An Aspirational Approach to the Mathematical Preparation of Teachers

The undergraduate preparation of prospective secondary mathematics teachers requires attention to their fluent understanding of the mathematical content they are to teach alongside an understanding of how to interact with other human beings and their mathematical work. How can we prepare undergraduates in mathematics content coursework to apply their mathematical understandings to the human context of teaching? This talk focuses on teaching applications, mathematical tasks that make concrete connections between the mathematics undergraduates learn in coursework serving a general population of undergraduates studying mathematics and the mathematics taught in secondary school. I report on a curriculum design study that gathered undergraduates’ ideas about mathematics and about teaching while using materials that include teaching applications. I highlight findings from use in undergraduate calculus, abstract algebra, introductory statistics, and discrete mathematics courses. Undergraduates identified the broad applicability of teaching skills, recognized the value of examining hypothetical learners’ mathematical work, and reported empathy for hypothetical learners.