How mathematicians assign homework problems in abstract algebra courses
Rupnow, Rachel L., 1990--
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While many aspects of the teaching and learning of advanced mathematics have been explored, the role, construction, and values of homework have been virtually ignored. This report draws on task-based interviews with six mathematicians to explore the relationship between an instructor’s learning goals and factors considered when selecting homework problems. All participants viewed homework as critical to student learning, and the majority of the participants’ claims focused on either the mathematics or how the problem would help students learn; no instructor gave primacy to evaluative reasons for homework. We highlight six themes used by participants to evaluate and select items for inclusion in homework. They are (1) knowing and recalling ax- ioms and definitions, (2) developing an arsenal of examples, (3) developing new problem ap- proaches, (4) remediating misconceptions, (5) making connections to prior and future material, and (6) valuing reading notes or text.