Assessment Problem:

If e + f = 8, what does e + f + g = ?

How do you know?

Common Responses:

15 (2%)

12 (26%)

8g (3%)

9 (6%)

Correct, 8 + g (41%)*

Mathematical Issues:

Student may struggle to understand that an "answer" can be an expression, not having the Acceptance of Lack of Closure (see Encyclopedia of Algebraic Thinking). The interviews indicate that the students may not be comfortable with leaving an expression such as “8 + g” and feel compelled to come up with a numerical answer. At the Letter Evaluated level of thinking the student figures out numbers for the letters using any means possible.

Domain:

Variables & Expressions

Theme:

Evaluating variables

Common Core Standards:

7.EE: Expressions and Equations

6.EE Expressions and Equations

A-SSE: Seeing Structure in Expressions

Research References:

Based on the work of Booth (1988), Collis (1974), and Kuchemann (1981).