Over the last forty years, standards and recommendations for teachers and learners of K-12 mathematics in the US have evolved to highlight mathematical practices (e.g., Common Core State Standards of Mathematics, Standards for Mathematical Practice [SMPs]). Practice standards (i.e., SMPs) describe mathematical competencies that should be developed in learners of mathematics at all levels. National organizations (e.g., Conference Board of Mathematical Sciences) have specifically called for attention to be given to SMPs in collegiate mathematics content courses for prospective elementary (ages 5-12) teachers (PTs). The goal of this paper is to help instructors of such courses, especially those new to the field of mathematics education, gain familiarity with the organizations and documents that support the development of these practices and conceptualize ways in which they might engage PTs in their content courses in SMPs. First, we synthesize the evolution of mathematics standards for K-12 learners and teachers in the US. Second, we report results from an investigation into the ways in which mathematics teacher educators (MTEs) are addressing SMPs in their content courses for PTs. In this study, SMP3: Construct viable arguments and critique the reasoning of others was reported by MTEs as being addressed in their courses more than any other SMP. This finding precipitated a qualitative analysis of the ways in which PTs were being provided opportunities to engage in SMP 3 within the descriptions and samples of tasks provided by the MTEs. We will share and discuss example tasks that provided opportunities for PTs to analyze others’ thinking. Lastly, we consider the potential benefits of leveraging children’s thinking in SMP 3-related tasks for PTs and provide resources for MTEs who are interested in utilizing samples of children’s thinking in their classes.
Max, B. & Welder, R. M. (June 2020). Mathematics teacher educators’ addressing the common core standards for mathematical practice in content courses for prospective elementary teachers: A focus on critiquing the reasoning of others. In A. Appova, R. M. Welder, and Z. Feldman, (Eds.), Supporting Mathematics Teacher Educators’ Knowledge and Practices for Teaching Content to Prospective (Grades K-8) Teachers. Special Issue: The Mathematics Enthusiast, ISSN 1551-3440, vol. 17, nos. 2 & 3, pp. 843–881. ScholarWorks: University of Montana. Retrieve (open access) from: https://scholarworks.umt.edu/tme