Solving Equations with Fractions: An Analysis of Prospective Teachers' Solution Pathways and Errors

Autor/inn/en	Jones, Dustin L.; Zientek, Linda Reichwein; Sharon, Valerie V.; Swarthout, Mary B.
Titel	Solving Equations with Fractions: An Analysis of Prospective Teachers' Solution Pathways and Errors
Quelle	In: School Science and Mathematics, 120 (2020) 4, S.232-243 (12 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Jones, Dustin L.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0036-6803
DOI	10.1111/ssm.12402
Schlagwörter	Problem Solving; Equations (Mathematics); Fractions; Error Patterns; Preservice Teachers; Arithmetic; Algebra; Mathematics Skills + Suchen Sie Ihr Suchwort? Problemlösen; Equations; Mathematics; Gleichungslehre; Bruchrechnung; Fehlertyp; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz
Abstract	We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the written solutions, determined which solution pathways led to the correct solution, and identified common errors in the solution pathways of respondents who incorrectly solved the equation. Respondents initially attempted different methods. The most common method was solving by using fractions, but the majority of respondents who solved by using mixed numbers were able to correctly solve the problem. Common errors related to fraction arithmetic and the distributive property. Nearly all of the abandoned pathways contained no errors, but ended with a step that likely would precede an operation with fractions. Our findings suggest that the ability to solve an arithmetic equation with no fractions was necessary, but not sufficient, to solve an arithmetic equation involving fractions, and that the problem of solving equations with fractions was more closely tied to one's difficulties with rational number arithmetic and less with one's understanding of algebra. (As Provided).
Anmerkungen	Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01