Assessment Problem:

What can you say about c if c + d = 10 and c is less than d?

Common Responses:

c < 5 (11%)

c = 1, 2, 3, 4 (systematic list) (19%)

c = 10 - d (4%)

Unsystematic list (1%)

One value only (usually c=4) (39%) I: Why 4?

S: Because four is less than five

Mathematical Issues:

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. The problem has got to be especially confusing for students who struggle with the idea of a letter representing something “unknown”--therefore they treat it as having a specific value.

Domain:

Variables & Expressions

Research References:

Hart, K.M.; Kerslake, D; Brown, ML; Ruddock, G; Kuchemann, DE; McCartney, M. (1981). “Algebra” in Children's Understanding of Mathematics: 11-16. London: John Murray Pub.