Promoting insight into algebraic formulas through graphing by hand
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 alge...
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Published in | Mathematical thinking and learning Vol. 23; no. 2; pp. 125 - 144 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Philadelphia
Routledge
03.04.2021
Taylor & Francis Ltd |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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Bibliography: | Refereed article. Includes bibliographical references. |
ISSN: | 1098-6065 1532-7833 |
DOI: | 10.1080/10986065.2020.1765078 |