The space between an unknown and a variable

The meaning given to letters is significant for students’ ability to be successful with algebraic tasks. Recent studies have noted that even when students have a sense of generalised number, they often have a natural number bias in the values they think a letter can take. This study analyses interviews from 13 students across two schools to explore the meaning they had for letters. The responses supported the idea that some students have a natural number bias and also that the notion of a letter representing a fraction is problematic. In addition, three other factors emerged which affected the meaning given to a letter: what was mentally stressed; the desire to avoid “messy” calculations; and viewing an equation as an example of a wider class of equations.