Algebraic procedures and creative thinking

Simplifying symbolic expressions is usually perceived in middle school algebra as an algorithmic activity, achieved by performing sequences of short drill-and-practice tasks, which have little to do with conceptual learning or with creative mathematical thinking. The aim of this study is to explore possible ways by which ninth-grade students can be encouraged to apply flexible and creative thinking in the context of a task that requires students to design a multiple-choice questionnaire on equivalent algebraic expressions. Fifty-six ninth-grade students answered Take-a-Quiz and Make-a-Quiz questionnaires. The findings indicate that students can be engaged in a satisfactory way in these kinds of non-routine tasks. Also, about two-thirds of the participating students were able to display a medium or high level of originality in their construction of equivalent expressions. In addition, an analysis of the non-equivalent expressions suggested by the participating students as distractors indicated a relatively high level of awareness to the most common errors that might occur in this type of activity.