%0 Journal Article %1 alcock2004csa %A Alcock, Lara %A Simpson, Adrian %D 2004 %I Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@ springer. com; Web site: http://www. springerlink. com. %J Educational Studies in Mathematics %K advanced analysis beliefs convergence definitions grounded learning limit limits mathematical mathematics postviva proof real representations sequences theory thinking visualization %N 1 %P 1-32 %T Convergence of Sequences and Series: Interactions between Visual Reasoning and the Learner %U http://www.springerlink.com/content/p8231k6886243545 %V 57 %X This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore links between the students' mathematical behavior in solving these problems and their perception of their roles as learners. We develop a theory in which the tendency to visualize, coupled with the students' view of their role, can be used to account for their mathematical behavior.

@article{alcock2004csa, abstract = {This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore links between the students' mathematical behavior in solving these problems and their perception of their roles as learners. We develop a theory in which the tendency to visualize, coupled with the students' view of their role, can be used to account for their mathematical behavior.}, added-at = {2008-08-21T14:41:23.000+0200}, author = {Alcock, Lara and Simpson, Adrian}, biburl = {https://www.bibsonomy.org/bibtex/24691381ea82a27763273e81658b8bad5/yish}, interhash = {40f47fed13fb266bb86435433a66fc88}, intrahash = {4691381ea82a27763273e81658b8bad5}, journal = {Educational Studies in Mathematics}, keywords = {advanced analysis beliefs convergence definitions grounded learning limit limits mathematical mathematics postviva proof real representations sequences theory thinking visualization}, number = 1, pages = {1-32}, publisher = {Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@ springer. com; Web site: http://www. springerlink. com.}, timestamp = {2008-08-21T14:41:24.000+0200}, title = {Convergence of Sequences and Series: Interactions between Visual Reasoning and the Learner}, url = {http://www.springerlink.com/content/p8231k6886243545}, volume = 57, year = 2004 }