%0 Journal Article %1 mamonadowns2001lib %A Mamona-Downs, Joanna %D 2001 %J Educational Studies in Mathematics %K definition dynamic formal graph image intuition learning limit mathematics meaning postviva sequences %P 259-288 %T Letting the Intuitive Bear on the Formal; A Didactical Approach for the Understanding of the Limit of a Sequence %U http://www.springerlink.com/content/57upglde04ekw29l/ %V 48 %X This theoretical paper provides: (1) a presentation of some tasks that maybe regarded as typical sources for forming students' intuitions and first understandings about limiting processes of real sequences, (2) an analysis of the formal definition of limit via identifying roles for each symbol that occurs to achieve a mental image firmly consonant with the definition, and (3) a description of how this mental imagery may be used to re-examine the validity of some intuitive beliefs. In particular a persistent issue found in (1) is that the sources encourage an intuitive image of a sequence as having an ultimate term associated with the limit; it is this belief that is mostly discussed in (3).

@article{mamonadowns2001lib, abstract = {This theoretical paper provides: (1) a presentation of some tasks that maybe regarded as typical sources for forming students' intuitions and first understandings about limiting processes of real sequences, (2) an analysis of the formal definition of limit via identifying roles for each symbol that occurs to achieve a mental image firmly consonant with the definition, and (3) a description of how this mental imagery may be used to re-examine the validity of some intuitive beliefs. In particular a persistent issue found in (1) is that the sources encourage an intuitive image of a sequence as having an ultimate term associated with the limit; it is this belief that is mostly discussed in (3).}, added-at = {2008-08-21T13:38:22.000+0200}, author = {Mamona-Downs, Joanna}, biburl = {https://www.bibsonomy.org/bibtex/28a4e33c462c2cc5eec0beb790d1dfc85/yish}, interhash = {4b3c6d586f8c4ee04538cd5cf01da7c6}, intrahash = {8a4e33c462c2cc5eec0beb790d1dfc85}, journal = {Educational Studies in Mathematics}, keywords = {definition dynamic formal graph image intuition learning limit mathematics meaning postviva sequences}, pages = {259-288}, timestamp = {2008-08-21T13:38:22.000+0200}, title = {Letting the Intuitive Bear on the Formal; A Didactical Approach for the Understanding of the Limit of a Sequence}, url = {http://www.springerlink.com/content/57upglde04ekw29l/}, volume = 48, year = 2001 }