Formative Assessment 67

Assessment Problem: 

Sarah, Rivka, Rachel and Leah discussed the question of whether or not their success on tests is related to the amount of time that they prepare for tests.
A. Sarah claimed that the more that she studies, the better her grades are.  Please construct a graph that represents Sarah’s claim.
B. Rivka argued that no matter how long she studies, she always gets the same grade. Please construct a graph that represents Rivka’s claim.
C. Rachel, however, said that when she studies up to three hours, the longer she students the better her grades; but, beyond three hours, she becomes tired and her grades are lower.  Please construct a graph that represents Rachel’s claim.
D. Leah confessed that for her, generally, when she studies more, her grades descrease. Please construct a graph that represents Leah’s claim. (Mevarech, 1997)

Common Responses: 

Students commonly chose to represent the information separately, either putting the information from each student on a separate graph or separate lines on the same graph. 
Many students also represented ALL scenarios with a positive slope although some did not show this relationship.

Mathematical Issues: 

There were 3 major categories for student mistakes: 1. Constructing an entire graph as a single point. 2. Constructing a series of graphs, each representing one factor from the relevant data. 3. Conserving the form of an increasing function under all conditions

Analysis of Change
Interpreting Graphs
Common Core Standards: 
A-SSE: Seeing Structure in Expressions
Research References: 
Reference Mevarech, Z. R., & Kramarski, B. (1997). From verbal descriptions to graphic representations: stability and change in students' alternative conceptions. Educational Studies in Mathematics, 32(3), 229-263.