Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series
journal contributionposted on 2011-09-28, 12:12 authored by Alejandro S. Gonzalez-Martin, Elena Nardi, Irene Biza
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.
- Mathematics Education Centre
CitationGONZALEZ-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
Publisher© Taylor and Francis
- AM (Accepted Manuscript)
NotesThis 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