Students' mathematical modeling in algebra

Mathematical modeling and algebraic reasoning are two important components of mathematics education. In this study, I taught a mathematical modeling lesson to high school Algebra I students. My goal was to understand how mathematical modeling and algebraic reasoning are related. To analyze students' modeling and reasoning, I adapted a coding scheme for identifying observable actions in mathematical modeling and created a coding scheme for identifying observable actions in algebraic reasoning. Using these coding templates, I analyzed three groups. I found that two groups followed iterative, non-linear modeling routes and used more algebraic reasoning, while one group followed a highly linear modeling route and did not use as much algebraic reasoning. In addition, I found that the later steps in the modeling cycle led to more algebraic reasoning than the early steps. The findings suggest that mathematical modeling does encourage algebraic reasoning, but not in all circumstances. In addition, the findings provide insight into tensions in teaching mathematical modeling and suggestions for the design of modeling lessons. To further understand how students learn algebra through mathematical modeling, I recommend further study in developing the coding template for identifying algebraic reasoning, studying the modeling behavior of more groups of students to understand other possible student modeling routes, and studying how students' modeling and reasoning changes over time