By Dave Kung
I remember when the need to modernize undergraduate math became crystal clear to me. I was teaching calculus, looking ahead to the next section: techniques of integration. Sure, I loved being able to sort similar-looking integrands into the ones that required a u-substitution, a trig substitution, partial fractions, or integration by parts. But how was I going to motivate this section to my students? I wasn’t. They would be better served exploring numerical approximations, modeling problems that required integration – or just more work to see the integral as a way to quantify a vast range of phenomena by adding up small, easily calculated pieces. But it was in the course description, so I – and my students – trudged on.
I’m not alone - over 450 math faculty publicly signed on to this call to modernize math – and the problem isn’t just in calculus. Throughout the undergraduate curriculum in the mathematical and statistical sciences, we continue to teach material that doesn’t meet our students' needs. You don’t have to look far to find examples.
In today’s digital world, we are awash in data. As a result, areas like linear algebra are more important than ever, in more places than ever. Yet most programs put this course behind a calculus paywall, keeping many students from learning vital material. And the theory-forward linear algebra that seemed appropriate decades ago pushes useful topics like singular value decomposition even further down students’ paths.
Even in fields where continuously varying functions provide deep insights into our world, the traditional calculus sequence doesn’t serve students very well. Biology students, including future doctors and researchers, benefit hugely from mathematics. But what they need is a conceptual understanding of dynamical systems and feedback loops that can explain and illuminate complex biological processes. The procedurally-focused one-variable calculus typically required does little to meet their mathematical needs.
These ideas, and many more, were the focus of the Modernizing Undergraduate Mathematics Summit hosted at Harvard, May 18-20. The summit was co-sponsored by COMAP, AMS, ASA, SIAM, MAA, and AMATYC and supported by philanthropic funding. Over three days, 60 leaders from a cross-section of institutions, organizations, and regions came together around a shared conviction: undergraduate mathematics must evolve to meet the rapidly-changing world students are entering. Summit activities were designed to seek consensus – and plan for action. Through presentations, panels, working groups, project discussions, and participant input, several clear areas of agreement emerged.
Principles for Modernizing Undergraduate Mathematics. The group agreed that the core strength of mathematics as a problem-solving discipline grounded in justification and proof needs to be preserved – while also adapting to the modern world by:
- Increasing the relevance of mathematics by expanding students’ experience with modeling, statistical reasoning, computational thinking, data, and technology-enabled exploration, leaving students prepared to apply their knowledge in academic, professional, and civic life.
- Making sure students have reasons to engage with mathematics by attending to motivation, curiosity, inquiry, and creativity.
- Crafting courses and degree programs around coherence and clear purposes, removing outdated material and ensuring that students understand how ideas connect within each course, across courses, and to careers after graduation.
Thankfully, we do not have to build new structures from the ground up. Many forward-thinking faculty members have been renovating existing courses and building new ones that better meet the needs of today’s students. Summit participants examined many of these innovative courses and identified several as particularly promising models worth adapting and scaling nationally.
Intro to Linear Algebra (without calculus as a prerequisite). Many students would benefit from an applied treatment of linear algebra, supporting majors like data science, computer science, and parts of engineering. Importantly, such a course would not need calculus as a prerequisite, a recommendation of the Linear Algebra Curriculum Study Group 2.0. Topics like abstract vector spaces and proofs could be studied by interested students in a second linear algebra course. Momentum for a modernized intro linear algebra course has grown recently with institutions as varied as the University of Oklahoma, Grand Valley State, and the City College of New York offering versions that adhere to some of these recommendations.
Modeling-first Calculus for Life Sciences. Rather than sticking to a single-variable, procedurally-focused treatment of calculus, many are finding that a modeling-first, dynamical systems approach serves students better. Building on the success and popularity of UCLA’s Math for Life Sciences class, such an approach has now spread to other institutions, with help from an NSF grant.
College-level Quantitative Reasoning. College courses in Quantitative Reasoning (QR) vary widely across different states and institutions. As a result, these courses, perfect for humanities majors, future nurses, and many others, are too often seen as less legitimate than College Algebra. Nearly one million students a year take College Algebra (which has the highest failure rate of any introductory college course), many of whom would find more relevance and success in a high-quality QR course that would improve their skills in quantitative decision-making. Creating more consistency for QR – possibly rebranded with a new name – would yield more legitimacy and better serve students.
The undergraduate mathematics curriculum isn’t meeting this moment. That isn’t our fault. We inherited a system that has been in place for decades. Technology is changing rapidly, as are the quantitative skills and knowledge that students need to benefit from, participate in, and contribute to those changes. But acting like we are powerless to adapt is not acceptable. It is our collective responsibility to do better – for the sake of workforce preparation, for the sake of our client disciplines, and most importantly, for the sake of our students.
To find out more and join the movement, visit the TPSE Math Modernizing Undergraduate Mathematics site.
TPSE Math’s Modernizing Undergraduate Mathematics site includes the summit’s Vision and ways you can join the movement.
Read the article, then join the convo at MAA Connect:
https://connect.maa.org/
Dr. Dave Kung has worked in the intersection of mathematics and equity for three decades. He served as the Director of Policy at the Charles A. Dana Center at The University of Texas at Austin, and as Director of MAA Project NExT. He also works closely with K-12 and higher ed organizations, especially concentrating on equity issues in mathematics. Kung was awarded the Deborah and Franklin Tepper Haimo Award, the MAA’s highest award in college math teaching, for his work at St. Mary’s College of Maryland. He resides there, serving as Executive Director of Transforming Post-Secondary Education in Mathematics (TPSE Math) and working as an independent consultant, as well as playing violin and running–never simultaneously, but sometimes alongside his partner and daughter. The views expressed in this column are Dave’s alone and do not represent those of any organizations he works with or for.
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