Mathematical modeling requires students to take multiple factors into account simultaneously as they work towards an undefined solution (Zawojewski, 2016). The process of starting with an open question, sorting through potential paths, analyzing meanings of results, and simultaneously being open to exploring different possibilities that have not been previously considered can be daunting for students, especially when approaching mathematical modeling situations for the first time. However, seeing mathematics used in contexts that are meaningful can help students see the importance of mathematical understanding (Blum & Ferri, 2016). It is up to the teacher to provide supports that can help students bridge the gap between the content knowledge that lives in the textbook and its messier real life applications.
Learning how to approach mathematical modeling situations involves the development of a new set of skills in order for students to productively engage with the problem and form potential answers. Bleiler-Baxter et al. (2016) identify three types of decisions that students must make as they work in these situations: simplification, relationship-mapping, and situation-analysis decisions. These types of decisions enable students to simplify the problem that is given to them by identifying key pieces of information, identify connections between the important aspects of the problem, and analyze the results of the steps that they take in order to progress towards and recognize their final response respectively (Bleiler-Baxter et al. 2016).
In order to assist students as they become familiar with the math modeling process and build their “modeling competency” (Blum & Ferri, 2016, p. 67) teachers need to understand “what it means to model with mathematics… (and) the knowledge and skills students bring to the modeling process” (Bleiler-Baxter et al., 2016, p.53). This requires a deep understanding of what authentic modeling opportunities look like, the mathematical content involved, the students’ background, and potential struggles that the students may face. Understanding common challenges can be especially beneficial for developing appropriate supports to help students adjust to this new way of using their mathematical knowledge.
One way for teachers to provide support is by incorporating a structure for students to follow as they work through a modeling task. Providing a scaffold, such as the solution plan developed by Schukajlow et al. (2015), can help them break down this process into manageable parts and support the development of modeling competency. Providing scaffolding for students as they transition into this new form of thinking about mathematics can be powerful, helping them to develop the skills that are needed while maintaining the authenticity of the mathematical modeling experience (Schukajlow et al., 2015).
Supports can also take different forms, such as teacher interactions during the mathematical modeling process. While teachers should not lead their students during the modeling process, they do have expertise which can be used to help provide students by posing questions that could provoke deeper thought in particular areas. Informal opportunities to check the students understanding through discussions or periodic reporting from the groups can also provide a valuable opportunity to support students as they create their models (Reins, 2016).
While there are various ways to support students during the mathematical modeling process, all of these supports have one thing in common. They do not take away the student’s autonomy. They provide a general guide and offer a foothold for students to use to progress, but they do not guide them to a predetermined path. This is key if students are to become independent thinkers who can make sense of the world around them and apply their knowledge to novel situations.
Bleiler-Baxter, S., Barlow, A., & Stephens, D. (2016). Moving beyond context: Challenges in
modeling instruction. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling
and modeling mathematics (pp. 53-64). National Council of Teachers of Mathematics.
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
Reins, K. (2016). Broadening the landscape of modeling by including an emergent view. In C.
R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics
(pp. 77-85). National Council of Teachers of Mathematics.
Schukajlow, S., Kolter, J., & Blum, W. (2015). Scaffolding mathematical modelling with a
solution plan. ZDM: The International Journal on Mathematics Education, 47(7), 1241–
Zawojewski, J. (2016). Teaching and learning about mathematical modeling. In C. R. Hirsch &
A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 51-52).
National Council of Teachers of Mathematics.