| 1. |
- Viirman, Olov, et al.
(författare)
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Different views – some Swedish mathematics students’ concept images of the function concept
- 2010
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Ingår i: Nordisk matematikkdidaktikk. - Göteborg : NCM. - 1104-2176. ; 15:4, s. 5-24
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 2. |
- Viirman, Olov
(författare)
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The functions of function discourse : University mathematics teaching from a commognitive standpoint
- 2014
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Ingår i: International journal of mathematical education in science and technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211. ; 45:4, s. 512-527
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Viirman, Olov
(författare)
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Discursive practices of two university teachers on the concept of ’linear transformation’
- 2011
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Ingår i: Developing mathematical thinking. - Ankara : PME. - 9789754292626 - 9789754292985 ; , s. 311-320
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 4. |
- Attorps, Iiris
(författare)
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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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| 5. |
- Kellner, Eva, 1961-, et al.
(författare)
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Kollegialt lärande om progression i biologi- och matematikundervisning
- 2014
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Ingår i: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; 41:4, s. 3-8
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Kan man utveckla undervisningen i biologi och matematik samtidigt? Ett lärarlag samarbetade med två forskare för att undersöka och svara på frågan. De undervisningsområden som valdes ut handlar om ekosystem och övergången mellan aritmetik och algebra.
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| 6. |
- Viirman, Olov, 1971-
(författare)
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The function concept and university mathematics teaching
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 7. |
- Bäckman, Kerstin, 1956-
(författare)
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Children's Play as a Starting Point for Teaching Mathematics in Preschool
- 2014
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Ingår i: POEM.
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Konferensbidrag (refereegranskat)abstract
- This presentation contributes to the knowledge about how children learn about and explore mathematics in their everyday activities. Children´s mathematical encounters in play activities give them experiences as a base for education. The understanding of children’s mathematical encounters in play and teachers’ teaching is presented as teachable and learnable moments in ‘here-and-now’ situations. The data used for this study consists of video recordings of young children’s play in four Swedish preschools. In the presentation I use two examples to illustrate and discuss how children’s play can be a starting point for teachers’ teaching. The results display that a teacher’s questions in play can support children’s explorations if the teacher observes, recognizes the mathematical content and asks questions.
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| 8. |
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| 9. |
- Kellner, Eva, et al.
(författare)
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The school–university intersection as a professional learning arena: evaluation of a two-year action research project
- 2020
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Ingår i: Teacher Development. - : Taylor & Francis. - 1366-4530 .- 1747-5120. ; 24:3, s. 366-383
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Tidskriftsartikel (refereegranskat)abstract
- This article presents the evaluation of a two-year action research project in biology and mathematics teaching involving a primary school and a university in Sweden. The aim of the study was to contribute knowledge about a school–university intersection as a professional learning arena. The teachers’ conceptions about the project implementation, the impact on their learning, teaching practices and pupil learning were made explicit by focus group interview. The evaluation revealed that several motivating factors in this specific learning community – the relevance of the project and connection to the continuing education course, mentors from university, planning tools and time for collaboration – were critical for project implementation and for professional learning to occur. Furthermore, it indicated how teacher learning and teaching practices were related to pupil learning in the professional learning community. The results are also discussed in the light of new research on teachers’ work identity and self-reported health.
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| 10. |
- Bäckman, Kerstin, 1956-
(författare)
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Teaching Mathematics in Swedish Preschool - Didactic Situations
- 2014
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Ingår i: 24th EECERA Conference : ‘Us, Them & Me: Universal, Targeted or Individuated Early Childhood Programmes’. ; , s. 94-
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Konferensbidrag (refereegranskat)abstract
- The aim with this paper is to present research about teaching in preschool and the meaning of education in the preschool context within the perspective of quality. More specific the research focus on teaching mathematics and didactical considerations.Teaching mathematics always consists of several components with teacher, children and the mathematical content as three major parts. One of these basic components includes preschool teachers' intentions, choices and actions in which the goal is to create opportunities for children's learning in mathematics. Another component is the children, with their own experiences, intentions and their own choices. A third component is the mathematical content of the teaching situation (Brousseau, 1997). Play is a keyconcept in mathematical activities (Bishop, 1992) and in teaching of a mathematical content (Brousseau, 1997).The research focus is on didactic situations and more specifically the social interaction in teaching so-called didactic contract (Brousseau, 1997). Didactic contract can be understood as the dilemma between the educational goals and the participants’ intentions. A case study illustrates didactic situations in one Swedish preschool.Permissions has been gathered from the parents. The ethical rules for researcher in Sweden have been followed.The findings show the teachers use of play aspects in didactic situations expands the learning opportunities. The didactic contract in teaching give learning opportunities for children. Preschool teachers use of play in didactic situations make the teacher's aware of the mathematical and didactic considerations in relation to context and thereby improve the teaching of mathematical content.
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