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The function concept and university mathematics teaching
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Högskolan i Gävle.
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 [en]
mathematics, university education, commognitive framework, function concept, discourse, teaching
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-31205ISBN: 978-91-7063-543-4 (print)OAI: oai:DiVA.org:kau-31205DiVA: diva2:693890
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
List of papers
1. Different views – some Swedish mathematics students’ concept images of the function concept
Open this publication in new window or tab >>Different views – some Swedish mathematics students’ concept images of the function concept
2010 (English)In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 15, no 4, 5-24 p.Article in journal (Other academic) Published
Abstract [en]

This study analyses what kind of concept images a group of engineering and teacher students have of the function concept, and how these concept images are related to the historical development of this concept. The study was conducted using questionnaires, and 34 students at a Swedish university participated. It is found that the students primarily rely on operational conceptions of the function concept, with only a minority of students possessing structural conceptions. The definitions given by the students mostly resemble an 18th or 19th century view of functions. The study also indicates that the character of the definitions given in the textbooks used by the students affect their concept images.

Place, publisher, year, edition, pages
NCM, 2010
Keyword
mathematics education, function concept, university mathematics, students, concept image
National Category
Pedagogical Work Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-31586 (URN)
Available from: 2014-02-27 Created: 2014-02-27 Last updated: 2017-12-05Bibliographically approved
2. Discursive practices of two university teachers on the concept of ’linear transformation’
Open this publication in new window or tab >>Discursive practices of two university teachers on the concept of ’linear transformation’
2011 (English)In: Developing mathematical thinking: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, PME , 2011, Vol. 4, 311-320 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper reports on an ongoing study focusing on the teaching of functions in undergraduate courses in mathematics at three Swedish universities. In this paper two excerpts of lectures on linear transformations are analysed, using commognitive theory. The two teachers' discursive uses of the terms 'linearity' and 'linear transformation' are described, and potential consequences for student learning are presented. One lecture displays a strong mathematical content while lacking contextualization, while the other is well grounded in everyday experience, but with a lack of attention to mathematical detail potentially detrimental to student learning.

Place, publisher, year, edition, pages
PME, 2011
Series
PME Conference Proceedings, ISSN 0771-100X
Keyword
mathematics education, function concept, university mathematics, teaching, discursive theory, commognition
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-31202 (URN)000343399800040 ()978-975-429-262-6 (ISBN)978-975-429-298-5 (ISBN)
Conference
35th Annual Conference of the International-Group-for-the-Psychology-of-Mathematics-Education (PME), Ankara, Turkey, July 10-15, 2011
Available from: 2014-02-27 Created: 2014-02-05 Last updated: 2016-08-09Bibliographically approved
3. The functions of function discourse: University mathematics teaching from a commognitive standpoint
Open this publication in new window or tab >>The functions of function discourse: University mathematics teaching from a commognitive standpoint
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) Published
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
Keyword
mathematics, university education, commognitive framework, function, discourse, teaching
National Category
Mathematics Pedagogical Work
Research subject
Mathematics; Physical Geography; Physical Geography
Identifiers
urn:nbn:se:kau:diva-31204 (URN)10.1080/0020739X.2013.855328 (DOI)
Available from: 2014-02-27 Created: 2014-02-05 Last updated: 2017-09-28Bibliographically approved
4. Manuscript: A commognitive analysis of the didactical aspects of teachers’ discursive practices in university mathematics lectures
Open this publication in new window or tab >>Manuscript: A commognitive analysis of the didactical aspects of teachers’ discursive practices in university mathematics lectures
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-31196 (URN)
Available from: 2014-02-05 Created: 2014-02-05 Last updated: 2014-02-27Bibliographically approved
5. What we talk about when we talk about functions: Characteristics of the function concept in the discursive practices of three university teachers
Open this publication in new window or tab >>What we talk about when we talk about functions: Characteristics of the function concept in the discursive practices of three university teachers
2013 (English)In: Proceedings of the EightCongress of the European Society for Research in Mathematics Educa / [ed] Behiye Ubuz, Çi ğ dem Haser, Maria Alessandra Mariotti, Middle East Technical University, Ankara, Turkey , 2013, 2466-2475 p.Conference paper, Published paper (Other academic)
Place, publisher, year, edition, pages
Middle East Technical University, Ankara, Turkey, 2013
National Category
Mathematics Pedagogy
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-31197 (URN)978-975-429-315-9 (ISBN)
Conference
Verme 8, 6-10 february 2013, Side/Antalya, Turkey
Available from: 2014-02-05 Created: 2014-02-05 Last updated: 2014-03-03Bibliographically approved

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Citation style
  • apa
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  • Other style
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Language
  • de-DE
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Output format
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