A Mathematician, a Chemist, and an Economist walk into a Classroom . . . to Work on Calculus Curricula
Suzanne Dorée
How do other disciplines use calculus at the undergraduate level? What mathematical questions will students see in partner discipline courses? What vocabulary and notation do other disciplines use to describe that mathematics? When will students use technology to address mathematical questions in other disciplines, and what technologies do they use?
Imagine a calculus course built around the answers. As part of a national consortium called SUMMIT-P 1, three mathematics faculty, a chemist, and an economist at Augsburg University spent the past six years doing just that. We worked with partner discipline faculty on mathematics curriculum and in the process learned how to build and sustain those interdisciplinary collaborations.
Why? Our interdisciplinary collaborations helped us focus our calculus courses, enhance their relevance, and improve student transference skills to improve student success in subsequent courses that use calculus.
Focus: By working with partner disciplines, we were able to adjust the depth and breadth of our calculus courses to focus on concepts and examples that students will see in other settings, and de-emphasize artificially complicated examples and special cases which were seldom used in practice. This shift gave us more time to implement more active and inquiry-based learning techniques that deepened student’s procedural fluency and conceptual understanding and increased student persistence in problem solving.
Relevance: Students care about why they need to learn mathematics, particularly students from underserved populations. Each day of our calculus class now starts with an exploratory activity based in applied contexts. By introducing new material in context—as opposed to doing an application after the theory—students can construct knowledge “from concrete to abstract.” We built many physics, engineering, and biology examples using ideas in our textbook, and then we worked with partner discipline faculty to add examples from chemistry, environmental science, and economics.
Transference: To succeed in STEM and quantitative fields, students need to recognize and apply mathematics in new contexts. This “transference” skill is notoriously difficult to teach. Our work with partner discipline faculty helped us understand not only what mathematics is used but also how it is used—for example, does it start with data, a graph, an equation, or something else? As a result we built weekly calculus labs that give students practice with transference. Instead of applying the current week’s material, we designed each lab to use material students learned a few weeks (or even months) earlier.
How? A quick hallway conversation with a partner discipline faculty member might be the start of a collaboration, but building shared ownership requires more deliberate structures. The key question for the SUMMIT-P project was how to build and sustain interdisciplinary partnerships to work on mathematics curriculum. As part of that project, Augsburg faculty used some project-wide collaboration strategies.
We built interdisciplinary learning communities of 3-5 faculty members from mathematics and partner disciplines who met regularly and worked closely over multiple years. Mathematicians learned how mathematics is used by other disciplines and faculty from partner disciplines learned how we teach mathematics. Together we developed ideas about better ways to teach all of our courses. This collaboration shifted the culture from mathematics “serving” the other disciplines, to our “partnering” with them.
We used fishbowl listening sessions where groups of faculty from the partner discipline sat in an inner circle to talk about how they used mathematics in their courses while mathematicians sat in an outer circle and listened without interruption. To kickstart the conversation, we asked faculty to reflect on the research findings of the Curriculum Foundations project. At times, we wanted to respond “but that’s not introduced until a differential equations course,” but instead we figured out how to introduce differential equations in Calculus 1. At other times we thought “oh, that’s just pre-calculus,” but in response we centered the calculus courses on modeling, covariational reasoning, and multiple representations of a function. We would have liked to explain “wait, that is what we already do,” but instead we identified areas that needed more time and emphasis.
We invited partner discipline faculty to write wishlists of content, cognitive skills, or habits of mind that they wanted students to learn in first year calculus. The lists gave us a touchstone to guide our work and served to reassure partner discipline faculty that we weren’t going to stop teaching core concepts, like derivatives in Calculus 1. There were a few surprises—topics that unexpectedly rose to the top of the list (e.g. differential equations) or topics that didn’t make the list (e.g. algebraic evaluation of limits).
Partner discipline faculty observed mathematics classes and taught us sample lessons from their classes. As a result, we learned, for example, that economists are less interested in the equilibrium price and more interested in how changes in demand or supply affect that price, and that to chemists bond attraction is a lot like romance—we want a comfortable proximity/intimacy because too far away and too close are each problematic. Partner discipline faculty posed wonderful mathematical questions, better than some we had asked.
We examined partner discipline textbooks for mathematics. We were surprised initially by the high level of abstraction in some textbooks. In conversations with our partner faculty, however, we learned that they presented the material in a more conceptual way in their introductory courses.
We also collaborated with faculty from other SUMMIT-P institutions through virtual and in-person meetings, site visits to other campuses, and common professional development activities. Seeing how curricular change was implemented in a different setting sparked new ideas for our own work. Having this support was especially helpful when getting started, when pivoting to online due to COVID-19, and when establishing structures that will last beyond our funding.
Want to learn more? At MAA MathFest 2022, look for talks and posters with SUMMIT-P in the title. For a more in-depth, hands-on learning experience, Victor Piercey and I are leading a minicourse Re-imaging the Mathematics Curriculum in the First Two Years in Collaboration with Partner Disciplines — the SUMMIT-P Model. Pre-registration is required and space is limited. Victor’s team at Ferris State University partnered with Nursing and Business faculty members in revising their Quantitative Reasoning course. Look for a new MAA Notes volume Engaging Students in Introductory Mathematics Courses Through Interdisciplinary Partnerships: the SUMMIT-P Model coming later this summer which features more about the process and includes classroom-tested activities developed with the partner disciplines.
Suzanne Dorée is Professor of Mathematics at Augsburg University in Minneapolis where she has taught for 33 years. She has contributed to the national conversation on introductory mathematics curriculum through her work with the MAA CRAFTY Committee, the MAA Council on Teaching and Learning, the Common Vision Project, Transforming Post Secondary Education in Mathematics, the Charles A. Dana Center, and, most recently, the SUMMIT-P project. She is an experienced practitioner of active learning and inquiry-based mathematics education and in 2019 she received the Deborah and Franklin Tepper Haimo Award, the MAA’s highest award for teaching.
1 This material is based upon work supported by the National Science Foundation under Award No. 1625142, lead Award No. 1625771. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.