Convergence of Sequences and Series: Interactions between Visual Reasoning and the Learner
L. Alcock, and A. Simpson. Educational Studies in Mathematics, 57 (1):
1-32(2004)
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.
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.
%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
}