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We study the ideas about teaching and learning mathematics that undergraduate students generate when they encounter tasks designed to embed approximations of teaching practice in mathematics courses taken by a general population of students. These tasks attend to the dual goals of developing an understanding of mathematics content and an understanding of how teachers provide classroom experiences that foster mathematics learning. The study employs a qualitative, multiple-case study methodology, with four cases bounded by the content areas of abstract algebra, single variable calculus, discrete mathematics, and introductory statistics. The data for the study come from undergraduate students’ written work on mathematical tasks, interviews with a subset of students from each course, and interviews with each instructor throughout the term during which they implemented the tasks. Our findings indicate that students identified the broad applicability of teaching skills (discussed by 32 of the 61 interviewed students), recognized the value of examining hypothetical learners’ mathematical work (discussed by 59 of the 61 interviewed students), and reported empathy for hypothetical learners (discussed by 38 of the 61 interviewed students). These findings persisted across the course content and course levels we studied, leading us to conclude that our findings can transfer to additional mathematics courses in secondary mathematics teacher preparation.

 

The Mathematical Education of Teachers II report by the Conference Board of the Mathematical Sciences (2012) recommends that undergraduate programs enhance prospective secondary mathematics teachers’ (PSMTs) understanding of connections between the advanced undergraduate mathematics content and the mathematics they will teach. This paper examines the connections to teaching made by one instructor and one undergraduate PSMT after implementation of two calculus lessons aimed at supporting connections to teaching. Each lesson embedded approximations of practice tasks in the learning of calculus content. Findings suggest that these lessons enabled both deepening mathematical content knowledge and insight into the work of teaching. 

The Mathematical Education of Teachers as an Application of Undergraduate Mathematics project provides lessons integrated into various mathematics major courses that incorporate mathematics teaching connections as a legitimate application area of undergraduate mathematics. One feature of the lessons involves posing tasks that require undergraduates to interpret or analyze the work of another student. This paper reports on thematic analysis of hour-long interviews for eight participants enrolled in an undergraduate abstract algebra course from two different implementation sites. We focus on student work and reactions to these interpreting or analyzing student thinking (AST) applications as they relate to their perceptions regarding the use of AST applications as a mechanism to both deepen their content knowledge and improve their skills for communicating mathematics. Several participants identify positive benefits, but more research is needed to determine the how to incorporate AST applications to accommodate some participants’ reluctance to engage in new mathematical contexts. 

When implementing lessons connecting advanced undergraduate mathematics to school mathematics, challenges arise for faculty and for the undergraduate students. The Mathematical Education of Teachers as an Application of Undergraduate Mathematics (META Math) project has created, piloted, and field-tested lessons for undergraduate mathematics and statistics courses typically part of a mathematics major that leads to secondary mathematics teacher certification. Lessons in calculus, discrete mathematics, algebra, and statistics explicitly link topics in college mathematics with high school mathematics topics prospective teachers will eventually teach. The goal of this poster presentation is to discuss our preliminary observations of the challenges faced by faculty and undergraduate students when implementing or using these lessons. We also wish to gather feedback and suggestions on the study design and potential directions for further research.