%0 Journal Article %1 Tall93 %A Tall, David %A Gray, Eddie %D 1993 %J Mathematics Teaching %K ch2 ijtme2006 mythesis procept symbols %P 6--10 %T Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept %V 142 %X Mathematics 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).

@article{Tall93, abstract = {Mathematics 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).}, added-at = {2006-03-07T17:56:12.000+0100}, author = {Tall, David and Gray, Eddie}, biburl = {https://www.bibsonomy.org/bibtex/259b376c8d028dee712b2ce55f36f3c78/yish}, citeulike-article-id = {532469}, comment = {"We define a procept to be a combined mental object consisting of a process, a concept produced by that process, and a symbol which may be used to denote either or both"}, interhash = {3a1606bce6483221f40f98042690ce43}, intrahash = {59b376c8d028dee712b2ce55f36f3c78}, journal = {Mathematics Teaching}, keywords = {ch2 ijtme2006 mythesis procept symbols}, pages = {6--10}, priority = {2}, timestamp = {2008-05-02T13:22:50.000+0200}, title = {Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept}, volume = 142, year = 1993 }