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dc.contributor.authorGray, Eddie M.en
dc.contributor.authorPinto, Marciaen
dc.contributor.authorPitta-Pantazi, Demetraen
dc.contributor.authorTall, Daviden
dc.creatorGray, Eddie M.en
dc.creatorPinto, Marciaen
dc.creatorPitta-Pantazi, Demetraen
dc.creatorTall, Daviden
dc.date.accessioned2017-07-27T10:42:19Z
dc.date.available2017-07-27T10:42:19Z
dc.date.issued1999
dc.identifier.urihttps://gnosis.library.ucy.ac.cy/handle/7/38041
dc.description.abstractThis paper begins by considering the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum. We base our theoretical development on fundamental cognitive activities, namely, perception of the world, action upon it and reflection on both perception and action. We see an emphasis on one or more of these activities leading not only to different kinds of mathematics, but also to a spectrum of success and failure depending on the nature of the focus in the individual activity. For instance, geometry builds from the fundamental perception of figures and their shape, supported by action and reflection to move from practical measurement to theoretical deduction and euclidean proof. Arithmetic, on the other hand, initially focuses on the action of counting and later changes focus to the use of symbols for both the process of counting and the concept of number. The evidence that we draw together from a number of studies on children's arithmetic shows a divergence in performance. The less successful seem to focus more on perceptions of their physical activities than on the flexible use of symbol as process and concept appropriate for a conceptual development in arithmetic and algebra. Advanced mathematical thinking introduces a new feature in which concept definitions are formulated and formal concepts are constructed by deduction. We show how students cope with the transition to advanced mathematical thinking in different ways leading once more to a diverging spectrum of success. © 1999 Kluwer Academic Publishers.en
dc.sourceEducational Studies in Mathematicsen
dc.source.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-17444404993&partnerID=40&md5=e508d8f42ea5d213b7bf0ae2c6c441e7
dc.titleKnowledge construction and diverging thinking in elementary & advanced mathematicsen
dc.typeinfo:eu-repo/semantics/article
dc.identifier.doi10.1023/A:1003640204118
dc.description.volume38
dc.description.issue01-Maren
dc.description.startingpage111
dc.description.endingpage133
dc.author.facultyΣχολή Κοινωνικών Επιστημών και Επιστημών Αγωγής / Faculty of Social Sciences and Education
dc.author.departmentΤμήμα Επιστημών της Αγωγής / Department of Education
dc.type.uhtypeArticleen
dc.description.notesCited By :34en
dc.source.abbreviationEduc.Stud.Math.
dc.source.otherScopus
dc.contributor.orcidPitta-Pantazi, Demetra [0000-0002-9580-5674]


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