Knowing Mathematics for Teaching Algebra

Michigan State University, East Lansing MI

Investigators

Abstract

Concerns about the quality of the mathematics achievement of K-12 students in the United States continue to dominate national dialogue in the academic and popular press. Students' performance in algebra is particularly worrisome, and this may be due in part to lack of appropriate teacher knowledge. The RAND Mathematics Study Panel (2003) notes the need for: clarification of the knowledge demands of teaching, tools for assessing mathematical knowledge for teaching across grade levels and mathematical domains, and deeper understanding of the ways in which prospective and practicing teachers have opportunities to acquire this kind of knowledge; they also single out algebra as a key area. Consequently, the proposed research project has three main objectives: 1. Instrument Design: To develop items and design reliable and valid instruments to measure knowledge in large scale settings for teaching algebra among pre-service and in-service secondary school mathematics teachers. 2. Framework Validation: To produce an empirically validated and comprehensive framework for knowledge for teaching algebra. 3. Status Study of Teacher Knowledge. To study the status and variation of knowledge for teaching algebra among pre-service and in-service teachers drawn from across the nation. An interdisciplinary MSU-based research team with collective expertise in mathematics, mathematics education, research design, psychometric analysis, and secondary school mathematics teaching and curriculum will lead the project, with the support of research collaborators around the country, a national advisory board, and item writers. Intellectual merit of the proposed activity: The study will contribute an empirically validated and comprehensive framework for knowledge for teaching algebra at the secondary school level, together with items and assessment instruments to measure this knowledge in large-scale settings. The result will be clarification and description of teacher knowledge in a crucial and problematic area of the K-12 mathematics curriculum. Broader impacts resulting from proposed activity: The items and assessment tools developed here will be of value for teacher educators, mathematicians who prepare teachers, designers of professional development, and evaluators interested in teacher learning in the area of algebra. Ultimately this work could have substantial impact on the improvement of secondary school algebra teaching and learning.