Symbols and the Bifurcation between Procedural and Conceptual Thinking [electronic resource] / David Tall, Eddie Gray and Maselan Bin Ali.

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 presentation, the discontinuities that occur in the learning path taken by different students,...

Full description

Saved in:
Bibliographic Details
Online Access: Full Text (via ERIC)
Main Author: Tall, David Orme
Other Authors: Gray, Eddie, Bin Ali, Maselan, Crowley, Lillie, DeMarois, Phil, McGowen, Mercedes, Pitta, Demetra, Pinto, Marcia, Thomas, Michael, Yusof, Yudariah
Format: Electronic eBook
Language:English
Published: [Place of publication not identified] : Distributed by ERIC Clearinghouse, 2000.
Subjects:

MARC

LEADER 00000nam a22000002u 4500
001 b6123667
003 CoU
005 20080220161337.3
006 m d f
007 cr un
008 000101s2000 xx |||| o ||| | eng d
035 |a (ERIC)ed467354 
040 |a ericd  |c ericd  |d MvI 
099 |f ERIC DOC #  |a ED467354 
100 1 |a Tall, David Orme.  |0 http://id.loc.gov/authorities/names/n81042680  |1 http://isni.org/isni/0000000108580968. 
245 1 0 |a Symbols and the Bifurcation between Procedural and Conceptual Thinking  |h [electronic resource] /  |c David Tall, Eddie Gray and Maselan Bin Ali. 
260 |a [Place of publication not identified] :  |b Distributed by ERIC Clearinghouse,  |c 2000. 
300 |a 27 pages. 
336 |a text  |b txt  |2 rdacontent. 
337 |a computer  |b c  |2 rdamedia. 
338 |a online resource  |b cr  |2 rdacarrier. 
500 |a ERIC Document Number: ED467354. 
500 |a ERIC Note: In: Canadian Journal of Mathematics, Science, and Technology Education, Volume 1, Number 1, 2000.  |5 ericd. 
520 |a 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 presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and procedural thinking, are considered. 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. (Contains 26 references.) (Author/MM) 
650 0 7 |a Algebra.  |2 ericd. 
650 0 7 |a Arithmetic.  |2 ericd. 
650 1 7 |a Concept Formation.  |2 ericd. 
650 1 7 |a Concept Mapping.  |2 ericd. 
650 0 7 |a Elementary Education.  |2 ericd. 
650 0 7 |a Geometry.  |2 ericd. 
650 0 7 |a Mathematics.  |2 ericd. 
650 0 7 |a Mathematics Instruction.  |2 ericd. 
650 1 7 |a Symbols (Mathematics)  |2 ericd. 
700 1 |a Gray, Eddie.  |0 http://id.loc.gov/authorities/names/no2005094533. 
700 1 |a Bin Ali, Maselan. 
700 1 |a Crowley, Lillie. 
700 1 |a DeMarois, Phil.  |0 http://id.loc.gov/authorities/names/n95031603  |1 http://isni.org/isni/0000000031443809. 
700 1 |a McGowen, Mercedes. 
700 1 |a Pitta, Demetra. 
700 1 |a Pinto, Marcia. 
700 1 |a Thomas, Michael.  |0 http://id.loc.gov/authorities/names/n84057244. 
700 1 |a Yusof, Yudariah. 
856 4 0 |u http://files.eric.ed.gov/fulltext/ED467354.pdf  |z Full Text (via ERIC) 
907 |a .b61236676  |b 07-05-22  |c 10-09-10 
998 |a web  |b 10-26-12  |c b  |d m   |e -  |f eng  |g xx   |h 0  |i 1 
907 |a .b61236676  |b 01-06-20  |c 10-09-10 
944 |a MARS - RDA ENRICHED 
907 |a .b61236676  |b 12-30-19  |c 10-09-10 
956 |a ERIC 
948 |a bslw19/20 : dec : ess 
999 f f |i 738028c5-aaa3-5e3e-a91b-666da7d655e6  |s cc835541-7553-55c9-afbf-2b9dd05b1129 
952 f f |p Can circulate  |a University of Colorado Boulder  |b Online  |c Online  |d Online  |e ED467354  |h Other scheme  |i web  |n 1