To support the use of mathematical modeling in K-5 classroom settings, Carlson et al. (2016) propose a framework, which breaks down the teacher and student practices in the modeling process at this level. This framework places emphasis on the teacher’s role by organizing the actions into three teacher-centered phases: developing and anticipating, enacting, and revisiting (Carlson et al., 2016). This teacher-centered approach can provide insights for educators who are new to mathematical modeling by highlighting different considerations for each step of the modeling process.
The first phase, developing and anticipating, takes place as the teacher creates the modeling task for their students. This involves a strong understanding of the students’ mathematical backgrounds, past experiences, and interests (Carlson et al., 2016). Although not identified by Carlson et al., problem structures also need to be considered, as altering the way a problem is worded can help increase student performance (Tran & Dougherty, 2014). In addition to creating quality tasks, it is essential to anticipate what types of strategies students may use, the different paths they may take, and prepare ways they plan to support students (Carlson et al., 2016). By incorporating all of these considerations we can help provide experiences that more closely mirror the way mathematics is used in STEM fields, where deep understanding, flexibility, and creativity are key (Zarwojewski, 2016).
The enacting phase looks at the teacher and student roles as the modeling activity takes place. Students working on the task are asked to go through a cycle of posing questions, building solutions, and validating their conclusions (Carlson et al., 2016). Throughout this process the teacher can provide support by posing questions that facilitate communication, prompt discussion, compare approaches, assist student reflection, or balance the mathematical demand of the situation (Carlson et al., 2016). During this time it is important to look at how individuals and groups are engaging in the task and provide support, while being careful to not direct students through the process (Gann et al., 2016; Stender & Kaiser, 2016).
The final phase identified by Carlson et al. (2016), revisiting, allows students to apply new thoughts and perspectives to tasks that they previously found potential solutions for. This helps students build on their previous models, revising and refining them with new mathematical and contextual ideas (Carlson et al., 2016). When developing lessons it is important to consider the benefits of revisiting previous tasks, as this has the potential to help students create more sophisticated plans and enable them to reflect on the progress they have made in their own learning.
References
Carlson, M., Wickstrom M., Burroughs E., & Fulton, E. (2016). A case for mathematical modeling in the elementary school classroom. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 121-130). 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.
Stender, P., & Kaiser, G. (2016). Fostering modeling competencies for complex situations. In C. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 107-128). National Council of Teachers of Mathematics.
Tran, D. & Dougherty, B. (2014). Authenticity of mathematical modeling. Mathematics Teacher, 107(9), 672–678.
Zawojewski, J. (2016). Mathematical modeling as a vehicle for stem learning. In C. R. Hirsch & R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 117-120). National Council of Teachers of Mathematics.