Dr. Zweck Math Connection
Calculus III Math Connection
UTeach Dallas Interns facilitate active learning in Calculus III
A group of mathematics and physics majors in the UTeach Dallas program at UT Dallas are playing a vital role in a project funded by the National Science Foundation to increase the effectiveness of student learning in a Calculus of Several Variables (Calculus III) course at UT Dallas. Each semester the course, MATH 2415, is taken by between 150 and 200 STEM undergraduates with majors ranging from mechanical engineering to biochemistry. For some students, MATH 2415 is their third calculus course at UT Dallas, while others transfer in from local-area community colleges or place into the course straight out of high school.
In Calculus III students learn mathematics used to study scientific phenomena that occur in more than one dimension and that often involve understanding the geometric properties of curves and surfaces in three-dimensional space. Such phenomena include gravitation, the flow of fluids, the vibration of mechanical structures, and the propagation of light and other electromagnetic fields.
Although mastery of Calculus III is extremely valuable to scientists and engineers, the subject material is challenging since it requires students to strengthen their geometric imagination skills and integrate those skills with more familiar algebraic/calculational modes of thinking.
To help students make the quantum leap required to understand multi-variable calculus, each week the students participate in a two-hour active learning problem session in which they solve problems in small groups at white boards. Each problem session is facilitated by a team consisting of a mathematics graduate student teaching assistant (TA) and a UTeach Dallas undergraduate intern who is a pre-service math/physics high school teacher.
The role of the undergraduate and graduate TAs is to listen to the students as they solve problems, making sure that the group members are working effectively together, and lending a hand when they get stuck. However, rather than providing the answer, the TAs help the students by formulating questions designed to guide them towards their goal. In addition, the students explain their solutions to the TAs since being forced to talk about mathematics increases students’ conceptual understanding. Finally, the TAs help students as they use 3D-printed models of curves and surfaces to help develop their geometric imagination skills.
In addition to applying their combined expertise in mathematics and education, since the UTeach Dallas interns have recently taken the course themselves, they can often better appreciate the challenges students face and can more effectively respond with encouragement and practical advice.
Finally, by working on the Calculus III instructional team, the UTeach Dallas interns gain a fuller understanding of how to prepare their future high school students for university-level mathematics.
The NSF award that supports this project is a Supplement to the UTeach Dallas Robert Noyce Scholarship award. The PI on the project is Dr. Mary Urquhart (SME) and the co-PIs include Drs. Sue Minkoff and John Zweck (Mathematical Sciences). For the web page about the 3D-printed models used in the course at
3D Printed Models for Calculus
UTeach Dallas interns who have participated in the project include Henry Curtis, Carl Finley, Dalia Franco Cortes, Andrew Marder, Mikaela McMurtry, Nikunj Patel, Matthew Portman, Erik Rinqvist, Jonathan Sok, and Josilyn Valencia.