This study explores how the goals and enactment of three tailored calculus courses, referred to as course variations (standard calculus, life sciences calculus, and physics calculus), at the same university impact students' mathematical identity. In this mixed-methods study, we draw on the framework of figured worlds to interpret how students'…

This paper is based on a large-scale empirical study designed to investigate Calculus I programmes across the United States to better understand the relationship between instructors' concerns about coverage, instructional practices, and the nature of the material covered. We found that there was no association between instructors feeling pressured…

In this paper we address practical questions such as: How do symbols appear and evolve in an inquiry-oriented classroom? How can an instructor connect students with traditional notation and vocabulary without undermining their sense of ownership of the material? We tender an example from linear algebra that highlights the roles of the instructor…

This paper provides an exposition of the unfolding and growing complexities of student and instructor gesturing over time. Specifically, it provides an account of how different forms of gestures, all related to the same mathematical idea, can create a chain of signs that support and enhance increasingly sophisticated understanding of one important…

This paper reports on research conducted to understand undergraduate students' ways of reasoning about systems of differential equations (SDEs). As part of a semester long classroom teaching experiment in a first course in differential equations, we conducted task-based interviews with six students after their study of first order differential…

Teaching in a manner consistent with reform recommendations is a challenging and often overwhelming task. Part of this challenge involves using students' thinking and understanding as a basis for the development of mathematical ideas (cf. NCTM, 2000). The purpose of this article is to address this challenge by developing the notion of "pedagogical…