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Studying the views of preservice teachers on the concept of function
Kristianstad University College, Department of Mathematics and Science. (LISMA)
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of an overview of the subject, where in particular five papers are put into a frame. The research conducted for the thesis concerns the views of preservice teachers on the concept of function. Preservice teachers’ conceptions of the function concept are in particular examined in relation to mathematical statements that can be related to different topics on a variety of levels in mathematics; in this research, concept mapping technique is a research tool of interest. Questions concerning preservice teachers’ conceptions of the significance of functions in mathematics, and the presence of functions in school mathematics, are also considered relevant aspects of their views of functions. The final part of the research study includes an intervention study regarding the concept of function, located to a calculus course as one of the concluding courses in mathematics on the educational programme.

There is a range of findings from the study that is summarized and further discussed in the overview part of the thesis. One result, is that preservice teachers in their reasoning show signs of knowledge compartmentalization which is an issue of concern in their development of conceptual frameworks rich in meaningful connections. This might have consequences for their abilities to operate in a constructivist environment and reason with their students from different points of view. The function concepts’ large network of relations to other concepts is frequently omitted in the preservice teachers’ reasoning. One reason for this is that to preservice teachers, properties of functions seem to be results of isolated procedures, associated with operational conceptions rather than structural conceptions of functions. The findings imply that preservice teachers should encounter functions in a variety of context, to develop their views of the concept of function – including frameworks rich of meaningful relations – and realize that the concept of function is one of the underlying concepts of mathematics, and an important concept to introduce to their future students. The preservice teachers’ reflections concerning functions in school mathematics contribute to emphasize the significance of the process of transformation of subject matter knowledge to pedagogical content knowledge. Further results of the research study, and an outline of the implications, are included in the concluding discussion of the overview part of the thesis.

The preservice teachers participating in the study are enrolled in a four and a half year teacher preparation program in mathematics and science, grades 4 to 9. The five papers included in the thesis, describe parts of a larger study essentially conducted until the sixth term during the concluding mathematics courses of the program.

Place, publisher, year, edition, pages
Luleå: Department of Mathematics, Luleå University of Technology , 2006. , p. 70
Series
Doctoral thesis / Luleå University of Technology, ISSN 1402-1544 ; 2006:22
National Category
Pedagogy
Identifiers
URN: urn:nbn:se:hkr:diva-6608OAI: oai:DiVA.org:hkr-6608DiVA, id: diva2:319554
Public defence
(English)
Supervisors
Available from: 2010-05-18 Created: 2010-05-18 Last updated: 2010-05-19Bibliographically approved
List of papers
1. Preservice teachers’ conceptions of y=x+5: do they  see a function?
Open this publication in new window or tab >>Preservice teachers’ conceptions of y=x+5: do they  see a function?
2003 (English)In: Proceedings of the 27th Conference of the International  Group for the Psychology of Mathematics Education held jointly with the  25th Conference of PME-NA: vol. 3 / [ed] N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Honolulu: University of Hawaii , 2003, p. 25-32Conference paper, Published paper (Refereed)
Abstract [en]

We are studying two groups of preservice teachers’ conceptions, progression and especially the concept of function in connection to y=x+5 when they are taking a course in algebra or one in calculus in their third and sixth term, respectively, in a teacher preparation program. There is a similar development in that they use to a higher degree a numerical interpretation before the course, which decreases after the course with a growth in linear and functional interpretation with the existence of two variables as a large and rather stable category. The group in their sixth term have a slightly more elaborated language and way of looking at y=x+5 than the group in the third term. For a majority of preservice teachers, in both groups, the concept of function is not evoked in connection to y=x+5.

Place, publisher, year, edition, pages
Honolulu: University of Hawaii, 2003
National Category
Pedagogy
Identifiers
urn:nbn:se:hkr:diva-6377 (URN)
Conference
PME27
Available from: 2010-03-07 Created: 2010-03-07 Last updated: 2010-05-18Bibliographically approved
2. Preservice teachers' views on the concept of function: a study including the utilization of concept maps
Open this publication in new window or tab >>Preservice teachers' views on the concept of function: a study including the utilization of concept maps
2004 (English)Licentiate thesis, monograph (Other academic)
Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2004
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757x ; 2004:49
National Category
Pedagogy Social Sciences
Identifiers
urn:nbn:se:hkr:diva-6025 (URN)
Presentation
(English)
Available from: 2010-02-17 Created: 2010-02-17 Last updated: 2013-07-02Bibliographically approved
3. Preservice teachers' views of y=x+5 and y=πx2 expressed through the utilization of concept maps: a study of the concept of function
Open this publication in new window or tab >>Preservice teachers' views of y=x+5 and y=πx2 expressed through the utilization of concept maps: a study of the concept of function
2005 (English)In: Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education: vol. 3 / [ed] Chick, H L & Vincent, J L, Melbourne: University of Melbourne , 2005, p. 97-104Conference paper, Published paper (Refereed)
Abstract [en]

This paper considers a group of preservice teachers’ construction of concept maps derived from y=x+5 and y=x2 with emphasis on their conceptual understanding of function. The two statements are perceived to represent a number of different concepts with indications of compartmentalized knowledge structures that might prevent the preservice teachers from building rich conceptual structures. The preservice teachers’ view on the concept of function contrasts with a view where the function concept is a unifying concept in mathematics with a large network of relations to other concepts. Different properties and categorizations of functions are less frequently recognized. In the preservice teachers’ response of drawing concept maps there are signs of metacognitive activity.

Place, publisher, year, edition, pages
Melbourne: University of Melbourne, 2005
National Category
Pedagogy
Identifiers
urn:nbn:se:hkr:diva-6027 (URN)
Conference
The 29th Conference of the International Group for the Psychology of Mathematics Education
Available from: 2010-02-17 Created: 2010-02-17 Last updated: 2013-07-02Bibliographically approved
4. Preservice teachers' conceptions of the function concept, its significance in mathematics and presence in school mathematics
Open this publication in new window or tab >>Preservice teachers' conceptions of the function concept, its significance in mathematics and presence in school mathematics
2005 (English)In: Proceedings of NORMA 05, Fourth Nordic Conference on Mathematics Education / [ed] C. Bergsten, B. Grevholm, H. Strømskag Måsøval & F. Rønning, Trondheim, Norway: Tapir Academic Press , 2005, p. 271-285Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Trondheim, Norway: Tapir Academic Press, 2005
National Category
Educational Sciences
Identifiers
urn:nbn:se:hkr:diva-6609 (URN)
Conference
The Fourth Nordic Conference on Mathematics Education
Available from: 2010-05-19 Created: 2010-05-19 Last updated: 2013-08-12Bibliographically approved

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