We describe a lecture-free problem-solving Mathematical Communication and Reasoning (MCR) course that helps students succeed in the Introduction to Advanced Mathematics course. The MCR course integrates elements from Uri Treisman's Emerging Scholars workshop model and Math Circles. In it students solve challenging problems and form a supportive…

A summative portfolio is a project completed at the end of the semester that gives a student an opportunity to look at a course as a whole. This study investigates whether collegiate mathematics students gain a deeper understanding of course material through the portfolio project, via an analysis of the students' work, and a survey of students'…

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this…

The Department of Mathematics at Bates College has offered a senior seminar capstone course for over a dozen years. In this article, we discuss the coexistence of seminar and thesis, our other capstone experience. We discuss in detail the goals of our seminar, various ways we structure the seminar to accomplish those goals, and methods of…

Most instructors desire to create a learning environment conducive to deep learning. However, in courses where grades are based upon the accumulation of points, students may focus on collecting points rather than on learning and achieving the course objectives. We discuss an alternative points-free course design based on the development of clear…

This study presents a primary trait analysis of a learner-centered, discrete mathematics course based on student-to-student instruction. The authors developed a scoring rubric for the primary traits: conceptual knowledge, procedural knowledge, application of understanding, and mathematical communication skills. Eleven students took an exam…

For most first semester students, the definition of a continuous function causes confusion. We discuss a presentation that leaves students with a better intuitive understanding of continuity, as well as an appreciation for the definition. (Contains 3 footnotes.)