In this talk, I will discuss some methods I used in an “Introduction to Proofs” class to try to address this question. These include discovery-based learning techniques in lectures and tutorials, an emphasis on the role of conjecture in mathematics, and alternative assessments. In particular, I will speak on the use of a “two-stage” midterm involving exploratory group work, and a long-term individual reflective/creative project, the “proof portfolio.”

Note that the large scale labyrinth making will take place in an extended hour-long workshop immediately following the 30 minute talk.

Through their conversations with undergraduate students, some of today's most notable Ramsey theorists talk about their first experiences with mathematics, their times as undergraduate and graduate students, their views about Ramsey theory and mathematics in general, and about their research interests.

As one of the students put it: “The podcast project we did was extremely helpful. It made me realize once again the reason for liking math. Talking with great mathematicians inspired me a lot. I realized my passion is not lost.”

In an attempt to combat the misconception that math is not connected to work in the real world, my colleagues and I are creating Calculus Stories: interviews with experts in applied fields who use calculus in their work. These stories highlight diverse math experiences and perspectives, focusing on who uses calculus in addition to how it is used. We ask our subjects how they came to do the work they do, what it is like to work in their field and collaborate in teams, and how they deal with frustration and failure.

By integrating our interviews into a large, coordinated calculus 2 class, we hope to affect students' motivation and mindset, encouraging exploration and redefining ``success'' in the course. In this talk, we will present details and examples from our Calculus Stories, as well as feedback from students and instructors who have used these materials.

A question many of us have grappled with in the last two years is: how do we fairly evaluate students in an online, heavily computational class, where there are online calculators freely available that can do most of the work for you? To give myself an opportunity to evaluate students on work that a calculator couldn’t do for them and to get students engaging with the course material in new ways in an asynchronous class, I chose to include a final project in my class, which asked students to write about an application of linear algebra that was of interest to them. The result was a number of wonderfully creative projects, and the sense that many students had a better appreciation of linear algebra than they did before. In this talk, I’ll speak about the evolution of this project, and what I (and my students) learned from it.