%0 Journal Article %1 alcock2005csa %A Alcock, Lara %A Simpson, Adrian %D 2005 %J Educational studies in mathematics %K advanced analysis beliefs convergence definitions learning limit limits mathematical mathematics postviva proof real reasoning representations sequences series symbolic thinking %N 1 %P 77-100 %T Convergence of sequences and series 2: interactions between nonvisual reasoning and the learner's beliefs about their own role %U http://www.springerlink.com/content/r160603466274361 %V 58 %X This paper examines the work of students who, when reasoning about real analysis, do so almost exclusively by means of verbal and algebraic reasoning, and tend not to incorporate visual images into their work. It examines the work of students from two parallel courses of introductory real analysis, whose reasoning ranges from those who introduce definitions appropriately and work with them competently, to those who cannot recall definitions and appear to manipulate notation without regard for its reference. It presents a theory that relates the differences to studentsrsquo expectations regarding their role as learners of mathematics. Throughout, the argument is illustrated with interview data from which the theory was inductively generated.

@article{alcock2005csa, abstract = {This paper examines the work of students who, when reasoning about real analysis, do so almost exclusively by means of verbal and algebraic reasoning, and tend not to incorporate visual images into their work. It examines the work of students from two parallel courses of introductory real analysis, whose reasoning ranges from those who introduce definitions appropriately and work with them competently, to those who cannot recall definitions and appear to manipulate notation without regard for its reference. It presents a theory that relates the differences to studentsrsquo expectations regarding their role as learners of mathematics. Throughout, the argument is illustrated with interview data from which the theory was inductively generated.}, added-at = {2008-08-21T14:47:01.000+0200}, author = {Alcock, Lara and Simpson, Adrian}, biburl = {https://www.bibsonomy.org/bibtex/2fe121d90558b8bb25ee67a717437332a/yish}, interhash = {2cd89c94219deeea72a475ef03dea767}, intrahash = {fe121d90558b8bb25ee67a717437332a}, journal = {Educational studies in mathematics}, keywords = {advanced analysis beliefs convergence definitions learning limit limits mathematical mathematics postviva proof real reasoning representations sequences series symbolic thinking}, number = 1, pages = {77-100}, timestamp = {2008-08-21T14:47:01.000+0200}, title = {Convergence of sequences and series 2: interactions between nonvisual reasoning and the learner's beliefs about their own role}, url = {http://www.springerlink.com/content/r160603466274361}, volume = 58, year = 2005 }