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Title: Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series
Authors: Gonzalez-Martin, Alejandro S.
Nardi, Elena
Biza, Irene
Keywords: Infinite series
Calculus
Visualization
Conceptual understanding
Tasks
Texts
Theory of registers of semiotic representation
Anthropological framework
Institutional dimension of learning
Post-compulsory education
Issue Date: 2011
Publisher: © Taylor and Francis
Citation: GONZALEZ-MARTIN, A.S., NARDI, E. and BIZA, I., 2011. Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series. International Journal of Mathematical Education in Science and Technology, 42 (5), pp. 565-589
Abstract: The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests.
Description: This article was published in the journal, International Journal of Mathematical Education in Science and Technology [© Taylor and Francis]. The definitive version is available at: http://www.tandfonline.com/doi/abs/10.1080/0020739X.2011.562310
Version: Accepted for publication
DOI: 10.1080/0020739X.2011.562310
URI: https://dspace.lboro.ac.uk/2134/8871
Publisher Link: http://www.tandfonline.com/doi/abs/10.1080/0020739X.2011.562310
ISSN: 0020-739X
Appears in Collections:Published Articles (Mathematics Education Centre)

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