| 1. |
- Ebbelind, Andreas, et al.
(författare)
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Learning fractions : transformations between representations from a social semiotic perspective of multimodality
- 2012
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Ingår i: Proceedings of Norma 11. - Reykjavík : University of Iceland Press. - 9789979549659 ; , s. 217-226
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Konferensbidrag (refereegranskat)abstract
- This study presents a tentative framework for studying the learning of fractions in the context of transformations between different forms of representations. The framework is used in an empirical sample of how eight 10-year-old students express understanding of activities which were developed to challenge them to reflect on different ways of representing aspects of the concept of fractions. The framework is based on a social semiotic perspective of multimodality.The analysis discloses how the framework helps in structuring our understanding of the interplay between representations in the learning of fractions. Specifically, we saw how concrete physical material and gestures complemented the symbolic and spoken language in the students’ solution strategies of different tasks.
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| 2. |
- Eckert, Andreas, 1984-
(författare)
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Contributing to develop contributions : a metaphor for teaching in the reform mathematics classroom
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis aims at contributing to the theoretical research discourse on teaching mathematics. More precise, to explore a teacher’s role and actions while negotiating meaning of mathematical objects in discursive transformative practices in mathematics. The focus is to highlight the teacher as an active contributor to the classroom mathematical discourse, having an important role in shaping the mathematics. At the same time, the teacher is acknowledged as an individual who learns and develops as a lesson and semester progress.Three research papers illustrate the state, at that time, of an inductive analysis of three teachers, teaching a series of lessons based on probability theory at two Swedish primary schools. The teachers worked together with the students to explore an unknown sample space, made up out of an opaque bottle with coloured marbles within that showed one marble at each turn of the bottle. They had to construct mathematical tools together to help them solve the mystery. The analysis focused on teacher–student interactions during this exploration, revealing complex connections in the process of teaching.The three papers presented the development of a theoretical framework named Contributing to Develop Contributions (CDC). The frameworks’ fundamental idea is that teachers learn as they teach, using the teaching metaphor learning to develop learning. That metaphor was developed, in light of the ongoing empirical analysis, into CDC by drawing on a theoretical idea that learning can be viewed as contributing to the collaborative meaning making in the classroom. Teaching and teacher learning are described and understood as reflexive processes in relation to in-the-moment teacher-student interaction.Contributing to develop contributions consists of three different ways of contributing. The analytical categories illustrate how students’ opportunities to contribute to the negotiation of mathematical meaning are closely linked to teachers’ different ways of contributing. The different ways are Contributing one’s own interpretations of mathematical objects, Contributing with others’ interpretations of mathematical objects, and Contributing by eliciting contributions. Each way of contributing was found to have the attributes Transparency, Role-taking and Authority. Together, these six categories show teacher– student interaction as a complex dynamical system where they draw on each other and together negotiate meaning of mathematical objects in the classroom.This thesis reveals how the teaching process can be viewed in terms of learning on different levels. Learning as thought of in terms of contributing to the negotiation of meaning in the moment-to-moment interaction in the classroom. By contributing you influence the collective’s understanding as well as your own. A teacher exercises and develops ways of contributing to the negotiation of meaning of mathematical objects, in order to develop students’ contributions. In a wider perspective, the analysis showed development over time in terms of transformation. The teachers were found to have transformed their understanding of classroom situations in light of the present interactions. Contributing to the negotiation of meaning in the classroom was understood as a process in such transformation, in the ever ongoing becoming of a mathematics teacher.
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| 3. |
- Harvey, Frida, 1985-
(författare)
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Kollegialt lärande i matematik : Ett verksamhetsteoretiskt perspektiv
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the last decade, Professional Learning Communities (PLCs) are increasingly used as models for teachers’ joint efforts in developing their teaching. The overall aim of this licentiate thesis is to expand the knowledge of PLCs in mathematics, by deepening the understanding of aspects that influence the establishment, organization, and implementation of PLCs in mathematics. Specifically, the aim is to contribute with an overview of how PLCs in mathematics are organized and framed, and also to explain what may enable and hinder PLCs in mathematics. To fulfill the purpose, two studies are conducted where Cultural Historical Activity Theory (CHAT) is used as a conceptual and analytical framework. In the first study, previous research of PLCs in mathematics are synthesized through a configurative literature review, resulting in a description of how PLCs in mathematics are organized and framed. In the study, similarities, and differences between different models of PLCs in mathematics are examined regarding subjects, objects, mediating artifacts, rules, community, division of labor and outcomes. The result shows three different activity systems, with different objects or motives for implementing the PLCs. The activity systems vary concerning the use of mediating artifacts, and what norms regulate the activity system, but are similar regarding participants, context, and division of labor. In the second study, contradictions, and their manifestations in PLCs in mathematics are analyzed. Contradictions may enable or hinder the work of PLCs depending on whether they are identified or not. Contradictions, and their manifestations, are in the study examined through interviews with teacher leader coaches with experience in coaching teacher leaders of PLCs in mathematics. In the study, four contradictions, in and between activity systems, are identified. These four contradictions are manifested through 26 conflicts and dilemmas. The identified contradictions are connected to the norms and traditions that are part of mathematics as a discipline as well as the teacher profession. Taken together, the result of the two studies can be useful in establishing, organizing, and implementing future PLC endeavors.
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| 4. |
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| 5. |
- Markkanen, Peter, 1964-
(författare)
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Representationer, visualisering och resonemang i geometri : Praktiknära studier i digitala lärmiljöer
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The aim of this dissertation was to gain a deeper understanding of how teaching in digital environments can be designed to give students opportunities to develop knowledge in two- and three-dimensional geometry. The dissertation consists of two sub-studies, the first using an ethnographic approach in which the researcher followed a teacher's teaching in a digital environment, in a Grade 9 class for a period of five weeks. In the first study, learning was defined based on reification theory, which describes that the understanding of mathematical concepts develops from operational to structural understanding. Data were collected through video-assisted observations, interviews and student tests. This material was analyzed with a focus on the ways the teacher used the digital tools to create mathematical situations that offered students opportunities to work with different representations and mathematical concepts. In the second study, characterized as educational design research,t he researcher along with two teachers designed teaching in two classes in Grades 8 and 9. The focus in this second study was shifted to how geometry teaching in digital environments can be designed to offer students the opportunity to develop their understanding of, and ways of interpreting, geometric figures. For support in designing lessons, Brousseau's theory of didactical situations, based on a constructivist approach to learning, was adopted. Data were collected through video-assisted observations and screen recordings of students´ work. This material was analyzed in two steps. First, the focus was on how students worked with the figures in relation to the assumptions made in the design. Thereafter, the attention was on properties of the designed environment that were considered to affect the students and to lead to changes in how they interpreted and used the figures when working with geometric tasks. The study resulted in five design principles that can serve as a guide for designing teaching in digital environments. Thus, taken together, the dissertation´s two sub-studies show that using digital tools in teaching gives the teacher not only more didactic variables to work with when creating lessons, but also, based on the needs that arise in teaching, more tools for shedding light on what some students may have difficulty detecting. Furthermore, the results show that digital tools can help in the creation of environments that stimulate students' way of examining, testing and reasoning about geometric figures and their properties, which are seen as important prerequisites for developing good knowledge in the field.
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| 6. |
- Nilsson, Per, 1967-, et al.
(författare)
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A contextual approach on learning probability
- 2008
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Ingår i: Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education. - Morelia. Mexico : Guevara Impresores.
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Konferensbidrag (refereegranskat)abstract
- This paper focuses on the learning of probability. The analytical construct of contextualization is used to explain how students deal with compound random phenomenon in an explorative ICT setting. In this setting the students were offered opportunities to interact with different representations of such phenomenon. The analysis follows a specific group of two students. The analysis shows how students’ understanding of the compound events varies with their interpretations of the situation. In particular, we notice how the two students differ when trying to connect theoretical and experimental representations of probability.
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| 7. |
- Nilsson, Per, 1967-, et al.
(författare)
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Collaborative design of mathematical activities for learning in an outdoor setting
- 2009
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Ingår i: Proceedings of the 6<sup>th</sup> Conference of the European Society for Research in Mathematics Education, CERME 6<em><em></em></em>. - 9782734211907 ; , s. 1101-1110
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Konferensbidrag (refereegranskat)abstract
- In recent years, teaching mathematics in an outdoor setting has become popular among teachers, as it seems to offer alternative ways to motivate children’s learning. These new learning possibilities pose crucial questions regarding the nature of how mathematical activities should be designed for outdoors settings. In this paper we describe our current work related to the design and implementation of mathematical activities in this particular environment in which a specific mathematical content was used as the central component in the design. We illustrate our collaborative design approach and the results from observations of two activities. Our initial results provide us with valuable insights that can help to better understand how to design and implement this kind of educational activities.
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| 8. |
- Nilsson, Per, 1967-, et al.
(författare)
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Collaborative design of mathematical activities for learning in an outdoor setting
- 2010
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Ingår i: Proceedings of CERME 6<em><em></em></em>. - Lyon : Institut National de Recherche Pedagogique. - 9782734211907 ; , s. 1101-1110
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Konferensbidrag (refereegranskat)abstract
- In recent years, teaching mathematics in an outdoor setting has become popular among teachers, as it seems to offer alternative ways to motivate children’s learning. These new learning possibilities pose crucial questions regarding the nature of how mathematical activities should be designed for outdoors settings. In this paper we describe our current work related to the design and implementation of mathematical activities in this particular environment in which a specific mathematical content was used as the central component in the design. We illustrate our collaborative design approach and the results from observations of two activities. Our initial results provide us with valuable insights that can help to better understand how to design and implement this kind of educational activities.
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| 9. |
- Nilsson, Per, 1967-
(författare)
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Conceptual variation and coordination in probability reasoning
- 2009
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Ingår i: Journal of Mathematical Behavior. - : Elsevier BV. - 0732-3123 .- 1873-8028. ; 28:4, s. 247-261
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Tidskriftsartikel (refereegranskat)abstract
- This study investigates students’ conceptual variation and coordination among theoretical and experimental interpretations of probability. In the analysis we follow how Swedish stu- dents (12–13 years old) interact with a dice game, specifically designed to offer the students opportunities to elaborate on the logic of sample space, physical/geometrical considera- tions and experimental evidence when trying to develop their understanding of compound random phenomena.The analytical construct of contextualization was used as a means to provide structure to the qualitative analysis performed. Within the frame of the students’ problem encounters during the game and how they contextualized the solutions of the problems in personal contexts for interpretations, the analysis finds four main forms of appearance, or of lim- itations in appearance, of conceptual variation and coordination among theoretical and experimental interpretations of probability.
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| 10. |
- Nilsson, Per, 1967-, et al.
(författare)
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Connecting Swedish compolsory schoolteachers' content knowledge of probability to their level of education, teaching years and self-assessments of probability concepts
- 2012
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Konferensbidrag (refereegranskat)abstract
- This paper reports on a survey on teachers’ content knowledge of probability and with connecting such knowledge to the teachers’ level of education, teaching years and self-assessments of probability concepts. Twenty-nine teachers in compulsory school answered a questionnaire calling for reflection on these issues. The teachers’ responses disclose that the teachers find probability to be a difficult subject. The survey reports that the teachers have low confidence in understanding key concepts of probability and that they have difficulties in applying the concepts in probability tasks. The test indicates no correlation between teaching years and confidence or between teaching years and results on the probability tasks.
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