A Computational Model of Fraction Arithmetic

Autor/inn/en	Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.
Titel	A Computational Model of Fraction Arithmetic
Quelle	(2017), (84 Seiten) PDF als Volltext kostenfreie Datei Verfügbarkeit
Zusatzinformation	Weitere Informationen
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
Schlagwörter	Arithmetic; Computation; Models; Mathematics Instruction; Teaching Methods; Hypothesis Testing; Problem Solving; Simulation; Fractions; Textbooks; Error Patterns; Mathematics Skills; Mathematical Concepts; Elementary Schools; Middle Schools + Suchen Sie Ihr Suchwort? Addition; Arithmetik; Arithmetikunterricht; Rechnen; Analogiemodell; Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Hypothesenprüfung; Hypothesentest; Problemlösen; Simulation program; Simulationsprogramm; Bruchrechnung; Textbook; Text book; Schulbuch; Lehrbuch; Fehlertyp; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Elementary school; Grundschule; Volksschule; Middle school; Mittelschule; Mittelstufenschule
Abstract	Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it with the problems from a widely used textbook series. The simulation generated many phenomena of children's fraction arithmetic performance through a small number of common learning mechanisms operating on a biased input set. The biases were not unique to this textbook series--they were present in two other textbook series as well--nor were the phenomena unique to a particular sample of children--they were present in another sample as well. Among other phenomena, the model predicted the high difficulty of fraction division, variable strategy use by individual children and on individual problems, relative frequencies of different types of strategy errors on different types of problems, and variable effects of denominator equality on the four arithmetic operations. The model also generated non-intuitive predictions regarding the relative difficulties of several types of problems and the potential effectiveness of a novel instructional approach. Perhaps the most general lesson of the findings is that the statistical distribution of problems that learners encounter can influence mathematics learning in powerful and non-intuitive ways. [At the time of submission, this article was in press with "Psychological Review."] (As Provided).
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01