Title: "Length times width equals area" and "Line times line equals parabola": Incorporating two RME models into a cohesive learning trajectory for quadratic functions.
Abstract: RME researchers have discussed two alternatives to the projectile motion model for
quadratic functions: (1) “line times line equals parabola” (Kooij, 2000), and (2) the area
model (Drijvers et al., 2010). Our learning trajectory incorporates and connects these
models in a cohesive unit that begins with a motivating contextual problem, guides students
to construct both of the above models, and concludes with formal algebraic representations.
We have used this unit for the past two years in our Algebra I courses. During this time, we
have collected a body of evidence that supports the approach: 1) Assessment results
suggest that students learn quadratic functions at or above the level expected in a typical
algebra course; 2) Student work suggests that learning multiple models leads to deeper
understanding and flexible problem solving; 3) Student feedback suggests that the models
help students solve problems and understand formal mathematics. Participants will receive
our complete unit in electronic form. Furthermore, we will discuss our lessons learned, and
avenues for extensions and future research.
- View our presentation online
- Download our presentation (PowerPoint file)
- Download the complete unit to use in your classroom (98 MB .zip file, MS Word and PDF reader required to view and edit files)
- Links to the applets we demonstrated:
- Applet home page
- The "geometric algebra 2D" applet that we demonstrated