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Understanding and Overcoming Barriers to Using Mathematics in Science

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Saved by Joe Redish
on July 17, 2016 at 10:12:48 am




This exploratory project addresses a significant national challenge impacting the success of STEM undergraduates, the difference between students learning mathematics and students being able to use it productively. Much of the previous work in this area has focused on identifying student difficulties. This project focuses on understanding the mechanisms that underlie these difficulties. Modeling physical systems using mathematics is a critical component of success in all STEM disciplines. This project studies undergraduates who have been successful in college level calculus as they take an Introductory Physics for Life Sciences (IPLS) course. From studying why and how students do and do not successfully understand and use mathematics to model systems, the project will weave a thread related to mathematical modeling to include: a coherent set of readings, quiz and clicker questions, homework problems, and exam questions intended to build students’ mathematical modeling skills throughout the class in a variety of contexts. This will help students both understand the structure of symbolic reasoning and its value for their chosen careers. This mathematical modeling thread will then be implemented in the IPLS course, and the effect on students’ ability to use mathematics in biology assessed.


The goal of this project is both to identify the mechanisms underlying students’ difficulties in applying mathematics in biological contexts, and to produce materials that can help them learn to use mathematics productively as scientists. The study combines qualitative research (problem-solving interviews and focus-group problem-solving) with quantitative studies of student responses to issues in mathematical modeling. The primary context for the study is the NEXUS/Physics IPLS course developed at the University of Maryland. It serves a diverse population containing many students who have been successful in calculus but have difficulty using mathematics in science. Students at the University of Maryland (a large state land-grant institution) will be the primary subjects. Students at two additional institutions using NEXUS/Physics materials will also be studied: Montgomery College (a two-year institution) and Swarthmore College (a four-year private institution). The project uses as its core analytic structure the Resources Framework, developed in part with prior NSF support, to create models of high-level thinking. This takes a dynamic knowledge-in-pieces approach that considers conceptual, epistemological, and affective resources and how they interact with each other and with the student's perception of their socio-cultural environment. It permits a dynamic, fine-grained approach to student thinking that provides specific tools for understanding the barriers to the use of mathematics in science and for guiding construction of materials and test questions. It also gives insight into modeling the cognitive elements and processes of learning the complex subject of using math in science.


The Intellectual Merit of this project is in developing a deeper understanding of the barriers STEM students face in learning to use math in science. The Broader Impact of this exploratory project is that both what is learned and the materials the project develops could be used in many STEM classes in many colleges and universities.



Development team


Advisory board




Associated Maryland faculty


Papers and Presentations

  1. Language of physics, language of math: Disciplinary culture and dynamic epistemology, E. F. Redish and E. Kuo, Science & Education, (2015-03-14) 30 pages. doi:10.1007/s11191-015-9749-7
  2. Barriers students face in learning to use math in science, E. F. Redish, seminar to the Science Education Group, Weizmann Institute, Rehovoth, Israel (23. March 2015). 
  3. Analyzing the role of math in scientific thinking, E. F. Redish, [dinner talk, MathBench Capstone Conference, College Park, MD, 24. June, 2015]  
  4. Analyzing the competency of mathematical modeling in physics, E. F. Redish [plenary talk, GIREP conference, Wrocław, Poland, 10. July, 2015] 
  5. Teaching physics standing on your head: Mathematics and epistemology in physics, E. F. Redish [Invited talk, AAPT National Meeting, College Park, MD, 27. July, 2015]
  6. Learning to use math in science, E. F. Redish [Colloquium, Dept. of Physics, University of Washington, Seattle, WA, 19. October, 2015]   
  7. Analyzing the competency of mathematical modelling in physics, E. F. Redish, invited talk, to be published in Proceedings of the GIREP/EPEC Conference 2015, Wroclaw, Poland, July 6-10, 2015.  
  8. Drawing physical insight from mathematics via epistemic games, M. Eichenlaub, D. Hemingway, & E. Redish, contributed poster,
    • AAAS STEM Education Symposium, Washington, DC, 4/28/16.  
    • PERC 2016, Sacramento, CA 7/21/16.   



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