A rollout of MATH 1200 and 1201 curricular changes occurred as recently as last fall, with further addenda planned for next year. The changes are in line with substantial revisions to the undergraduate calculus curriculum, involving resequencing or removing existing material and adding new content that the Vanderbilt math department has been enacting since 2023.
The revisions, which were originally recommended to the math department by The College of Arts and Science before many of their facilitators came to Vanderbilt, involved cooperation across the math department and others. The economics department helped mold the curriculum to give students across different majors a better understanding of mathematical elements within their field of study.
Department Chair Dan Margalit said that the reform to the calculus curriculum was implemented in an effort to dispel the inconsistencies and “weed-out” culture once prevalent in undergraduate math teaching.
“There were complaints about unfairness,” Margalit said. “[Students would say] well, ‘the other instructor, across the hall, was doing it this way. I would have gotten an A if I was in the class across the hall.’ As a result, we made a huge push to eliminate the idea that [undergraduate calculus classes] are “weed-out” courses. We have done a lot to make them more active with worksheets in a lot of the classes. We have introduced course coordination across pretty much all of the 2000 level classes. We’ve just increased the consistency.”
Regarding specific changes, Margalit said that the department added more course content applicable to the social sciences and economics in particular to the MATH 1200 calculus sequence. Additionally, MATH 1200 and 1300 were redesigned to involve more theory and problem-solving to ensure students gain essential logical thinking and conceptual skills needed for their future careers.
“MATH 1200 used to be, basically, the high school calculus course. So, the first semester is derivatives, and you learn all the techniques, and you crank out lots of computations, and the second semester is integrals, and they’re in the different techniques, and [you] crank out all the computations. Now, I mean, I look at the exams in MATH 1200 and 1201, they’re just at a higher level. They’re really checking the understanding of the concepts,” Margalit said.
According to Margalit, MATH 1300 and 1301 students — primarily engineering, physics and math majors — are likely to encounter problems in real life that would require mathematical modeling and making assumptions. He explained that to solve those problems, they need to understand the definitions taught in math, which are crucial for breaking problems down into simpler parts.
Pursuant to the math department’s desire to teach students foundational skills early on, Margalit also said that starting next fall, MATH 1300 will cover exponential and logarithmic functions — both concepts that are currently introduced in MATH 1301.
Alice Mark, professor of mathematics and director of Undergraduate Math Education, worked closely with Margalit in implementing the changes to the curriculum. She said that the resequencing of calculus material was done to maintain rigor while boosting student understanding.
“We introduced collapsing collections [to MATH 1300] in Fall 2024. It’s a different treatment of how you prove that the limit of a function is a particular value or to disprove that the function has a limit. It’s an alternative to the way that we used to teach it, which was using the epsilon delta method for proving limits. Collapsing collections is intended to describe the same thing in a way that’s equally mathematically rigorous, but a little more intuitive for students to understand,” Mark said.
Looking to MATH 1200 and 1201, Mark said that concepts like probability, Lagrange multipliers, constrained optimization and differential equations were added by request of the economics department so students can have a solid background in these topics before taking them on in economics classes.
According to professor of mathematics Jacob Haley, economics applications and topics adjacent to the field of economics were a significant part of the curriculum revisions.
“[The economics department] has given us the most feedback in terms of what they want from MATH 1200, 1201, and [it is] our largest client base by a mile. We implemented the partial derivatives and Lagrange multipliers unit by their request. We have finance applications at the end of 1201. Probability, you have to take in Econ stats all over the place. They don’t necessarily emphasize it as much as we do in 1201, but these PDFs and CDFs, which we added, are constantly at work in the background,” Haley said.
Haley said that now the curriculum for MATH 1200 and 1201 has roughly been established, with modifications being made as needed. The department will continue adjusting classroom pacing and designing classes with the goal of helping students retain important ideas by incorporating more predictable exams and homework assignments, among others.
First-year Patrick Meng took both MATH 1300 and 1301 and said that while there was still some memorization involved, especially for formulas, most of the course’s content was about applying learned knowledge to different kinds of problems that would show up on exams. Meng mentioned that the exams were changed to include more challenging practice problems.
Meng also expressed that the increased coordination between classes seemed to be working.
“In [the discussion section], we all get the same material, and then our tests and our homework are all coordinated. We get the same test. It’s not like one person gets a baby mode test, and another professor drops a God mode test. [They’re] just all the same [tests across different sections],” Meng said.
First-year Michael Lee, who took MATH 1200 and 1201 this year, thought that the timing of the economics applications could have been better.
“The fact that we [learned the economics content in math] after we had already learned this stuff in Econ, I feel like that made it like I was learning a concept that I already knew about,” Lee said.
