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Viirman, Olov

Open this publication in new window or tab >>The function concept and university mathematics teaching### Viirman, Olov

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##### Abstract [en]

##### Place, publisher, year, edition, pages

Karlstad: Karlstads universitet, 2014. p. 100
##### Series

Karlstad University Studies, ISSN 1403-8099 ; 2014:12
##### Keywords

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

### Jaworski, Barbara

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##### Supervisors

### Attorps, Iiris

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Available from: 2014-02-27 Created: 2014-02-05 Last updated: 2015-12-29Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Högskolan i Gävle.

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.

Loughborough University, UK.

Högskolan i Gävle.

Open this publication in new window or tab >>The functions of function discourse: University mathematics teaching from a commognitive standpoint### Viirman, Olov

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_some",{id:"formSmash:j_idt204:1:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_otherAuthors",{id:"formSmash:j_idt204:1:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_otherAuthors",multiple:true}); 2014 (English)In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 45, no 4, p. 512-527Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis Group, 2014
##### Keywords

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)
#####

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#####

Available from: 2014-02-27 Created: 2014-02-05 Last updated: 2017-09-28Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.

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.

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### Viirman, Olov

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_some",{id:"formSmash:j_idt204:2:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_otherAuthors",{id:"formSmash:j_idt204:2:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_otherAuthors",multiple:true}); 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, p. 2466-2475Conference 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
#####

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Available from: 2014-02-05 Created: 2014-02-05 Last updated: 2014-03-03Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.

Open this publication in new window or tab >>Discursive practices of two university teachers on the concept of ’linear transformation’### Viirman, Olov

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_some",{id:"formSmash:j_idt204:3:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_otherAuthors",{id:"formSmash:j_idt204:3:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_otherAuthors",multiple:true}); 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, p. 311-320Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

PME, 2011
##### Series

PME Conference Proceedings, ISSN 0771-100X
##### Keywords

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
#####

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Available from: 2014-02-27 Created: 2014-02-05 Last updated: 2016-08-09Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.

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.

Open this publication in new window or tab >>Different views – some Swedish mathematics students’ concept images of the function concept### Viirman, Olov

### Attorps, Iris

### Tossavainen, Timo

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##### Abstract [en]

##### Place, publisher, year, edition, pages

NCM, 2010
##### Keywords

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)
#####

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Available from: 2014-02-27 Created: 2014-02-27 Last updated: 2017-12-05Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.

University of Eastern Finland .

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.