Promoting Insight into Algebraic Formulas through Graphing by Hand

Autor/inn/en	Kop, Peter M. G. M.; Janssen, Fred J. J. M.; Drijvers, Paul H. M.; van Driel, Jan H.
Titel	Promoting Insight into Algebraic Formulas through Graphing by Hand
Quelle	In: Mathematical Thinking and Learning: An International Journal, 23 (2021) 2, S.125-144 (20 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Kop, Peter M. G. M.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1098-6065
DOI	10.1080/10986065.2020.1765078
Schlagwörter	Algebra; Mathematics Instruction; Teaching Methods; Secondary School Students; Mathematical Formulas; Grade 11; Intervention; Thinking Skills; Retention (Psychology); Mathematics Tests; Protocol Analysis; Student Attitudes; Pretests Posttests; Multiple Choice Tests; Task Analysis; Foreign Countries; Netherlands + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Sekundarschüler; Mathematische Formel; School year 11; 11. Schuljahr; Schuljahr 11; Denkfähigkeit; Merkfähigkeit; Schülerverhalten; Multiple choice examinations; Multiple-choice tests, Multiple-choice examinations; Multiple-Choice-Verfahren; Aufgabenanalyse; Ausland; Niederlande
Abstract	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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01