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ERIC Number: EJ1090860
Record Type: Journal
Publication Date: 2013
Pages: 16
Abstractor: As Provided
ISSN: EISSN-2295-3159
Longer Bars for Bigger Numbers? Children's Usage and Understanding of Graphical Representations of Algebraic Problems
Lee, Kerry; Khng, Kiat Hui; Ng, Swee Fong; Ng Lan Kong, Jeremy
Frontline Learning Research, v1 n1 p81-96 2013
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.
European Association for Research on Learning and Instruction. Peterseliegang 1, Box 1, 3000 Leuven, Belgium. e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education; Grade 2; Primary Education; Early Childhood Education; Grade 5; Intermediate Grades; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Singapore
Grant or Contract Numbers: N/A