Promoting insight into algebraic formulas through graphing by hand

Kop, P.M.G.M.; Janssen, F.J.J.M.; Drijvers, P.H.M.; Driel, J.H. van (2020)

Article / Letter to editor

Student insight into algebraic formulas, including the ability to identify the structure of a formula and its components and to reason with and about formulas, is an issue in mathematics education. In this study, we investigated how 16- and 17-year-old pre-university students’ insight into algebraic formulas can be promoted through graphing formulas by hand. In an intervention of five 90-min lessons, 21 grade 11 students were taught to graph formulas by hand. The intervention’s design was based on experts’ strategies in graphing formulas, that is, using a combination of recognition and qualitative reasoning, and on principles of teaching complex skills. To assess the effect of this intervention, pre-, post-, and retention tests were administered, as well as a post-intervention questionnaire. Six students were asked to think aloud during the pre- and posttests. The results show that all students improved their abilities to graph formulas by hand. The think-aloud data suggest that the students improved both on recognition and reasoning, and give a detailed picture of how students used recognition and qualitative reasoning in combination. We conclude that graphing formulas by hand, based on the interplay of recognition and qualitative reasoning, might be a means to promote students’ insight into algebraic formulas.

• Algebra
• Graphing formulas
• Insight into algebraicformulas
• Qualitative reasoning
• Symbol sense

• All authors: Kop, P.M.G.M.; Janssen, F.J.J.M.; Drijvers, P.H.M.; Driel, J.H. van
• Date: 2020-05-25
• Journal: Mathematical Thinking and Learning
• Volume: 23
• Issue: 2
• Pages: 125 - 144
• DOI: doi:10.1080/10986065.2020.1765078