STUDENTS ’ DIFFICULTIES WITH APPLYING A FAMILIAR FORMULA IN AN UNFAMILIAR CONTEXT

This paper discusses problems many tenth grade students have when asked to apply a familiar formula in an unfamiliar context: specifically factoring a compound expression. Some of their attempts at solution are presented and discussed in terms of structure sense. Students who have previously displayed proficiency at using algebraic techniques often have difficulty in applying these techniques in unfamiliar contexts. Specifically we have observed that many students are unable to use the formula () ()bababa +−= − 22, which is familiar to them, to factor the expression ( ) ()44 33 +− − xx, which they have probably never met before. Rauff (1994) has classified students ’ beliefs about factoring and shows how these beliefs affect how students approach a factoring exercise. Rauff’s categories of students ’ beliefs about factoring are: reversal – the process of undoing a multiplication; deconstructive- the process of breaking down or simplifying; evaluative – a process that can be checked by multiplying out; formal – a factored expression is in the form of a product; numeric – decomposing numbers into product