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Modeling with & Using Representations in Mathematics
Course Description
Course Description
Examine the role of modeling and representing in mathematics learning and teaching. Investigate ways in which teachers and students use representations and translations across representations in support of mathematics teaching and learning. Finally, consider how using representations support equitable teaching.
Essential Questions
Essential Questions
What is the role of representation across the mathematics curriculum including those “invented” by students and “presented” and/or emphasized by teachers?
What is modeling with mathematics? How is this the same or different from modeling mathematics and models for mathematics?
What are the links between representation, modeling, and equitable teaching?
Required Texts
Required Texts
Select one of the following based on grade level.
Arnold, E. G., Burroughs, E. A., Carlson, M. A., Fulton, E. W., & Wickstrom, M. W. (2021). Becoming a teacher of mathematical modeling grades K-5. National Council of Teachers of Mathematics.
or
Arnold, E. G., Burroughs, E. A., Carlson, M. A., Fulton, E. W., & Wickstrom, M. W. (2021). Becoming a teacher of mathematical modeling grades 6-12. National Council of Teachers of Mathematics.
Download or purchase.
Consortium for Mathematics and Its Applications (COMAP) and Society for Industrial and Applied Mathematics (SIAM). (2019). Guidelines for assessment and instruction in mathematical modeling (GAIMME), 2nd Edition. Author.
Attend Anywhere
Attend Anywhere
Face-to-face @ Multnomah Education Service District
Online via Zoom, see calendar invitation
Course Schedule
Course Schedule
Dates: Monday, 6/23/2025 through Friday, 6/27/2025
Time: 8:30 am - 4:00 pm
Required Readings
Required Readings
Anhalt, C. O., & Cortez, R. (2015). Mathematical modeling: A structured process. Mathematics Teacher, 108(6), 446-452.
Bush, S. B., Gibbons, K., Karp, K. S., & Dillon, F. (2015). Epidemics, exponential functions, and modeling. Mathematics Teaching in the Middle School, 21(2), 90-97.
Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In C. W. Hirsch & A. R. McDuffie (Eds.) Mathematical modeling and modeling mathematics, Annual Perspectives in Mathematics Education (pp. 3-16). National Council of Teachers of Mathematics.
Common Core Standards Writing Team. (2022). Progressions for the Common Core State Standards for Mathematics. Institute for Mathematics and Education, University of Arizona. https://mathematicalmusings.org/wp-content/uploads/2023/02/Progressions.pdf.
Czocher, J. A., & Moss, D. L. (2017). Mathematical modeling: Are prior experiences important? The Mathematics Teacher, 110(9), 654-660.
Dibbs, R., Beach, J., & Rios, D. (2018). Gotta walk them all: Mathematical modeling and Pokémon Go. The Mathematics Teacher, 112(1), 34-39.
English, L. D., Fox, J. L., & Watters, J. J. (2005). Problem posing and solving with mathematical modeling. Teaching Children Mathematics, 12(3), 156-163.
Felton, M. D., Anhalt, C. O., & Cortez, R. (2015). Going with the flow: Challenging students to make assumptions. Mathematics Teaching in the Middle School, 20(6), 342-349.
Hendrickson, K. A. (2015). Fracking: Drilling into math and social justice. Mathematics Teaching in the Middle School, 20(6), 366-371.
Hernández, M. L., Levy, R., Felton-Koestler, M. D., & Zbiek, R. M. (2017). Mathematical modeling in the high school curriculum. Mathematics Teacher, 110(5), 336-342.
Hodges, T. E., & Johnson, M. (2017). Representations as tools for mathematical understanding. In D. A. Spangler & J. J. Wanko (Eds.) Enhancing classroom practice with research behind Principles to Actions (pp. 27-36). National Council of Teachers of Mathematics.
Kirwan, J. V. (2017). Using visualization to generalize on quadratic patterning tasks. Mathematics Teacher, 110(8), 558-593.
Koestler, C., Felton, M. D., Bieda, K. N., & Otten, S. (2013). Connecting the NCTM process standards and the CCSSM practices. National Council of Teachers of Mathematics.
Meyer, D. (2015). Missing the promise of mathematical modeling. Mathematics Teacher, 108(8), 578-583.
Moore, T. J., Doerr, H. M., Glancy, A. W., & Ntow, F. D. (2015). Preserving pelicans with models that make sense. Mathematics Teaching in the Middle School, 20(6), 358-364.
Moyer-Packenham, P. S. (2005). Using virtual manipulatives to investigate patterns and generate rules in algebra. Teaching Children Mathematics, 11(8), 437-444.
Nabbout-Cheiban, M., Fisher, F., & Edwards, M. T. (2017). Using Technology to Prompt Good Questions about Distributions in Statistics. The Mathematics Teacher, 110(7), 526-532.
Özgün-Koca, S. A. (2016). Strategically fostering dynamic interactive environments. The Mathematics Teacher, 110(2), 142-145.
Poling, L. L., Naresh, N., & Goodson-Espy, T. (2018). Empowering mathematicians through modeling. Mathematics Teaching in the Middle School, 24(3), 138-147.
Preston, R. V., & Garner, A. S. (2003). Representation as a vehicle for solving and communicating. Mathematics Teaching in the Middle School, 9(1), 38-43.
Reiten, L. (2018). Promoting student understanding through virtual manipulatives. The Mathematics Teacher, 111(7), 545-548.
Simic-Muller, K. (2015). Social justice and proportional reasoning. Mathematics Teaching in the Middle School, 21(3), 162-168.
Simic-Muller, K., Turner, E. E., & Varley, M. C. (2009). Math club problem posing. Teaching Children Mathematics, 16(4), 206-212.
Smith, M. S., Hillen, A. F., & Catania, C. L. (2007). Using pattern tasks to develop mathematical understandings and set classroom norms. Mathematics Teaching in the Middle School, 13(1), 38-44.
Smith, M. S., Silver, E. A., & Stein, M. K. (2005). Improving instruction in algebra: Using cases to transform teaching and learning, volume 2. Teachers College Press.
Swanson, P. E. (2015). Toy stories: Modeling rates. Teaching Children Mathematics, 22(2), 76-83.
Turner, E. E., & Strawhun, B. T. F. (2007). Posing problems that matter: Investigating school overcrowding. Teaching Children Mathematics, 13(9), 457-463.
Other Resources
Other Resources
Cuoco, A. A., & Curcio, F. R. (Eds.)(2001). The roles of representation in school mathematics, 2001 yearbook. National Council of Teachers of Mathematics.
Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio (Eds.) The roles of representation in school mathematics, (pp. 1-23).National Council of Teachers of Mathematics.
Hirsch, C. W., & McDuffie, A. R. (Eds.) (2016). Mathematical modeling and modeling mathematics, Annual Perspectives in Mathematics Education. National Council of Teachers of Mathematics.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier, (Ed.), Problems of representations in the teaching and learning of mathematics (pp. 33-40). Lawrence Erlbaum.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author. https://www.nctm.org/standards/
National Governors Association Center for Best Practices and Council of Chief State School Officers (2010). Common core state standards for mathematics. Author. https://learning.ccsso.org/common-core-state-standards-initiative
Nielsen, M. E., & Bostic, J. D. (2018). Connecting and using multiple representations. Mathematics Teaching in the Middle School, 23(7), 386-393.
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