The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

Instructors are constantly struggling to help students understand mathematical concepts as well as the relevance of mathematics to the real world. In calculus, students possess misconceptions of the limit concept. "Pushing the Limit" refers to a semester-long calculus class project that required students to read about, interview calculus…

This article examines the transition process of 14 international teaching assistants (TAs), who teach mathematics courses in U.S. college contexts. In particular, this study documents several major aspects of changes in their teaching, including their curriculum choice and instructional practices over time. This study reveals how the institutional…

Many undergraduate students have difficulty with the transition to proof-based courses in mathematics. This paper discusses students' beliefs about proof and justification in mathematics just prior to entry into such courses. The paper is based on in-depth interviews with students. The data suggests that some students have beliefs that may in part…