Using comparison to develop flexibility for teaching algebra

In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students’ flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent student discussion of these multiple solution methods to highlight the similarities and differences among problem-solving techniques. The goals of the professional development activity were to make teachers aware of how to use comparison effectively in their instruction, as well as to impact teachers’ own flexibility in algebra by using comparison instructionally during the professional development. Our analysis of teachers’ experiences in the professional development activity suggests that when teachers were presented with techniques for effective use of comparison, their own understanding of multiple solution methods was reinforced. In addition, teachers began to question why they relied exclusively on one familiar method over others that are equally effective and perhaps more efficient and started to draw new connections between problem-solving methods. Finally, as a result of experiencing instructional use of comparison, teachers began to see value in teaching for flexibility and reported changing their own teaching practices.