Are standards really standard? How preservice teachers’ Desmos activities address a given function standard

Mathematics teacher educators (MTEs) need to prepare preservice teachers (PSTs) who are capable of interpreting state mathematics content standards and ensuring the activities they use align with those standards. Given the ever-increasing role of technology in K-12 education, such activities include those that use mathematical action technology such as Desmos. To do this work, however, MTEs first need to understand how PSTs design lessons which use mathematical action technology around a given content standard. With this understanding, MTEs can plan more purposeful learning opportunities to support PSTs' standards interpretation and lesson design. This paper shares a study which examined the Desmos activities designed by two classes of secondary mathematics PSTs at two different institutions around a given standard focused on functions. Findings show that the mathematical ideas focused on, and mathematical representations used by PSTs, varied even though all activities were supposed to address the same standard. Findings also indicate that while PSTs faced challenges regarding their plans for lesson implementation and their horizon content knowledge, they also demonstrated sufficient understanding of key function concepts and pedagogical ideas. Implications for MTEs and authors of standards are discussed.