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Innovations in College-Level Mathematics Teaching

This page is intended to be an evolving account of eff orts made by mathematicians in U.S. colleges and universities to improve college-level mathematics education. The goal is to showcase existing programs and to encourage further innovation. Perhaps together we can share our positive experiences in order to promote new teaching methods that might scale up to help address the national imperative of training more well-prepared STEM graduates.

The AMS has published a statement of policy concerning the role of mathematicians in college-level teaching of STEM (Science, technology, engineering, and mathematics) students.

Examples of Ongoing Educational Collaborations

Cornell University: Engineering & Mathematics

Beginning in the 1960s, faculty members from the Engineering College have collaborated with faculty from the Mathematics Department to create a 2-year mathematics sequence tailored for engineering students. A renewed effort began in 2007, when a group of engineering and mathematics faculty began to infuse core engineering mathematics courses with engaging and diverse problem-solving workshops, incorporating example applications from the physical sciences and engineering. Mathematicians and engineers have each played an essential role in designing and implementing the improvements to the engineering mathematics curriulum. Assessment of the effectiveness of the workshops is now under way. Over the past 50 years, these reforms have been supported by the NSF (National Science Foundation) and by the Colleges of Engineering and Arts & Sciences at Cornell.

Distance Learning Calculus at Georgia Institute of Technology

This program teaches calculus to high school students.These students are high-performing, have already taken AP-Calculus, and are accepted under competitive admission from preapproved high schools with larger numbers of such students. Students in the program take Georgia Tech Calculus 2 in the fall term, and Calculus 3 in the spring.  These are regular university calculus classes, with 200+ on-campus freshman enrolled. With live video-conferencing technology, the 400+ high school students can interact with their TAs and Professor in real time, from their own high school. The program reaches dozens of counties across the state, providing high-level mathematics instruction to students who otherwise would have no mathematics to take. Visit the FAQ, and read more about this program.

Program contact information: Tom Morley, program creator.

Emory University: Biology & Mathematics

Life sciences faculty at Emory wanted to improve the quantitative training of their majors, while maintaining coursework that would satisfy the admissions requirements for medical schools. The Mathematics Department responded to this need, and in collaboration with the life scientists created a new calculus sequence for students in the life sciences. The year-long sequence includes differential and integral calculus, an introduction to mathematical modeling with differential equations, and basic probability and statistics. In addition to lectures, there are discussion sections where the students come to grips with biological applications. This sequence is the recommended mathematics sequence for biology majors.

University of Colorado: Engineering & Mathematics

Faculty from Applied Mathematics and Aerospace Engineering teamed to introduce pre-examination “oral assessments” in first and second semester calculus courses. Students meet in small groups with a facilitator, ahead of examinations, and they are asked penetrating questions about the important concepts in the course. The students must explain how and why certain procedures can be used in certain circumstances. This oral reinforcement has strengthened students’ understanding of important math concepts and their capacity to apply knowledge in new situations. This program was initiated with support from the University of Colorado and the NSF. There are now a dozen universities, colleges, and schools where oral assessments are being implemented in a variety of courses. Thus, this reform appears transferable and scalable; however, it requires significant resources.

University of Minnesota: Biology & Mathematics

Life sciences majors at the University of Minnesota were unmotivated by the calculus sequence largely filled with examples from physics and engineering. To address this, Claudia Neuhauser designed a new year-long mathematics sequence drawing heavily on examples from ecology and biology. The course develops many of the important concepts from single-variable calculus and also touches on differential equations, matrix algebra, and the basics of multivariable calculus. Neuhauser’s textbook, Calculus for Biology and Medicine, is now in its third edition and has become a standard in courses tailored to biology majors and pre-med students.

The University of Utah: Engineering & Mathematics

The College of Engineering at the University of Utah wanted to increase retention of its undergraduate majors and decrease time to graduation. Having identified mathematics as a stumbling block, the engineers worked with their colleagues in the Mathematics Department to revise and enhance the curriculum for the first two years of undergraduate engineering mathematics education. This included adding twice-weekly recitations which allow real-time remediation, opportunities to explore engineering applications of the mathematics, and the creation of a learning community among the students. The University of Utah has allocated significant resources to the Mathematics Department to achieve this transformation. The experiment is just beginning, and assessment will follow.

Vector Calculus Bridge Project

The Vector Calculus Bridge project seeks to align the teaching of vector calculus in mathematics courses with the ways in which this material is used in other disciplines, notably physics.  Among other things, it contains a set of classroom-tested activities emphasizing geometric visualization, together with a lengthy instructors guide. Copies of our dozen or so publications on this topic are also available.

If you teach college-level mathematics, please share your innovations and teaching methods.