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This study examines how elementary preservice teachers incorporated mathematics content standards, standards for mathematical practice (SMPs), and equity-based mathematics teaching practices (EBTPs) while designing tasks referencing diverse picture books. The researchers created a mathematics task planning template and an accompanying reflection guide to assist preservice teachers in connecting these three sets of principles during their task design. Findings indicate that the preservice teachers relied more on the mathematics content standards than the SMPs or the EBTPs when designing their tasks. They also better integrated the SMPs and the EBTPs into their tasks when narrowing their focus to fewer practices. Recommendations suggest that mathematics teacher educators reflect on how to support PSTs in developing connections across these three sets of principles.