a persistent challenge in mathematics education. Very few measures exist that allow researchers to reliably assess the nature of teachers' mathematical knowledge. The purpose of this study is develop measures of mathematical knowledge for teaching in both novice and experienced elementary teachers to more effectively assess teacher knowledge and its relationship to student learning. This study will take advantage of recent psychometric and methodological advances to develop more sophisticated and sensitive measures of teachers' mathematical knowledge for teaching. The proposal includes a set of four studies. The first study will examine how mathematical knowledge for teaching differs for novice vs. experienced teachers. The second study will examine the development of teacher mathematical knowledge for teaching and its relationship to the experience of teaching topics in that area. The third study will examine how student learning of specific mathematics concepts is related to teacher knowledge of those concepts. The fourth study will involve classroom observations to examine how mathematical knowledge for teaching is related to corresponding aspects of mathematics instruction. The methodology makes use of diagnostic classification models to characterize teacher knowledge in particular domains of mathematics--fractions and decimals. This project is supported by NSF's EHR Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development. The program supports the accumulation of robust evidence to inform efforts to understand, build theory to explain, and suggest intervention and innovations to address persistent challenges in STEM interest, education, learning and participation.