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Understanding and Overcoming Barriers to Using Mathematics in Science

Page history last edited by Joe Redish 10 months, 1 week ago




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.


*This work is supported in part by US National Science Foundation under award DUE-15-04366. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.



Development team


Advisory board


Former advisory board members

  • Joe Wagner (Xavier University – Learning Sciences 2015-16)




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, (14 March 2015) 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, Rehovot, 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 modeling in physics, E. F. Redish, invited talk, in Proceedings of the GIREP/EPEC Conference 2015, Wroclaw, Poland, (6-10 July 2015)
  8. Evaluating the Math Epistemic Games Survey, D. Hemingway, M. Eichenlaub, W. Losert & E. F. Redish, talk, Losert Lab Research Group, University of Maryland, College Park, MD (26 August 2015)
  9. Drawing physical insight from mathematics via epistemic games, M. Eichenlaub, D. Hemingway, & E. F. Redish, contributed poster,
    • AAAS STEM Education Symposium, Washington, DC (28 April 16)
    • PERC 2016, Sacramento, CA (21 July 16)
  10. Drawing physical insight from mathematics via extreme case reasoning, M. Eichenlaub, D. Hemingway, & E. F. Redish, Physics Education Research Conference, Sacramento CA (20 July 2016) 
  11. Incorporating Research-Based, Biologically-Authentic Physics Problems in IPLS,  D. Hemingway, M. Eichenlaub, W. Losert & E.F. Redish, 
    1. talk, Losert Lab Research Group, University of Maryland, College Park, MD (11 July 2015) 
    2. talk, Association of American Physics Teachers, Sacramento, CA (18 July 2016)
    3. poster, Physics Education Research Conference, Sacramento, CA (20 July 2016)
    4. paper, Physics Education Research Conference Proceedings (submitted)
  12. Authenticity as a Lens for UMD's NEXUS/Physics IPLS Course, D. Hemingway & K. Moore [Invited talk, Physics Education Research Conference, Sacramento, CA (21 July 2016)]
  13. Comparing factor analysis and network methods to cluster test questions, M. Eichenlaub [Contributed talk, AAPT National Meeting, Sacramento CA (20 July 2016)]
  14. Examining student attitudes in introductory physics via the Math Attitude and Expectations Survey (MAX), D. Hemingway, M. Eichenlaub, W. Losert, & E. F. Redish [talk, American Physical Society, Washington, DC (30 January 2017)]
  15. Understanding student use of mathematics in IPLS with the Math Epistemic Games Survey (MEGS), M. Eichenlaub, E. F. Redish, & D. Hemingway [poster, American Physical Society, Washington, DC (30 January 2017)] 
  16. Interdisciplinary teaching as inter-cultural research, E. F. Redish & C. Turpen
    1. poster, Foundations and Future of Physics Education Research, Bar Harbor, ME (21 June 2017)
    2. poster, Transforming Research in Undergraduate STEM Education (TRUSE), St. Paul, MN (7 July 2017) 
  17. Student attitudes towards using mathematics in an introductory physics course: Math attitude and expectations survey, D. Hemingway, M. Eichenlaub, & E. F. Redish [poster, Association of American Physics Teachers, Cincinnati, OH (24 July 2017)]
  18.  Teaching biology students to use math in science: Uncovering issues of language, culture, and identity, E. F. Redish, M. Eichenlaub, D. Hemingway, & C. Turpen [Poster, Physics Education Research Conference, Cincinnati, OH (27 July 2017)] 
  19. Using math in introductory physics: They're measurements, not numbers! Edward F. Redish, Mark Eichenlaub, and Deborah Hemingway [Contributed talk, AAPT National Summer Meeting, Washington DC, 2018]. 
  20. Learning to use math in science: Teaching epistemic tools, E. F. Redish, M. Eichenlaub, & D. Hemingway  [Poster presented at PERC 2018, Washington, DC, August 2018]. 
  21. Comparing Insights from Different Methods for Clustering Multiple-Choice Test Questions, Mark Eichenlaub [Contributed talk, AAPT National Summer Meeting, Washington DC, 2018]. 
  22. Blending physical knowledge with mathematical form in physics problem solving, Mark Eichenlaub and Edward F. Redish, in Mathematics in Physics Education, G. Pospiech, M Michelins, & B. Eylon, eds. (Springer Verlag, 2019). (preprint, arXiv 1804.01639)
  23. Analysing the Competency of Mathematical Modelling in Physics. In: Greczyło T., Dębowska E. (eds) Key Competences in Physics Teaching and Learning. Springer Proceedings in Physics, vol 190. (2017, Springer, Cham). doi: 10.1007/978-3-319-44887-9_3 (free access to preprint through link)
  24. Applying Conceptual Blending to Model Coordinated Use of Multiple Ontological Metaphors, B. W. Dreyfus, A. Gupta, and E. F. Redish, Int. J. Sci. Ed. 37:5-6 (2015) 812-838. doi:10.1080/09500693.2015.1025306 (free access to preprint) 
  25. Using math in physics - Overview, E. F. Redish, The Physics Teacher 59 (2021) 314-318. (arXiv preprint)
  26. Using math in physics - 1. Dimensional analysis, E. F. Redish, The Physics Teacher 59 (2021) 397-400. (arXiv preprint)
  27. Using math in physics - 2. Estimation, E. F. Redish, The Physics Teacher, 59 (2021) 525-528. (arXiv preprint)
  28. Using math in physics - 3. Anchor equations, E. F. Redish, The Physics Teacher, 59 (2021) 599-604.(arXiv preprint)
  29. Using math in physics - 4. Toy models, E. F. Redish, The Physics Teacher, 59 (2021) 683-688. (arXiv preprint)
  30. Using math in physics - 5. Functional dependence, E. F. Redish, The Physics Teacher, 60 (2022) 18-21 (arXiv preprint 



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