## Elephant Delta Day 3 – Renee LaRue from West Virginia University on Optimization in first semester calculus: A look at a classic problem

Photo of Renee LaRue available here.

Co-author Nicole Engelke Infante

Classic problem: Fence along a barn. Minimize amount of fencing given a fixed amount of fencing.

Literature: 4 versions of this problem. More difficult when students have to set up problem from words.

Carlson and Bloom (2005) Problem-Solving Framework

Tall and Vinner (1981) Concept image

7 students (pilot with 3 students), just before final exam involving optimization.

Recordings of students thinking aloud.

Questions about rectangles – what happens to perimeter if area changes?

5 students solved without intervention, 3 perfectly, 2 forgot about barn. Other 2 needed much help.

Responses showed gaps in reasoning.

Six key maths concepts that played a role:

- Use 2x + y or 2y + x? 2l + 2w = 2y + 2x (matching variables to what they think they must mean).
- Function notation. Haphazard use of equal signs. Student said you can’t write 2x + y as f(x) because y = f(x).