Assessment Problem:

Which is larger, 2n or n + 2?

Common Responses:

> 2n (71%)

> n + 2 or “the same” (16%)

> Correct conditional response: (e.g. 2n, when n > 2) (6%)

Mathematical Issues:

This problem is good for differentiating which students understand the concept of a variable. A comprehensive understanding of variables goes beyond simply knowing that the unknown value changes. Students need to how the values of an unknown change—which is made evident in their answer. Understanding is indicated here by students’ ability to describe a second-order relationship--how variation in one set of values depends on variation in another set. To get a sense of students understanding of operations on variables and what variables can represent, including integers.

Domain:

Variables & Expressions

Theme:

Representation

Common Core Standards:

7.EE: Expressions and Equations

Research References:

Booth, L. (1984)