Formative Assessment 106

Assessment Problem: 

The two graphs at right are y= x^2 - kx and y=3.  Use the information given to solve the following equations for x.
x^2 -kx = 3
x^2 - kx = 0

Mathematical Issues: 

In spite of substantial emphasis on viewing functions via multiple representations, students tend to have a favorite representation they revert to whenever possible. They often do not see the different representations of a function as carrying the same information and simply highlighting certain parts of it differently (e.g., x-intercepts).

Common Responses: 

Many students could not see how the graphs could help.  Instead, students often attempted to solve the equation algebraically even though the given information is graphical.

Patterns & Functions
Multiple Representations
Research References: 
Gray, R., & Thomas, M. (2001). Quadratic Equation Representations and Graphic Calculators: Procedural and Conceptual Interactions. Paper presented at the 24th Annual Mathematics Education Research Group of Australasia Conference, Sydney, Australia.