Longer Bars for Bigger Numbers? Children's Usage and Understanding of Graphical Representations of Algebraic Problems

Autor/inn/en	Lee, Kerry; Khng, Kiat Hui; Ng, Swee Fong; Ng Lan Kong, Jeremy
Titel	Longer Bars for Bigger Numbers? Children's Usage and Understanding of Graphical Representations of Algebraic Problems
Quelle	In: Frontline Learning Research, 1 (2013) 1, S.81-96 (16 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2295-3159
Schlagwörter	Foreign Countries; Elementary School Students; Mathematics Instruction; Word Problems (Mathematics); Algebra; Mathematical Concepts; Graphs; Learning Strategies; Age Differences; Grade 2; Grade 5; Problem Solving; Mathematics Tests; Visual Aids; Elementary School Mathematics; Statistical Analysis; Mathematics Skills; Singapore + Suchen Sie Ihr Suchwort? Ausland; Mathematics lessons; Mathematikunterricht; Textaufgabe; Grafische Darstellung; Learning methode; Learning techniques; Lernmethode; Lernstrategie; Age; Difference; Age difference; Altersunterschied; School year 02; 2. Schuljahr; Schuljahr 02; School year 05; 5. Schuljahr; Schuljahr 05; Problemlösen; Anschauungsmaterial; Elementare Mathematik; Schulmathematik; Statistische Analyse; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Singapur
Abstract	In Singapore, primary school students are taught to use bar diagrams to represent known and unknown values in algebraic word problems. However, little is known about students' understanding of these graphical representations. We investigated whether students use and think of the bar diagrams in a concrete or a more abstract fashion. We also examined whether usage and understanding varied with grade. Secondary 2 (N = 68, M[subscript age] = 13.9 years) and Primary 5 students (N = 110, M[subscript age] = 11.1 years) were administered a production task in which they drew bar diagrams of algebraic word problems with operands of varying magnitude. In the validation task, they were presented with different bar diagrams for the same word problems and were asked to ascertain, and give explanations regarding the accuracy of the diagrams. The Küchemann algebra test was administered to the Secondary 2 students. Students from both grades drew longer bars to represent larger numbers. In contrast, findings from the validation task showed a more abstract appreciation for how the bar diagrams can be used. Primary 5 students who showed more abstract appreciations in the validation task were less likely to use the bar diagrams in a concrete fashion in the production task. Performance on the Küchemann algebra test was unrelated to performance on the production task or the validation task. The findings are discussed in terms of a production deficit, with students exhibiting a more sophisticated understanding of bar diagrams than is demonstrated by their usage. (As Provided).
Anmerkungen	European Association for Research on Learning and Instruction. Peterseliegang 1, Box 1, 3000 Leuven, Belgium. e-mail: info@frontlinelearningresearch.org; Web site: http://journals.sfu.ca/flr/index.php/journal/index
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01