]> BibSonomy publications for /author/Tall http://www.bibsonomy.org/burst/author/Tall BibSonomy BuRST Feed for /author/Tall 2008-08-21T13:29:35+02:00 Knowledge construction and diverging thinking in elementary & advanced mathematics http://www.bibsonomy.org/bibtex/2e89a9909011cb6e12d7d4e4b4dcbbf18/yish yish 2008-05-30T05:46:02+02:00 advanced concepts elementary mathematics mythesis object procepts process product thinking
Knowledge construction and diverging thinking in elementary & advanced mathematics
Eddie Gray and Marcia Pinto and Demetra Pitta and David Tall Educational Studies in Mathematics 38 111-133 (1999)
to advanced concepts elementary mathematics mythesis object procepts process product thinking by yish on 2008-05-30 05:46:02 ]]> Educational Studies in Mathematics1111-133Knowledge construction and diverging thinking in elementary & advanced mathematics381999advanced concepts elementary mathematics mythesis object procepts process product thinking 2008-05-30 05:46:02.0This 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. Constructing different concept images of sequences and limits by programming http://www.bibsonomy.org/bibtex/2b8b457c76c0b838028f27458983addd8/yish yish 2008-05-30T00:59:52+02:00 constructionism ijtme2006 infinity limit mythesis process-product programming sequences
Constructing different concept images of sequences and limits by programming
L. Li and David O. Tall the 17th International Conference for the Psychology of Mathematics Education 41-48 (1993)
to constructionism ijtme2006 infinity limit mythesis process-product programming sequences by yish on 2008-05-30 00:59:52 ]]> Tsukuba, Japan.the 17th International Conference for the Psychology of Mathematics Education41-48Constructing different concept images of sequences and limits by programming21993constructionism ijtme2006 infinity limit mythesis process-product programming sequences 2008-05-30 00:59:52.0As a transition between an informal paradigm in which a limit is seen as a never-ending process and the formal eﾖN paradigm we introduce a programming environment in which a sequence can be defined as a function. The computer paradigm allows the symbol for the term of a sequence to behave either as a process or a mental object (with the computer invisibly carrying out the internal process) allowing it to be viewed as a flexible procept (in the sense of Gray \& Tall, 1991). The limit concept may be investigated by computing s(n) for large n to see if it stabilises to a fixed object. Experimental evidence shows that a sequence is conceived as a certain kind of procept, but the notion of limit remains more at the process level. Deep epistemological obstacles persist, but a platform is laid for a better discussion of formal topics such as cauchy limits and completeness. Descriptions and definitions in the teaching of elementary calculus http://www.bibsonomy.org/bibtex/26b56d9e8a39f0a3c2f987f5dd5082344/yish yish 2008-05-28T03:34:20+02:00 AMT calculus learning limit mathematics mythesis teaching
Descriptions and definitions in the teaching of elementary calculus
Victor Giraldo and Luiz Mariano Carvalho and David Tall Proceedings of the 27 thAnnual Conference of the International Group for the Psychology of Mathematics Education 445-452 (2003)
to AMT calculus learning limit mathematics mythesis teaching by yish on 2008-05-28 03:34:20 ]]> Proceedings of the 27 thAnnual Conference of the International Group for the Psychology of Mathematics Education445-452Descriptions and definitions in the teaching of elementary calculus2003AMT calculus learning limit mathematics mythesis teaching 2008-05-28 03:34:20.0In this paper, we discuss the (potentially positive) pedagogical role of intrinsic limitations of computational descriptions for mathematical concepts, with special focus on the concept of derivative. Our claim is that, in a suitable approach, those limitations can act for the enrichment of learners’ concept images. We report a case study with a first year undergraduate student and place this in a broader empirical and theoretical context. On projection operator method in statistical mechanics; derivation of the Balescu-Lenard master equation Physica Ahttp://www.bibsonomy.org/bibtex/2cb147df6b53d8f322e1e5615ac46f206/smicha smicha 2008-04-22T10:36:30+02:00 Statistical mechanics
On projection operator method in statistical mechanics; derivation of the Balescu-Lenard master equation
Moustapha Sadibou Tall and Maurice Ndeye and Di{\`e}ne Ndiaye and Christian Sina Diatta and Ismaila Diedhiou Physica A: Statistical and Theoretical Physics 333 168--182 (2004)
to Statistical mechanics by smicha on 2008-04-22 10:36:30 ]]> Physica A: Statistical and Theoretical PhysicsFeb168--182On projection operator method in statistical mechanics; derivation of the Balescu-Lenard master equation3332004Statistical mechanics 152008-04-22 10:36:30.0 Advanced Mathematical Thinking http://www.bibsonomy.org/bibtex/24fb79694d7d47ea8e3a1439d76d53f2d/rmosvold rmosvold 2007-04-02T20:40:05+02:00 mathematics thinking
Advanced Mathematical Thinking
D.O. Tall (1991)
to mathematics thinking by rmosvold on 2007-04-02 20:40:05 ]]> Advanced Mathematical Thinking1991mathematics thinking 2007-04-02 20:40:05.0 Compact spaces, elementary submodels, and the countable chain condition. dblphttp://www.bibsonomy.org/bibtex/261de838f9e88b2f195ce53caa1f4a58b/dblp dblp 2007-02-27T00:00:00+01:00 dblp
Compact spaces, elementary submodels, and the countable chain condition.
Lúcia R. Junqueira and Paul Larson and Franklin D. Tall Ann. Pure Appl. Logic 144 107-116 (2006)
to dblp by dblp on 2007-02-27 00:00:00 ]]> Ann. Pure Appl. Logic1-3107-116Compact spaces, elementary submodels, and the countable chain condition.1442006dblp 2007-02-27 00:00:00.0 Algebra, Symbols, and Translation of Meaning http://www.bibsonomy.org/bibtex/222894e18582331a31bb08c14ade87445/yish yish 2006-09-19T02:44:52+02:00 algebra equals gmx ijceell06 narrative notation procepts representation
Algebra, Symbols, and Translation of Meaning
Lillie Crowley and Michael Thomas and David Tall Proceedings of the 18th International Conference for the Psychology of Mathematics Education (PME) 240--247 (1994)
to algebra equals gmx ijceell06 narrative notation procepts representation by yish on 2006-09-19 02:44:52 ]]> Proceedings of the 18th International Conference for the Psychology of Mathematics Education (PME)240--247Algebra, Symbols, and Translation of MeaningII1994algebra equals gmx ijceell06 narrative notation procepts representation 2006-09-19 02:44:52.0 Limits http://www.bibsonomy.org/bibtex/24d07c55a77a0cdd4f2f532968905371a/yish yish 2006-03-07T17:56:12+01:00 bibtex-import ijtme2006 infinity limit misconceptions mythesis process-product
Limits
B. Cornu Advanced Mathematical Thinking 153--166 (1991)
to bibtex-import ijtme2006 infinity limit misconceptions mythesis process-product by yish on 2006-03-07 17:56:12 ]]> DordrechtAdvanced Mathematical Thinking153--166Limits1991bibtex-import ijtme2006 infinity limit misconceptions mythesis process-product 2006-03-07 17:56:12.0 Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept http://www.bibsonomy.org/bibtex/259b376c8d028dee712b2ce55f36f3c78/yish yish 2006-03-07T17:56:12+01:00 ch2 ijtme2006 mythesis procept symbols
Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept
David Tall and Eddie Gray Mathematics Teaching 142 6--10 (1993)
to ch2 ijtme2006 mythesis procept symbols by yish on 2006-03-07 17:56:12 ]]> Mathematics Teaching6--10Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept1421993ch2 ijtme2006 mythesis procept symbols 2006-03-07 17:56:12.0Mathematics is an enigmatic subject in which a few succeed with disarming ease, whilst others seem doomed to failure. After analysing the responses of many children performing simple tasks in arithmetic, we find a phenomenon occurring which suggests a reason for this catastrophic divergence in performance. Quite simply we find that those who fail are doing a more difficult kind of mathematics compared to those who succeed. This difference arises out of the manner in which individuals cope with the progression from procedures of counting to the processes of arithmetic and the concept of number. Whilst the more able progress to use their knowledge in a flexible and powerful way, the less able seek security in counting procedures which work promisingly in simple tasks but fail to generalise when greater sophistication is required (Gray 1991). Conflicts in the Learning of Real Numbers and Limits http://www.bibsonomy.org/bibtex/286ac87394f5a3b7579c012c67f1b4d0b/yish yish 2006-03-07T17:56:12+01:00 as_conv convergence ijtme2006 limit mythesis
Conflicts in the Learning of Real Numbers and Limits
David O. Tall and Rolph L. E. Schwarzenberger Mathematics Teaching 82 44--49 (1978)
to as_conv convergence ijtme2006 limit mythesis by yish on 2006-03-07 17:56:12 ]]> Mathematics Teaching44--49Conflicts in the Learning of Real Numbers and Limits821978as_conv convergence ijtme2006 limit mythesis 2006-03-07 17:56:12.0