| 11. |
- Attorps, Iiris
(författare)
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Definitions and Problem Solving : Problem Solving in Mathematics Education Proceedings of the ProMath meeting June 30- July 2, 2004 in Lahti, Finland
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this article student teachers’ conceptions of equations are discussed. Data was gathered from 75 student teachers by interviews and questionnaires. Both the quantitative and qualitative research methods were applied in the study. The research results indicate that some specific examples of concepts, which at first appear in teaching, and learning of mathematics are more central to the student teachers than other examples. The former examples are often called prototypes. The investigation shows that students tend to identify the concept equation with one of the prototypical examples and that the concept image develops from one unique prototypical example to include more examples of increasing distance from the prototypical example. The results also indicate that the student teachers’ concept images include erroneous conceptions of the concept equation.
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| 12. |
- Attorps, Iiris, 1955-, et al.
(författare)
-
Erfarenheter av ”Learning Studies” som ett pedagogiskt verktyg i skola och högskola
- 2010
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Ingår i: Toisensa kohtaavat ainedidaktiikat [Möte med ämnesdidaktik]. - Tampere : Juvenes Print. ; , s. 25-33
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Konferensbidrag (refereegranskat)abstract
- I detta dokument diskuterar vi pågående projekt i matematikdidaktik vid Högskolan i Gävle. Syftet med projektet är att utveckla och testa metoder för att förbättra lärande i matematik från förskolan till universitetsnivån. Dessutom är syftet att utveckla en forskningsmiljö för lärande i matematik som kan fungera som en plattform för att utveckla lärarnas kompetens i matematik. Den övergripande forskningsfrågan är: Hur påverkar lärarens sätt att hantera lärandeobjekt (t.ex. funktionsbegrepp, integralbegrepp etc.) i klassrummet elevens/studentens lärande? Vilka är de kritiska aspekterna för studenternas lärande? Som ett teoretiskt ramverk använder vi Learning Study modellen designad av Marton et al. (2004). Modellen bygger på variationsteorin (Marton et al. 2004), som härrör från den fenomenografiska forskningstraditionen och som introducerades i Sverige under senare delen av 1960-talet och i början av 1970-talet. Resultaten av studierna antyder bl.a. att det är betydligt enklare att hitta olika typer av konkreta men användbara representationer av lärandeobjektet i undervisningen av den elementära matematiken jämfört med undervisningen av den högre matematiken. Troligen beror det på att universitetsmatematik är mer abstrakt och bygger på den tidigare erhållna kunskapen.
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| 13. |
- Attorps, Iiris, et al.
(författare)
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Ett helhetsgrepp för likvärdig skola
- 2021
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Ingår i: Nämnaren. - Göteborg. - 0348-2723. ; :3, s. 35-39
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Tidskriftsartikel (populärvet., debatt m.m.)
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| 14. |
- Attorps, Iiris, et al.
(författare)
-
Generating the patterns of variation with GeoGebra : the case of polynomial approximations
- 2016
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Ingår i: International Journal of Mathematical Education in Science and Technology. - 0020-739X .- 1464-5211. ; 47:1, s. 45-57
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students’ learning opportunities in the study group compared with the control group.
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| 15. |
- Attorps, Iiris, 1955-, et al.
(författare)
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Improving undergraduate mathematics teaching
- 2010
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Ingår i: The proceedings of MADIF7; The 7th Swedish Mathematics Education Research Seminar, Stockholm, January 26-27, 2010..
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Konferensbidrag (refereegranskat)
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| 16. |
- Attorps, Iiris, 1955-, et al.
(författare)
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Is there always truth in equation?
- 2009
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Ingår i: Nordic Research in Mathematics Education. Proceedings from NORMA 08. - Rotterdam : Sense Publishers. ; , s. 143-149
-
Konferensbidrag (refereegranskat)abstract
- In this study we analyse conceptions that prospective teachers in mathematics have about equations and how these conceptions are related to the truth value (of mathematical statements). Our phenomenographic research reveals that there exists a large variety of fundamentally different conceptions about equations and that in students’ actual concept image of equation it is commonly assumed that a mathematical expression must possess the truth value ‘true’ in order to be an equation in spite of the fact that any consideration related to the truth value only rarely appears in concept definitions given by students.
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| 17. |
- Attorps, Iiris, et al.
(författare)
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Is there equality in equation?
- 2007
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Ingår i: European research in mathematics education 5.
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Konferensbidrag (refereegranskat)
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| 18. |
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| 19. |
- Attorps, Iiris
(författare)
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Mathematics teachers' conceptions about concept learning in algebra
- 2007
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Ingår i: Current state of research on mathematical beliefs XII. - Helsinki : University of Helsinki. - 9789521038587
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In this article I discuss the mathematics teachers’ conceptions about concept learning in algebra from school and university time. The study has a focus on the particular topic of equations. The data was gathered by interviews and questionnaires. Both newly graduated and experienced secondary school teachers were participated in this study. The phenomenographic research method in order to analyse research outcomes was applied in the investigation. The research results indicated that the teachers experience the learning of equations from school and university time on four qualitatively different ways. Learning was apprehended as doing routine problems, as memorizing and reproduction of rules and models, as doing applications and as interaction with other students.
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| 20. |
- Attorps, Iiris
(författare)
-
Mathematics teachers' conceptions about equations
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The aim of this study is to describe and to clarify the mathematics teachers’ subject matter and pedagogical content conceptions about equations. As the basis of these conceptions, the teachers’ experiences of the concept learning of equations from their own school time are described. The early research of conceptions has been concentrated on pupils’ conceptions of the topic as a contrast to scientific conceptions since the middle of the 1970s. Research of teachers’ conceptions of mathematics and mathematics teaching and learning has grown during the last decade. However, in these studies teachers’ conceptions of a specific content area in mathematics have not been investigated. In the theoretical background of the research, different traditions of school mathematics learning and teaching are treated. By using theories of experiential learning, it has been possible to study such learning situations and experiences, which may lead to the development of subjective conceptions of mathematical concepts. In order to understand difficulties concerning the concept formation in mathematics the theory of the concept image and the concept definition as well as the theory based on the duality of mathematical concepts have been studied. The acquired experiences from school time seem to lay the basis of both the teachers’ subject matter and pedagogical content-specific conceptions and decisions. Different components in teacher knowledge base together with current research both in teachers’ subject matter and pedagogical content knowledge are therefore presented at the end of the theoretical framework. By combining different kinds of methods like questionnaires, recorded interviews, videotape recording of six lessons in mathematics and observations the research empirical material was collected. In this investigation, five novice, five expert and 75 student teachers in mathematics participated. The preliminary investigation included 30 student teachers. In the study the phenomenographic approach is used in order to reveal differences between the teachers’ conceptions and experiences about equations. The research results indicate that equations are not apprehended as complete, static objects. Conceptions about equations reveal that equations are closely related to the symbols x and y and solving procedures. The teachers’ experiences of learning and teaching of mathematics may have formed their conceptions. The conceptions about equations seem to be based on the teachers’ experiences in arithmetic and their first impressions of learning the process of solving equations. The teachers apprehend equation teaching as a study of procedures rather than as a study of central ideas and concepts of algebra. Both aspects are however equally important at compulsory school, since the teaching of algebra should develop pupils’ ability both to use and to understand the basic algebraic concepts. Some of the teachers do not have a clear conception what the pupils should attain in algebra at compulsory school according to the specific goals in Swedish mathematics curriculum. The research results further show that both the expert and the novice teachers have various apprehensions of the pupils’ difficulties concerning equations.
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