How is Reasoning with Quantities Limited in Mathematical Modeling?

One reason mathematical modeling remains highly challenging for students is because it requires knowledge about both mathematics and the real-world. Recent work suggests promoting the learning of mathematical modeling as conceiving quantities and establishing relationships among quantities could help students overcome the challenges they experience. While promising, this approach may be oversimplistic in its claims. Through analyzing data collected via a teaching experiment methodology, we present one student’s (Szeth’s) work on two tasks to illustrate how Szeth’s reasoning with quantities was limited during his model construction process in the following ways: Szeth (i) used already constructed mathematical expressions to reason about how quantities vary, and (ii) did not construct a mathematically correct expression despite having reasoned with quantities.