By David Bressoud @dbressoud
As of 2024, new Launchings columns appear on the third Tuesday of the month.
The recent New York Times article, “They Spent Years on a Math Problem. Then They Were Scooped by A.I.” is one illustration of how fast and dramatically the mathematical landscape is changing. We do not need a wholesale overturning of the undergraduate mathematics education. But we do need a careful and thorough re-evaluation of what and how we teach within the mathematical sciences. This applies across the entire spectrum, from those who are climbing toward the forefronts of research to those who simply need preparation for living in our quantitatively intense world.
A significant step forward was taken on May 18–20 at a summit convened by TPSE Math (Transforming Post-Secondary Education in Mathematics) at Harvard University. Sixty leaders representing AMATYC, AMS, ASA, COMAP, MAA, and SIAM, as well as our partner disciplines gathered to begin to chart our way forward.
There were a number of principles on which this group agreed:
- We agreed that undergraduate math must be rigorous, relevant, and usable.
- We agreed that students need stronger reasons to engage with mathematics.
- We agreed that the learning environments we provide must be more welcoming and intellectually safe for all students.
- We agreed that data, statistics, computation, modeling, and technology must be more central to our courses and programs.
- We agreed that courses and degree programs need clearer purposes and more coherence.
We also agreed that promising innovations already exist, but they need to be promoted, connected, and scaled. Some of those that are ready for action include Introductory Linear Algebra as a first-year course (without a Calculus pre-requisite), elevating Statistics and Quantitative Reasoning as replacements for College Algebra or Precalculus for students who do not intend to study Calculus, and greater adoption of modeling-forward Calculus, especially for majors in the life sciences or engineering. Promoting and encouraging these options is work that requires continued encouragement, coordination, and evaluation.
A white paper with much more information about this summit and its ongoing work is or soon will be available on the website tpsemath.org/mum.
Efforts to reform undergraduate mathematics are not new, and the list of principles upon which the undergraduate program should be based is not particularly controversial. But we are at a unique point where substantial change should be possible. This is the result of many factors, not least of which is the challenge created by Artificial Intelligence to what and how we teach. There also is the recognition that the level of student preparation has slid while the demands to equalize opportunities have grown. Procedural facility has become less important, while the ability to think and reason quantitatively is more important than ever. The future is one reason why this is a critical nexus in time. But the past also shapes this moment. As we look to the future, it is helpful to reflect on where we are and how we got to this point.
We owe many of the strengths of present moment to the Calculus Reform movement of the late 1980s and early ’90s. It did not achieve all that was hoped. But it has had a significant impact on how we think about undergraduate mathematics education. This month I will say just a little about how it arose. Next month I will begin a series that goes into greater detail on where it came from and how it has come to shape our present moment.
Ron Douglas was the driving force behind Calculus Reform. In part, this was a reaction to a 1983 conference that had argued that finite mathematics should replace calculus as the foundational university course in mathematics. Ron had come to the conclusion that calculus should retain its position while recognizing that calculus instruction was in serious need of attention. Demand for calculus instruction had grown dramatically during the 1980s, but failure rates were unacceptably high, sometimes exceeding 50%. In addition, most students were not really learning calculus. They were learning how to turn a function into its derivative or indefinite integral or to solve a template problem taken from the standard repertoire. But they were developing little conceptual understanding of what they were doing or why they were doing it. Furthermore, technology was changing what students needed to know and how they could learn mathematics.
Ron obtained funding for a four-day conference, the Tulane conference held in January 1986 with 25 participants and the theme “Toward a Lean and Lively Calculus.” Among the participants were Lida Barrett, Susanna Epp, Andrew Gleason, John Kenelly, Peter Lax, Louise Raphael, Stephen Rodi (the one two-year college faculty member), Alan Schoenfeld, Don Small, Lynn Steen, Tom Tucker, and Paul Zorn. Together they laid out a vision for what calculus instruction could and should be. The presentations and collective work from this conference are available as the MAA Notes volume #6, Toward a Lean and Lively Calculus.
And they planned for a major launch of the effort to reform calculus. This was held in Washington, DC in October 1987 with 600 participants. It was jointly sponsored by the National Academies and the Mathematical Association of America and funded by the Sloan Foundation and the National Science Foundation. Its presentations and reports were published as MAA Notes volume #8, Calculus for a New Century: A Pump Not a Filter.
At Tulane, Ron had proposed the creation of a single calculus textbook that would epitomize the way calculus should be taught. Instead, NSF sponsored the creation of eight texts, each taking slightly different approaches. All found ways of taking advantage of the current state of technology. All emphasized dealing with functions not just as algebraic expressions but also graphically or as represented by a table of numerical values. They varied in the extent to which they privileged modeling as the driving vehicle. An excellent summary of these texts and their approaches can be found in Appendix E of the MAA Report Assessing Calculus Reform Efforts: A Report to the Community, edited by Alan Tucker and Jim Leitzel and published by the MAA in 1995. Only one of these texts survived the consolidation of the textbook industry. It is the work of the Calculus Consortium based at Harvard University, what has come to be known as “The Harvard Calculus”. But one other text, Calculus in Context, a modeling-driven curriculum created by the Five College Calculus Project, is still available as a free pdf.
As promised, next month I will begin the task of showing what led up to this effort and how it has shaped work on undergraduate mathematics in the succeeding decades.
References
Barber, G. (2026) They spent years on a math problem. Then they were scooped by A.I.. New York Times, June 8, 2026. https://www.nytimes.com/2026/06/08/science/ai-scoop-young-mathematicians.html
Callahan, J., Cox, D., Hoffman, K., O’Shea, D., Pollatsek, H., & Senechal, L. (2008). Calculus in Context. https://open.umn.edu/opentextbooks/textbooks/1285
Douglas, R. G. (Ed.). (1986). Toward a lean and lively calculus (No. 6). MAA Press. https://maa.org/wp-content/uploads/2024/10/NTE6_optimized.pdf
Hughes-Hallett, D., Gleason, A. M., & McCallum, W. G. (2020). Calculus: Single and multivariable. John Wiley & Sons.
Steen, L. A. (1988). Calculus for a New Century: A Pump, Not a Filter. Papers Presented at a Colloquium (Washington, DC, October 28-29, 1987). MAA Notes Number 8. Mathematical Association of America https://maa.org/resource/notes-volume-8-calculus-for-a-new-century
Tucker, A., & Leitzel, J. R. (1995). Assessing calculus reform efforts: A report to the community (Vol. 6). Mathematical Association of America (MAA)
David Bressoud is DeWitt Wallace Professor Emeritus at Macalester College and former Director of the Conference Board of the Mathematical Sciences. Information about him and his publications can be found at davidbressoud.org