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The functions of function discourse: University mathematics teaching from a commognitive standpoint
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
2014 (English)In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 45, no 4, 512-527 p.Article in journal (Refereed) Epub ahead of print
Abstract [en]

This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions using a discursive approach, the commognitive framework of Sfard. In the paper a categorization of the construction and substantiation routines used by the teachers is presented, for instance various routines for constructing definitions and examples, and for verifying whether an example satisfies a given definition. The findings show that although the overall form of the lectures is similar, with teachers using ‘chalk talk’, and overt student participation limited to asking and answering questions, there are in fact significant differences in the way the teachers present and do mathematics in their lectures. These differences present themselves both on the level of discursive routines and on a more general level in how the process of doing mathematics is made visible in the teachers’ teaching practices. Moreover, I believe that many of the results of the study could be relevant for investigating the teaching of other mathematical topics.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2014. Vol. 45, no 4, 512-527 p.
Keyword [en]
mathematics, university education, commognitive framework, function, discourse, teaching
National Category
Mathematics Pedagogical Work
Research subject
Mathematics; Physical Geography; Physical Geography
Identifiers
URN: urn:nbn:se:kau:diva-31204DOI: 10.1080/0020739X.2013.855328OAI: oai:DiVA.org:kau-31204DiVA: diva2:699308
Available from: 2014-02-27 Created: 2014-02-05 Last updated: 2015-07-29Bibliographically approved
In thesis
1. The function concept and university mathematics teaching
Open this publication in new window or tab >>The function concept and university mathematics teaching
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the teaching of mathematics at university level, with a particular focus on the teaching of the function concept. The main aim of the thesis is describing and analysing the teaching practices of university mathematics teachers regarding the function concept, and how this concept is constituted through these practices. To this end, video recordings of lectures by seven mathematics teachers at three Swedish universities were analysed using a discursive perspective, Sfard’s commognitive framework. The observed teaching was traditional in form, with teachers using “chalk talk” – simultaneously talking and writing on the board. The results show that the teaching practices of the teachers belong to two distinct but intertwined discourses – a mathematical discourse, and a discourse of mathematics teaching. Classifications of important aspects of these discourses are presented, and it is found that the teachers’ discursive practices, while sharing overall form, still display considerable differences. Other results include an analysis of the levels of objectification displayed by the teachers in their discursive constitution of the function concept. The study contributes to a small but growing body of empirical research on university mathematics teaching practice.

Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2014. 100 p.
Series
Karlstad University Studies, ISSN 1403-8099 ; 2014:12
Keyword
mathematics, university education, commognitive framework, function concept, discourse, teaching
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-31205 (URN)978-91-7063-543-4 (ISBN)
Public defence
2014-03-21, 99:133, Hus Freja, Högskolan i Gävle, Gävle, 13:00 (English)
Opponent
Supervisors
Available from: 2014-02-27 Created: 2014-02-05 Last updated: 2015-12-29Bibliographically approved

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