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Symbols and the bifurcation between procedural and conceptual thinking
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Tall, David, Gray, Edward Martin, Bin Ali, Maselan, Crowley, Lillie, DeMarois, Phil, McGowen, Mercedes, Pitta, Demetra, Pinto, Marcia, Thomas, Michael and Yusof, Yudariah. (2001) Symbols and the bifurcation between procedural and conceptual thinking. Canadian Journal of Science, Mathematics and Technology Education, Vol.1 . pp. 81104. ISSN 14926156

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Abstract
Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to d o mathematical problems and to think about mathematical relationships.
In this presentation 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 is taken from a number of research studies recently performed for doctoral dissertations at the University of Warwick by students from the USA, Malaysia, Cyprus and Brazil, with data collected
in the USA, Malaysia and the United Kingdom. All the studies form part of a broad investigation into why some students succeed yet others fail.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics L Education > L Education (General) 

Divisions:  Faculty of Social Sciences > Institute of Education ( 2013)  
Library of Congress Subject Headings (LCSH):  Signs and symbols, Mathematics  Research, Mathematical ability, Mathematics  Study and teaching  
Journal or Publication Title:  Canadian Journal of Science, Mathematics and Technology Education  
Publisher:  Routledge  
ISSN:  14926156  
Official Date:  2001  
Dates: 


Volume:  Vol.1  
Page Range:  pp. 81104  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Open Access  
References:  Ali, M. b. (1996). Symbolic Manipulation Related to Certain Aspects Such as Interpretations of 
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