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What is the difference between Modeling Mathematics and Mathematical Modeling?

Modeling mathematics and mathematical modeling are concepts that are discussed in a wide range of research and standards. Both provide different benefits for students and can be leveraged in a classroom setting, but it is important to know the differences between these two terms. Specific definitions may vary but, the overarching ideas are consistent (Cirillo et al., 2016).

Modeling mathematics is the process of using representations to help students understand mathematical concepts (Cirillo et al., 2016). These experiences help clarify mathematical concepts for students, but they do not provide insights into how the concepts can be used to solve real-world situations.

For example, a teacher who uses a rectangular array to demonstrate the concept of multiplication would be modeling mathematics. This use of a physical representation helps students understand the mathematical concept of multiplication, but does not require students to apply mathematics to a real-world situation. The modeling that is happening here begins in the mathematical world and helps to explain a mathematical concept.

Mathematical modeling refers to the process of applying mathematical concepts to genuine real-world situations that do not have a single anticipated mathematical path to a solution (Cirillo et al., 2016). The process for finding a solution must be developed by the person considering the problem, while using different mathematical ideas and reflecting on decisions in the context of the problem. These experiences can help students see connections between different subjects, develop the ability to critically analyze, and deepen their understanding of mathematical concepts (Anhalt et al., 2018).

For example, a teacher may pose a question such as: Can a cat reasonably have 2000 descendants in 18 months? (MAP Classroom Challenge). This type of question asks students to take a real-world situation and apply their mathematical knowledge to come to an answer. Each student's path and answer may differ, as they are working towards a solution that they feel is sufficiently supported by their chosen constraints and mathematical work.

So remember, the order of these two words matters! Both modeling mathematics and mathematical modeling are important concepts to understand when reviewing educational research and standards. Both can be used to support different aspects of students’ learning, leading to a deeper understanding of the concepts and purpose of mathematics.

For more resources on Mathematical Modeling:


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.

Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical

modeling and modeling mathematics (pp. 3-16). National Council of Teachers of Mathematics.


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