| 1. |
- Björklund, Camilla, et al.
(author)
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Matematikkundervisning
- 2013
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Book (other academic/artistic)abstract
- Denna boken är skriven av en grupp erfarna norska och svenska lärarutbildare i matematik. Boken bygger på utprövad erfarenhet - såväl egen som andras - och på aktuell, relevant forskning i matematikdidaktik. Texten väver samman matematik och matematikdidaktik, det vill säga ämnet som det undervisas i och frågor om hur ämnet kan läras och undervisas. Boken innehåller det som är absolut viktigast att få med sig i den grundläggande lärarutbildningen i matmatik.
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| 2. |
- Grevholm, Barbro, et al.
(author)
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Lära och undervisa matematik : från förskoleklass till åk 6
- 2012
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Book (other academic/artistic)abstract
- Lära och undervisa matematik - från förskoleklass till åk 6 är en grundbok i matematik och matematikämnets didaktik. Den vänder sig till lärarstuderande och till verksamma lärare som vill aktualisera sina kunskaper och ta del av den senaste forskningen samt sätta sig in i de nya kursplanerna och kunskapskraven i matematik.
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| 3. |
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| 4. |
- Danielsson, Helena, et al.
(author)
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Multimodal mathematical context and video as a tool for teachers´assessment
- 2015
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Conference paper (peer-reviewed)abstract
- Multimodal mathematical context And video as a tool for teachers´ assessment Helena Danielsson, PhD, Associate professor Art and media education - hdn@du.se Eva Taflin, PhD, Senior Lecturer Mathematics education - evat@du.seDalarna UniversityThis presentation will discuss some experiences from a four year school research study. The aim of our research was to examine teachers develop when they were part of collaborative discussions based on video recordings and video edited material from specific lessons in their own practice. Our study had two focus; one was to investigate methods and tools that teachers can use to develop their ability in assessment when their students where working with multimodal tasks and the other was to examine how video can be used by teachers wanting to obtain knowledge about assessing.Our study is based on several theories about when teachers collaborate to create new knowledge. The first is the design theoretical approach – where visual ethnography and a semiotic approach contribute to problematize the use and mixture of different modes. A basic assumption of the framework here is that meanings are made and communicated in mathematics through a wide range of semiotic modes. By using video as an essential tool in our research our framework theories concerning visual ethnography, video documentation and individuals as reflective practitioners are also needed.We will choose to highlight some findings that concern the following themes: The use of tasks for assessment, The collaborative talk, The equipment, Ethical dilemmas. Most common was one choice of esthetical mode at a time (combined with written and verbal text), but there were also lessons with mixtures such as stations with different activities. Collaborative talks were evaluated as a meaningful way of sharing knowledge, and the video tool for this, although it raised important ethical discussions. Working with the assessment framework was of great interest to the teachers but it took a lot of time from their ordinary work. In this way the project highlighted more general aspects of school development.The relevance to Nordic educational research also concerns teachers´ use of collaborative talks in assessment work, multimodal tasks in mathematics and video as a research tool in general.
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| 5. |
- Danielsson, Helena, et al.
(author)
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Multimodal mathematical context and video as a tool for teachers´assessment
- 2014
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In: Conference proceedings - 4th international Designs for Learning conference 6-9th May 2014.
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Conference paper (other academic/artistic)abstract
- Project aims and research questionsThis presentation will discuss some experiences from a three year school research study now in its’ final stage. The aim of our research is to examine what kinds of knowledge teachers develop when they are part of collaborative discussions based on video recordings and video edited material from specific lessons in their own practice. Theses specific lessons are designed with multimodal mathematical tasks and students work in a multimodal process. The project has been formulated in close collaboration between teachers, other community representatives and us as researchers. Our study has two focus; one is to investigate methods and tools that teachers can use to develop their ability in assessment when their students are working with multimodal tasks and the other is to examine how video can be used by teachers wanting to obtain knowledge about assessing “creative and aesthetics learning processes” (Skolverket, 2011).The research questions are: How can teachers and pupils assess mathematics abilities shown through creative and esthetic learning processes? How can video be used as a method to contribute to teacher professional development regarding formative and summative assessment? What kind of tools do teachers believe they need in order to assess pupils knowledge in multimodal processes?A part of the study is (together with the teachers) to construct a matrix for assessment of students´ mathematical abilities. The matrices that are created are meant to be adapted to a completed lesson which was characterized by a multimodal task, a task in which not only the spoken or written word is important but also activities and interactions by way of documents, glances and gestures. The multimodal task might accommodate various forms of work – such as laboratory activities with different materials. The matrices that are created within the project framework are planned to be adapted for use by both teachers and students.Theoretical frameworkOur study is based on several theories about when teachers collaborate to create new knowledge (Carlgren 2012). The first is the design theoretical approach – where visual ethnography and a semiotic approach contribute to problematize the use and mixture of different modes. Other theories that are relevant for the study are Jaworskijs (1991) Teaching Triad as developed into inquiry and development of the teachers´ competence, along with Cobbs Design Theory (2000), where the specific mathematics is identified in the school discourse. The design theories expressed in different texts are used, e.g. by Kress & Van Leeuwen (2001); Kress (2010); Selander & Kress (2010), and concerning the discourse work and by Jewitt (2011; 2012) more explicit for the analyze workThe epistemological view we represent is inspired by Vygotsky´s (1978) theory of ZDP and cultural aspects in communication. The study uses sociocultural theory as described by Säljö (2005; 2012). By using multimodal tasks we presume that multimodal tasks contribute toa more qualifiedlearning in which students candevelop theirown explanations, solve problems withdifferentstrategies dispute and present mathematical arguments, discussand comparesolutionspresentedbyvariousforms of representation (Taflin 2007). Previous studies (e.g. Danielsson 2002; Öhman Gullberg 2006; Leijon 2010) have shown that different modalities of “production forms” and media reception may even influence theexperienceofauthenticityand ownershipin a different waythan traditionalschoolwork. A basic assumption of the framework here is therefor that meanings are made and communicated in mathematics through a wide range of semiotic modes (Jewitt 2011; Machin 2011).By using video as an essential tool in our research our framework theories concerning visual ethnography, video documentation and individuals as reflective practitioners are also needed. Appropriate theories are taken from Aull Davies (2008); Pink (2012); Schön (1991); Spencer (2011) and also from Heikkilä & Sahlström (2003).From (audio-)visual cultural theories we are inspired by Wingstedt (2012) who speak ofmultimodalityfor exponential growthofunderstanding.MethodsThe study has been conducted in two steps. First a prestudy over one year, where two primary schools participated (focus on four classes; grade 5 and grade 9). Knowledge gained from the prestudy was used in a more extended study and during the two last years we have had contact with teachers from different schools and levels in four municipalities. With the exception of two researchers we have a group of class teachers from grade 1 to grade 9 participating (about 15 regularly active, while others have been participating at some elected occasions). Two headmasters, two doctorial students and a film maker are also connected to the project. Data collection has been made by both us as researchers, by the teacher themselves and by a professional film maker. In order to learn more about video as a tool we wanted to experiment with different kinds of video equipment in order to examine their functionality for use in a school context. The participating teachers were allowed to use different models but could also choose to use other techniques such as audio recording, photographs, scanning or material copying. Furthermore, they were offered to let students try these it, as part of developing self-assessment and peer assessment. All multimodal tasks in the math lessons were prepared and organized by the teachers themselves. In their second lesson they decided to sometimes try similar ones – in order to develop comparable material, perhaps useful for the matrix discussion. The teachers´ ambition was to design tasks to see if and how they could work to support teachers' assessment of pupils' skills. The researchers empiric data collection, however, both in the prestudy and the second phase of the main study, followed by the same order; Information and presentation sessions in all places and classes. Filming of lessons. After that the film maker edited the material into shorter parts. The edited excerpts were used in a situation of stimulated recall. At this occasion both teachers, colleagues and researchers took part in a video recorded collaborative talk for analysis session (using two cameras). This process was repeated in altogether seven seminars. The video recordings from the seven meetings along with photographs and audio recordings were presented later on at a summing up meeting, where all the main participants took part.We are currently in the process of preparing survey questions, addressed to the teachers, for the final data collection. Some findingsAs the final results not yet complete, we have chosen to highlight some findings that we consider of interest to discuss and reflections upon. They concern the following themes: The framework for assessment, Editing concerns, The equipment, ethical dilemmas.Framework for assessment: Quite early in the project the teachers at one of the schools made a framework (matrix) in order to test it for assessment in maths – and made it available for use by other teachers in the project (that meant that four different municipalities were able to test it). These frameworks were made from the point of view that the multimodal tasks were designed as a “creative and esthetical learning process”. Interesting here was that the teachers also active in the first grades in school also tried parts of this advanced models. In the project matrices constructed for art education also played a role in maths.Editing concerns: The edited video material was critical in the analyse process. Through the edited film teachers were reminded about moments in the lesson – they saw or heard details that could give a more complete picture of the lesson.The equipment: The qualities of video cameras of different sizes were discussed a lot. One finding was that sound was sometimes more important than the pictures. In some classes the teachers preferred to use only sound recording in order to be more discrete. In other classes mainly stills were used and copies made of pupils work.Ethical dilemmas: The use of video recording, stills or sound material raised unexpected ethical issues. In some schools there were immigrant children with protected identities. Other classes contained students with neurological diagnoses. The parents of these children were hesitant to letting their children be filmed. How could we as researchers handle this? The ethic council at our university expressed doubts about the use of video at all while observing children in a school context. Is this attitude similar in other countries, other university councils? We live in a society where the use and presence of digital resources is increasing, but authorities views here might raise limitations to the use of video as a visual research method. The task, in our opinion, must be to learn how to handle this, not to avoid it. Our studies give an insight into information that can be used to increase this ability.In summary all the teachers formulated their personal designed tasks in order to test different modes. Most common was one choice of esthetical mode at a time (combined with written and verbal text), but there were also lessons with mixtures such as stations with different activities. Teachers commented that the reflection time at the end of lessons became of great importance to sum up questions around the pupils individual learning processes - something they partly developed and stressed more after watching the film excerpts.Working with the assessment framework was of great interest to the teachers but it took a lot of time from their ordinary work, and in some cases the teachers received no support from their headmaster. In this way the project highlighted more general aspects of school development.
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| 6. |
- Danielsson, Helena, et al.
(author)
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Rapport från projektet Multimodala uppgifter och bedömning i matematik : Video och kollaborativa samtal som metod vid lärares bedömning av elevers matematiska kunskaper
- 2015
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Reports (other academic/artistic)abstract
- This research will discuss some experiences from a four year school research study. It was conducted in cooperation with teachers from four municipalities in Dalarna. The aim of the research was to examine teachers´ professional development when they participated in collaborative discussions based on video recordings and video edited material from specific lessons in their own practice. The study had two foci one was to investigate methods and tools that teachers can use to develop their ability to assess their students while working on multimodal tasks. The other was to examine how video can be used by teachers wanting to obtain knowledge about assessing students. The study is based on several theories about when teachers collaborate to create new knowledge. The first is the design theoretical approach – where visual ethnography and a semiotic approach contribute to problematize the use and mixture of different modes. A basic assumption of the framework here is that meanings are made and communicated in mathematics through a wide range of semiotic modes. By using video as an essential tool in the research the framework theories concerning visual ethnography, video documentation and individuals as reflective practitioners were also needed. The findings can be divided into the following themes: the use of tasks for assessment, collaborative discussion, equipment, ethical dilemmas. Collaborative discussions were evaluated as a meaningful way of sharing knowledge. The use of video recordings in association with these discussions raised important ethical issues. Working with the assessment framework was of great interest to the teachers but it took a lot of time from their ordinary work. In this way the project highlighted more general aspects of school development. The research also concerns teachers´ use of collaborative discussions in assessment work, multimodal tasks in mathematics and video as a research tool in general.
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| 7. |
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| 8. |
- Dimenäs, Jörgen, et al.
(author)
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Teaching in action: A model to understand the complexity of teachers' decisions in teaching mathematics
- 2018
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In: International Journal of Advanced Research in Education and Literature. - 2208-2441. ; 4:1, s. 10-24
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Journal article (peer-reviewed)abstract
- In this article, we focus on the teaching of mathematics in classrooms. The aim of the present study is to create, describe and test a model for teachers' decisions in action when teaching mathematics. We focused on the classroom as a very complex environment and videotaped three excellent teachers teaching mathematics. An inductive iterative research process was selected to generate theory and conclusions directly rooted in data. The model was tested in different teacher groups, and the categories changed and analyses proceeded. The model relates to Jaworski´s (1992), theory the “teaching triad”. By using the developed model “teaching in action” it is possible to analyze and describe teaching in mathematics classrooms and find examples of teachers’ decisions in action. The model “teaching in action” show the complexity of teachers’ work.
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| 9. |
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| 10. |
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| 11. |
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| 12. |
- Nyman, Rimma, et al.
(author)
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Rika lösningar på rika problem : att dela smörgåsar
- 2016
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In: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; 199:3, s. 21-24
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Journal article (pop. science, debate, etc.)abstract
- I tre artiklar med början i denna vill vi ta upp erfarenheter från att ha arbetat med rika matematiska problem. Först ut är vår beskrivning av hur vi engagerade lärare, lärarstudenter och deras elever i problemet Att dela smörgåsar.
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| 13. |
- Nyman, Rimma, et al.
(author)
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Rika lösningar på rika problem : att välja glasskulor
- 2018
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In: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; 45:1, s. 9-12
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Journal article (pop. science, debate, etc.)abstract
- I en serie av tre artiklar tar vi upp erfarenheter från arbete med rika matematiska problem. I den förra artikeln presenterade vi problemet Att dela smörgåsar. I denna andra del har vi valt en enkel variant av ett klassiskt kombinatorikproblem i en elevnära kontext. Vi har samlat in lösningar från elever i årskurs 2–3 och synliggör olika uttrycksformer.
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| 14. |
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| 15. |
- Nyman, Rimma, 1983, et al.
(author)
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Rika lösningar på rika problem: Att välja glasskulor
- 2018
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In: Nämnaren. ; 2018:1, s. 9-12
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Journal article (other academic/artistic)abstract
- I denna artikel presenterar vi problemet Att dela smörgåsar, ett klassiskt kombinatorikproblem i en elevnäsa kontext. Vi har samlat in lösningar från elever i åk 2-3 och synliggör olika uttrycksformer och hur man kan arbeta med ett rikt matematisk problem.
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| 16. |
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| 17. |
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| 18. |
- Taflin, Eva
(author)
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Matematikproblem i skolan : för att skapa tillfällen till lärande
- 2007
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Doctoral thesis (other academic/artistic)abstract
- The general purpose of this dissertation is to define and explore what mathematical problem solving entails. Seven criteria for rich problems will also be formulated. Rich problems are defined as problems which are especially constructed for mathematics education in a school context. The first part of the dissertation presents a sketch of what mathematical problem solving can entail in the teaching and learning process. The second part of the dissertation is a presentation and analysis of two ´rich´ problems. The analysis points out where mathematical ideas - concepts, procedures, conventions, strategies and formulae – appear in a problem solving process. The dissertation concludes with examples of the ways in which pupils and teachers together create occasions to utilize accepted mathematical ideas as well as the new range of ideas they devise in order to solve the problems. The concept of ´rich problems´ enables pupils with different mathematical backgrounds and capabilities to work with the same problem and solve it with various mathematical ideas. Research methods have included video- and audio recordings, stimulated recall with pupils and teachers, interviews and pupils drawings.
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| 19. |
- Taflin, Eva, et al.
(author)
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Perspektiv på handledning och den handleddes roller i lärarutbildningens verksamhetsförlagda delar
- 2022
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In: Nordisk Tidskrift för Allmän Didaktik. - Göteborg : Göteborgs universitet. - 2002-1534. ; 8:1, s. 20-34
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Journal article (peer-reviewed)abstract
- Within teacher education supervision of teacher students is a central and appreciated element. It is also witnessed as a dilemma when the academy meets supervisors in schools with different perspectives and expectations. The area of interest of the present study is to identify different perspectives on supervision roles among supervisors and teacher students in relation to expectation, power and influence. The question is how we can describe and understand the roles of teacher students from different supervision perspectives during work integrated learning activities at schools. A conceptual starting point has been taken from Foucault’s power perspective and empirical data is related to analysis of interviews and documents. The results from the study shows that the roles of teacher students can be understood on the basis of subordinated management and a lower degree of scientific approach and are referred to roles as assistants and apprentices. Secondly, the roles can be understood as equal management based on a higher degree of scientific approach and be referred to as colleagues and co-researchers. One conclusion is that the four ways of understanding the different roles of teacher students are something that should be understood over time and that the roles can vary from situation to situation.
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| 20. |
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| 21. |
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| 22. |
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| 23. |
- Teledahl, Anna, et al.
(author)
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Assessment in distance courses in mathematics and mathematics education
- 2012
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In: Proceedings of <em>NORMA</em> 11: the sixth Nordic conference on mathematics education in Reykjavik, May 11-14 <em>2011</em>.. ; , s. -50
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Conference paper (peer-reviewed)abstract
- The aim of this study is to increase general understanding of the factors influencing teachers’ choices of assessment tasks in distance courses in university mathematics and mathematics education. Six interviews were conducted in which teachers elaborated on their reasoning concerning choices of assessment tasks. The results show that the forms of assessment tasks used in distance education, along with the reasoning preceding the choice of these tasks, differ little from those used in campus based education. One possible explanation for this can be that nearly all assessment tasks described in the interviews were conducted in face-to-face situations. The technical aspects of modern distance education seem to have a minor influence on the choice of form ofassessment.
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| 24. |
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| 25. |
- Teledahl, Anna, 1972-
(author)
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Knowledge and writing in school mathematics : a communicational approach
- 2016
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Doctoral thesis (other academic/artistic)abstract
- This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.
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