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ERIC Number: EJ1081952
Record Type: Journal
Publication Date: 2015-Nov
Pages: 14
Abstractor: As Provided
ISSN: ISSN-1863-9690
Flow-Chart Proofs with Open Problems as Scaffolds for Learning about Geometrical Proofs
Miyazaki, Mikio; Fujita, Taro; Jones, Keith
ZDM: The International Journal on Mathematics Education, v47 n7 p1211-1224 Nov 2015
Recent research on the scaffolding of instruction has widened the use of the term to include forms of support for learners provided by, amongst other things, artefacts and computer-based learning environments. This paper tackles the important and under-researched issue of how mathematics lessons in junior high schools can be designed to scaffold students' initial understanding of geometrical proofs. In order to scaffold the process of understanding the structure of introductory proofs, we show how flow-chart proofs with multiple solutions in "open problem" situations are a useful form of scaffold. We do this by identifying the "scaffolding functions" of flow-chart proofs with open problems through the analysis of classroom-based data from a class of Grade 8 students (aged 13-14 years old) and quantitative data from three classes. We find that using flow-chart proofs with open problems support students' development of a structural understanding of proofs by giving them a range of opportunities to connect proof assumptions with conclusions. The implication is that such scaffolds are useful to enrich students' understanding of introductory mathematical proofs.
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Publication Type: Journal Articles; Reports - Research
Education Level: Junior High Schools; Secondary Education; Middle Schools; Grade 8; Elementary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A