What is Mathematical Modeling?
A mathematical model is ...
A representation of a system or scenario that is used to gain qualitative and/or quantitative understanding of some real-world problems and to predict future behavior (Bliss et al., 2014)
Benefits of mathematical modeling:
Help students see the importance of mathematical understanding (Blum & Ferri, 2016)
Deepen understanding of mathematical concepts (Anhalt et al., 2018)
Raise student interest and build awareness of real-world applications (Cirillo et al., 2016)
Bolster problem-solving skills, encourage creative and critical thinking (Anhalt et al., 2018; Gann et al. , 2016)
Opportunities to express, modify, and refine ways of thinking (Lesh et al., 2003)
Potential to incorporate additional STEM content and Standards for Mathematical Practice (Maiorca & Stohlmann, 2016)
Modeling Cycle (Blum, 2011)
Modeling Cycle (Bliss et al., 2014)
What does a modeling task look like?
This is part of our Fast Food Task available on the Modeling Tasks page.
Modeling tasks allow for multiple answers and help develop student agency through the use of assumption-making, various entry points, and connections to real-world scenarios. Mathematical modeling encourages students to make their own choices instead of simply following procedures or plugging values into formulas.
References
Anhalt, O., C., Cortez, R., & Bennett, A. B. (2018). The emergence of mathematical modeling competencies: An investigation of prospective secondary mathematics teachers. Mathematical Thinking and Learning, 20(3), 202-221.
Bliss, K. M., Fowler, K. R., & Galluzzo, B. J. (2014). Math modeling: Getting started and getting solutions. Society for Industrial and Applied Mathematics (SIAM).
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (Vol. 1, pp. 15-30). Springer.
Blum, W., Ferri, R. (2016). Advancing the teaching of mathematical modeling: Research-based concepts and examples. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 53-64). National Council of Teachers of Mathematics.
Cirillo, M., Bartell, T., & Wager, A. (2016). Teaching mathematics for social justice through mathematical modeling. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 53-64). National Council of Teachers of Mathematics.
Gann, C., Avineri, T., Graves, J., Hernandez, M., & Teague, D. (2016). Moving students from remembering to thinking: The power of mathematical modeling. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 97-106). National Council of Teachers of Mathematics.
Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 35-58). Lawrence Erlbaum Associates, Inc.
Maiorca, C., & Stohlmann, M. (2016). Inspiring students in integrated STEM education through modeling activities. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 153-162). National Council of Teachers of Mathematics.