Formative Assessment 113

Assessment Problem: 

The graph of y=x^2 - 2x is at right. Use this graph and any other lines which you may need to add to it to solve the equations given. Briefly explain your method.
x^2 - 2x = 3
x^2 - 2x = x
(needs image)

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.