I describe a modern approach to teaching introductory statistics that leverages logic, theory, and computational methods to engage students in critical quantitative analysis. I explore how integrating open-source software tools into this curriculum enables learners to participate in an interdisciplinary process of knowledge construction: defining terms and propositions and applying statistical concepts to social issues. This approach can strengthen both technical proficiency and critical thinking. I then discuss the structure of a related package, critstats, which informs a community model...

One of the major sticking points for departments thinking of coordinating their courses is buy-in from faculty. Will coordination mean that certain people just don’t teach that course? Do people just have to get on board, like it or not? Who has a say, and how? Do some faculty just get to opt out of the whole endeavor? Perhaps most importantly, how do we remain in collegial dialogue when we’ve decided to do this but don’t agree on all aspects...

Flipped learning is often presented as an all-or-nothing instructional choice, which can make it feel inaccessible or risky—especially in content-heavy mathematics courses. In this talk, I share my lessons from 10+ years of experience implementing both fully flipped and partially flipped models across a range of mathematics courses at the Colorado School of Mines, including Calculus II, Linear Algebra, Foundations of Advanced Mathematics, and Topology. I discuss how different flipping choices supported student learning, how the model scales to multi-section...

We are four years into the generative AI era and we can confidently say: (1) it is the most novel new technology of the last two decades, (2) it has fallen well short of expectations in education. Teacher usage remains lower than predicted. Schools operate identically now as years ago. Generative AI’s greatest contribution to education, so far, is the generation of important questions about the capacities of the technology, the needs of students, and the nature of teaching. We...

I will introduce the structure and pedagogy of a new math course at UC Santa Cruz: a modeling-based course in mathematics for the life sciences. Adapted from LS30 at UCLA, the UCSC course uses the dynamics of biological systems as a foundation for teaching relevant concepts from calculus, dynamics, and linear algebra. After a broad introduction to the content and structure of the course, I’ll discuss a pedagogical approach which guides our active learning discussion sections. Some are deliberately high-tech,...

After the College of Engineering completed a self-study about math preparation for their programs, our Math Department was invited to create two new courses that are expected to become the core for all first year engineering students. The first is a linear algebra course and the second a condensed calculus course that combines ideas from our current Calc I–Calc II sequence, emphasizes a “numerical” perspective (as opposed to analytic), incorporates more modern engineering applications, and recognizes that over 95% of...

The school curriculum is shaped by a fundamental tension: while much of mathematics is motivated by real-world intuition, the mathematics that emerges ultimately outgrows any single model that inspired it. Fractions sit squarely in this tension, and it is never fully resolved in the curriculum. Students first meet fractions as commands—circle a third of the kittens—and then as concrete parts of a whole—a third of a pie. Fractions are not numbers per se until we place them on the number...