Promoting insight into algebraic formulas through graphing by hand

• Published in: Mathematical thinking and learning Vol. 23; no. 2; pp. 125 - 144
• Main Authors: Kop, Peter M. G. M., Janssen, Fred J. J. M., Drijvers, Paul H. M., van Driel, Jan H.
• Format: Journal Article
• Language: English
• Published: Philadelphia Routledge 03.04.2021; Taylor & Francis Ltd
• Subjects: Algebra; Cognitive skills; College Students; Colleges & universities; Foreign Countries; Grade 11; graphing formulas; Graphs; insight into algebraic formulas; Intervention; Mathematical Formulas; Mathematical thinking; Mathematics Education; Mathematics Instruction; Mathematics teaching; Mathematics Tests; Multiple Choice Tests; Pretests Posttests; Protocol Analysis; Qualitative reasoning; Questionnaires; Recognition; Retention (Psychology); Secondary education; Secondary School Students; Student Attitudes; Students; symbol sense; Task Analysis; Teaching Methods; Thinking Skills; Netherlands
• ISSN: 1098-6065; 1532-7833
• DOI: 10.1080/10986065.2020.1765078

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.