Formative Assessment 123

Assessment Problem: 

Write an equation for the following statement: “There are six times as many students as professors at this university.” Use S for the number of students and P for the number of professors. (Alternatively - Write an equation using the variables C and E to represent the following statement: There are 8 times as many people in China as there are in England.)

Common Responses: 

6s = p

Mathematical Issues: 

This is known as the reversal error. There are a number of different potential issues underlying this error. (See modeling encyclopedia entries: Syntactic issues in problem solving, variables as labels in modeling, and English language learners and modeling) This problem can be used to assess how students are using variables and the extent to which students rely on sentence structure to construct symbolic representations.

Modeling & Word Problems
Translating words to symbols
Common Core Standards: 
7.EE: Expressions and Equations
Research References: 
Bernardo, A. B. I., & Okagaki, L. (1994). Roles of symbolic knowledge and problem-information context in solving word problems. Journal of Educational Psychology, 86(2), 212-220. Clement, J., Lochhead, J., & Monk, G. (1981). Translation difficulties in learning mathematics. American Mathematical Monthly, 88, 286-290. Clement, J. (1982). Algebra Word Problem Solutions: Thought Processes Underlying a Common Misconception. Journal for Research in Mathematics Education, 13(1), 16-30.