Formative Assessment 86

Assessment Problem: 

When is the following true – always, never or sometime?

Mathematical Issues: 

One of the well-documented misconceptions is the convention of interpreting letters, namely a belief that different letters must represent different values. This misconception is illustrated by students’ responses of “never” to the question. In contrast with the understanding of a letter as a specific unknown value, a generalised number is able to take more than one value. A distinction can be made between the idea of a letter taking on several values in turn and a letter representing a set of values simultaneously. If letters have specific values, then the answer must be “never”. This is even true if students are moving towards an advanced understanding of variables and consider M and P as sets. When is set M and set P the same? Most likely “never”.

Common Responses: 

Sometimes, when M = P (25%)
Sometimes.  Or M and P given a specific value. (14%)
Never (51%)
I: Why “Never”?
S: Because M and P are two different things.

Variables & Expressions