Connecting Unique Factorization Domains With the Teaching of High School Algebra in Approximations of Practice
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We designed approximations of practice (AoPs; Grossman et al., 2009) that pose hypothetical classroom scenarios of high school students learning about factoring polynomials. We investigated the ways in which prospective and in-service teachers leverage their understanding of unique factorization domains to inform their teaching practices of attending, interpreting, and deciding how to respond to students’ thinking in the AoPs with the goal of making explicit connections between abstract algebra and the teaching of secondary mathematics.