Symbols and the bifurcation between procedural and conceptual thinking
Date
2001Author
Tall, DavidGray, Eddie M.
Ali, Maselan Bin
Crowley, Lillie
DeMarois, Phil
McGowen, Mercedes
Pitta-Pantazi, Demetra
Pinto, Marcia
Thomas, Michael
Yusof, Yudariah
ISSN
14926156Source
Canadian Journal of Science, Mathematics & Technology EducationVolume
1Issue
1Pages
81-Google Scholar check
Metadata
Show full item recordAbstract
Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this article we consider the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and procedural thinking. Evidence will be given from several different contexts in the development of symbols through arithmetic, algebra, and calculus, then on to the formalism of axiomatic mathematics. This evidence is taken from a number of research studies recently conducted for doctoral dissertations at the University of Warwick by students from the United States, Malaysia, Cyprus, and Brazil, with data collected in the United States, Malaysia, and the United Kingdom. All the studies form part of a broad investigation into why some students succeed, while others fail. ABSTRACT FROM PUBLISHER]; Copyright of Canadian Journal of Science, Mathematics & Technology Education is the property of Routledge and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)