| 8281. |
- Dyrvold, Anneli
(författare)
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Conceptualising Translations Between Representations
- 2018
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Ingår i: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education. - Umeå : PME. - 9789176019030 ; , s. 379-386
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Konferensbidrag (refereegranskat)abstract
- Representations and translations between them are central in mathematics education. For example, in the NCTM standards it is emphasized students need to be able to “select, apply, and translate among mathematical representations to solve problems” (NCTM 2000, p.67). A variety of research studies have contributed to the knowledge about translations the last decades. This variety is both an asset and an obstacle when this research is used to implement new strategies in the school practice or as a base to plan new research studies. To enable an accumulation of the emerging knowledge there is a need to categorize studies that focus on similar questions and that conceptualizes translation similarly. The current paper suggests some classifications that such a categorization can be based on in an emerging framework.
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| 8282. |
- Dyrvold, Anneli, 1970-
(författare)
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Conceptualising translations between representations : Volume 2
- 2018
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Ingår i: PME 42. Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education. - Umeå : PME. - 9789176019030 ; , s. 2-379-2-386
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Konferensbidrag (refereegranskat)abstract
- Representations and translations between them are central in mathematics education. For example, in the NCTM standards it is emphasized students need to be able to “select, apply, and translate among mathematical representations to solve problems” (NCTM 2000, p.67). A variety of research studies have contributed to the knowledge about translations the last decades. This variety is both an asset and an obstacle when this research is used to implement new strategies in the school practice or as a base to plan new research studies. To enable an accumulation of the emerging knowledge there is a need to categorize studies that focus on similar questions and that conceptualizes translation similarly. The current paper suggests some classifications that such a categorization can be based on in an emerging framework.
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| 8283. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Digital teaching platforms : the use of dynamic functions to express mathematical content
- 2023
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Ingår i: Scandinavian Journal of Educational Research. - : Routledge. - 0031-3831 .- 1470-1170.
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Tidskriftsartikel (refereegranskat)abstract
- This article explores how seven Swedish digital teaching platforms in mathematics make use of the affordances provided by various modalities and dynamic functions. A model based on social semiotics is used to analyse how dynamic functions are used, whether or not the language is technically oriented, if relational or operational processes are emphasised, and the logic in the text. The analysis focuses on how the dynamic elements in teaching materials are used and potential consequences of their use. The results reveal a tendency to predominantly allocate dynamic and interactive elements to tasks related to theoretical parts and examples, and also that the most common dynamic element, film, has substantial potential to support meaning-making in several respects. For example, a voice-over can easily contribute a personal touch, add further logic to the content, or give an explanation based on an operational process.
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| 8284. |
- Dyrvold, Anneli, 1970-
(författare)
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Ett ramverk för att analysera matematiktexter medavseende på relationer mellan textens delar : [A framework for mathematics task text analysis – focusing on cohesion between natural language, mathematical notation, and images]
- 2016
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Ingår i: ICT in mathematics education: the future and the realities. - Karlstad : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 9789198402407 ; , s. 150-150
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Konferensbidrag (refereegranskat)abstract
- In order to understand more about difficulties related to the reading of mathematics text it is important to understand the role different features of the tasktext plays in the interpretation of the text. The proposed framework enables ananalysis of particular textual features that make a text stick together, namelycohesive features. The framework is based on theory for cohesion and hasbeen developed to catch important features of a mathematics text. Nine different types of cohesive relations are defined; these relations exist both withinnatural language, and between natural language and other semiotic resources.The framework has been developed to enable reliable coding of a substantialamount of text for the purpose of statistical analyses.
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| 8285. |
- Dyrvold, Anneli, et al.
(författare)
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Exploring teaching traditions in mathematics
- 2019
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Ingår i: NERA 2019 Education in a globalized world, 6 - 8 March, 2019, Uppsala, Sweden, Abstact book 2019-03-06. - Uppsala University. ; , s. 269-270
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Konferensbidrag (refereegranskat)
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| 8286. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Exploring teaching traditions in mathematics
- 2019
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Konferensbidrag (refereegranskat)abstract
- The background to the actions that take place in classrooms are formed during a long time period. This kind of content formation is sometimes referred to as the emergence of teaching traditions, which can bedefined as “regular patterns of choices of content which have been developed over time within a specific subject” (Almqvist et al., 2008). Content patterns form a certain education culture which constitutes whatis considered as adequate teaching and relevant content. Exploring teaching traditions can provide knowledge with respect to what values a specific educational culture holds.Within the Swedish field of science education, there has been much research on teaching traditions during the past decade. The results reveal three established teaching traditions in science education: an‘academic tradition’, an ‘applied tradition’, and a ‘moral tradition’ (Marty et al., 2018). In mathematics education, the focus of this study, such typology of teaching traditions has not yet been formed.Considering mathematics as an academic discpline within the STEM field, it is reasonable to assume similar, but not identical, teaching traditions as in science. During the last decades, there has been aheavy emphasis on comptencies within mathematics education, which has affected teachers’everyday practice. In addition, the focus on mathematical literacy has the potential to impact teaching traditions in mathematics. The aim of this study is to identify teaching traditions in the Swedish mathemaics curriculum and contrast these traditions with those developed within science. The study is embedded in Chevallard’s theory of transposition of knowledge, where the curriculum is regarded as thestep between the transposition from scholarly knowledge to the taught knowledge in the classroom.This study is a first step towards a more comprehensive conceptualization of teaching traditions inmathematics. The mathematics curricula with commentary materials for primary and upper secondary school will be analyzed, which allows comparisons between compulsory courses and courses thatprepare for university studies. The analytical tool is based on Roberts (1982) curriculum emphases andon the teaching traditions developed within science (Marty et al., 2018). A broader view will however beadopted to ensure that traditions unique for mathematics are also included. One such example is the analysis of emphases on literacy.Our preliminary analysis indicates a pronounced emphasis on abilities in mathematics whereas inscience knowledge is emphasized. The final results will consist of a conceptualization of teaching traditions in the Swedish curricular materials in mathematics. These results provide a means to evaluate mathematical practices with a more comprehensive scope than mathematical competencies. This is relevant for all Nordic countries considering their structural similarities of policy documents.
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| 8287. |
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| 8288. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Meeting the needs of today’s society – developing collaborative problem solving skills
- 2019
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Ingår i: NERA 2019 Programme. ; , s. 501-502
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Konferensbidrag (refereegranskat)abstract
- In a globalized world, the ability to collaborate in problem solving is essential. Increasingly high demands are placed on the ability to collaborate with people with different perspectives and cultural background, and our educational systems plays an eminent role in the development of such an ability. On the other hand, both private and professionally, aspects of individualism and expectations to compete are very common. Accordingly, it may not be a clear-cutdecision for individuals to prioritize the development of collaborative problem solving skills. The PISA survey has been investigating problem solving skills since 2003 and in PISA 2015 collaborative problem solving was tested for the first time (OECD, 2017). The results show good individual problem solvers are not necessarily successful in collaborative problem solving.The aim of the study is to contribute knowledge about how a designed milieu can contribute to collaboration in problem solving and to development of collaborative problem solving skills. In particular, it is stressed how different features of the milieu become important throughout the collaborative work. Theoretically the study is framed by Brouesseau’s theory of didactical situations, the concept of milieu and three types of situations: situations of situations of action, situations of formulation, and situations of validation (Brousseau, 2006). Data is collected from collaborative problem solving in mathematics, where a designed tool-box with requests to interact is included in the milieu toencourage and support the collaborative work. The negotiation of meaning and the extent to which real collaboration come into being is analyzed in the three types of situations. A detailed analysis ofthe extent to which the students’ milieu is shared and the role the tool-box has for the milieu will contribute in-depth knowledge about how the development of collaborative problem solving skills can be supported.Preliminary analyses reveal students’ interactions with the design element of the milieu, the toolbox, do largely influence which types of situations the students engage in and how the collaboration proceeds. Unexpectedly, the collaboration resulting from the use of the tool-box was not only fruitful. In some cases, it was used in arather mechanical manner, distorting the collaboration from the problem solving. Social conventions also seem to hinder the validation to proceed, because of a strive for agreement.The study is relevant in a modern society where collaboration skills are essential. In addition, collaborative problem solving seems to be an equality issue in the Nordic countries. In all nordic countries except Norway the percentage of top performers in collaborative problem solving among top performers in science, reading and mathematics is higher than the OECD average (OECD,2017). This may indicate it is mainly the top performers that are given support in development of collaborative problem solving skills, something that needs to be considered in education.
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| 8289. |
- Dyrvold, Anneli
(författare)
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Missed opportunities in digital teaching platforms : Under-use of interactive and dynamic elements
- 2022
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Ingår i: The Journal of computers in mathematics and science teaching. - : Association for the Advancement of Computing in Education. - 0731-9258 .- 1943-5908. ; 41:2, s. 135-161
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Tidskriftsartikel (refereegranskat)abstract
- Digital media offer new opportunities to visualise mathematics and to engage students in interactive activities. The launching of digital teaching platforms in mathematics has, however, been met with some hesitation, and printed textbooks still play a substantial role in classrooms. This study addresses questions about how affordances of the digital media are utilised in contemporary digital teaching platforms in mathematics. An analysis using a typology capturing variation in interactivity and dynamics reveals substantial influence from textbooks on the design of digital teaching platforms. Static features and lecture-like films are mainly used when new concepts are introduced; whereas interactive activities are most common in tasks. When it comes to mathematical processes, there is a tendency to use a combination of different types of elements when relations between mathematical objects are in focus, as opposed to when the focus is on “doing”, which indicates that digital features are utilised where most needed. The sparse use of dynamic and interactive features is discussed, and some suggestions are made for the development of digital teaching platforms.
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| 8290. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Multimodal resources in school mathematics and their potential to express meaning in digital and printed teaching materials
- 2018
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Ingår i: ECER 2018 Programme.
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Konferensbidrag (refereegranskat)abstract
- This study addresses the language of the school subject mathematics and the aim is to investigate the potential of multimodal resources to express meaning in textbooks and digital teaching materials. An emphasis is in the analysis laid on the distinction between subject specific and everyday multisemiotic register. Language used in teaching materials in mathematics is often multisemiotic, which means that various semiotic resources such as natural language, symbolic notation, and images are used together. These semiotic resources have different potential to express meaning (Schleppegrell, 2007; Lemke, 1990; Unsworth, 1997; Abel & Exley, 2008). Natural language, is argued to be a very poor resource for formulating for example quantity, continuous co-variation, and gradation (Lemke, 1998) and therefore there is also a need for other resources to express meaning in mathematics. When various semiotic resources are used together in a text, the text can express both more and other things, compared to the use of the different semiotic resources separately, a phenomenon referred to as meaning multiplication (Lemke, 1998). This multiplicativity of meaning is possible since in a multisemiotic text, the different semiotic resources contribute differently to the text, and the meaning afforded by one resource can modulate the meaning afforded by another resource. In mathematics education today these various semiotic resources are extensively used, both in print and on computer screens. Images together with natural language and mathematical notation is used as resources in teaching, in order to strengthen the student’s conceptual knowledge (Brenner, Herman, Ho & Zimmer, 1999). During the 20 th century the presence of images in mathematics teaching materials has increased (Dimmel & Herbst, 2015), but most often, students get no education about the role and function of images (Kress & van Leeuwen, 2006). Lemke (2000) emphasizes the importance of deepening the understanding about the role of different semiotic resources. Such an understanding is also required by a student to master a subject, as part of the content knowledge since representations have such an intrinsic role in the subject mathematics. It is therefore of importance to find out more precisely how various semiotic resources are used in school mathematics, and if these resources are used differently in different kinds of teaching materials. To learn more about the semiotic resources used in teaching materials in school mathematics the current study adopts a social semiotic theoretical perspective (see e.g., Kress and van Leeuwen, 2006; O’Halloran, 2007). This perspective provides tools to investigate both how aspects of language, such as various semiotic resources, are used in acts of communication, and at the same time analyze how these chosen forms of language express and thus offer meaning to the reader in different ways (see e.g. Knain, 2005). The backbone of the study is an analysis focusing on the three metafunctions: the interpersonal, ideational and textual function (Halliday & Matthiessen, 2014). The inclusion of all three metafunctions makes it possible to highlight different semantic perspectives of interest both in relation to research about mathematics texts and for teaching. Method: A qualitative analysis is used to thoroughly understand how different textual means are used in mathematics teaching material and which meaning that is offered to the reader. A sample of mathematics texts that introduces proportionality are analysed. In this study both digital and printed teaching material are referred to as text. The texts are of different types to obtain a breadth and to enable a comparison between texts with different purposes. Both teaching materials used in the primary school (11 years old) and teaching materials intended for a sub-group of upper secondary school students (16 years old) are analysed. These two types of texts are analysed to illuminate how the language resources are used for students at different levels in the education. Both printed texts and digital teaching materials are also analysed. Digital teaching material and printed mathematics text have different means available; in the digital media sound, film and interactive elements may be utilized. Those elements are important to include in the analysis to represent the whole composition of representations offered by the teaching material. However, in the initial analysis of the digital teaching materials only texts and images has been analysed in detail, something that has been taken into account in relation to these preliminary results. The final analysis will be complemented with a multimodal analysis focusing on interactive elements, film, and sound in the digital teaching material (see O’Halloran, 2011); focusing on how these elements interact with other components of the material. The analytical tool has been developed based on previous work by Kress and van Leeuwen (2006), O’Halloran (2005, 2007), and Royce (2007). An emphasis is in the analytical tool put on its ability to distinguish between subject specific and everyday multisemiotic register, and on how particular affordances of the semiotic resources are used . In this study subject specific register is defined as language with a technical meaning or used with a technical meaning in the subject of mathematics, language that is not part of the everyday language for the intended readers. The analysis of digital and printed teaching material is conducted at two levels; first the natural language and the images are analysed separately. Thereafter the intersemiotic complementarity of the texts is analysed. The inclusion of both levels of analysis is motivated since the different elements of the text both function separately and together as a whole to express meaning. Expected outcomes: The study will contribute with knowledge about the potential of multimodal resources to express meaning in textbooks and digital teaching materials. The preliminary analysis show that by taking advantage of the affordances of the different semiotic resources the ideational meaning can be expressed in a coherent way. Such an example can be found in a text introducing proportionality with an example. Speed is illustrated by a cartoon image representing a moving person and an explanatory sentence. Thereafter the mathematical content is presented utilizing subject-specific expressions, in natural language and in a graph. The cartoon is however included in the graph, which gives coherence to the text by making relations between the everyday content and the subject specific more pronounced. An opposite to this use of images are when images are used in a solely illustrative purpose. Another result is that in the textbook as well as in the digital material for year 5, there is an evident personal voice expressed by persons present in the images or by proper names or personal pronouns in the written text. These features serves as subjects in the texts as well as in the images. The personal voice can signal to the reader that mathematics is something that concerns people's everyday lives. In the analysed material for upper secondary school, personal voice is used more sparsely. Instead, the mathematical objects functions a subjects, both in the texts and in the images. In this way, a distance between the reader and the mathematical content is expressed. In summary the results from the analysis of material written for different student groups, both in print and digital media, contribute with examples of how the different semiotic resources can function as meaning making resources. References: Abel, K. & Exley, B. (2008). Using Halliday’s functional grammar to examine early years worded mathematics texts. Australian Journal of Language & Literacy. 31(3), 227-241. Brenner, M. E., Herman, S., Ho, H-Z., & Zimmer, J. M. (1999). Cross National Comparison of Representative Competence. Journal for Research in Mathematics Education, 30 (5), 541–557. Dimmel, J. K., & Herbst, P. G. (2015). The semiotic structure of geometry diagrams: How textbook diagrams convey meaning. Journal for Research in Mathematics Education, 46 (2), 147-195. Halliday, M., & Matthiessen, C. (2014). Halliday's introduction to functional grammar (4.th ed.). Abingdon, Oxon; New York: Routledge. Knain, E. (2005). Identity and genre literacy in high-school students' experimental reports', International Journal of Science Education, 27:5, 607 - 624. Kress, G. (2005). Gains and losses: New forms of texts, knowledge, and learning. Computers and Composition, 22, 5–22. Kress, G. & van Leeuwen, T. (2006). Reading images. The grammar of visual design. 2nd edition. London: Routledge. Kress, G. (2010). Multimodality: A social semiotic approach to contemporary communication. Milton Park, Abingdon, Oxon: Routledge. Lemke, J. L. (1990). Talking Science: Language, Learning, and Values. Ablex, Norwood, N.J. Lemke, J. (1998). Multiplying meaning. Visual and verbal semiotics in scientific text. In J. R. Martin, & R. Veel. Reading images. London: Routledge. (pp. 87-113) Lemke, J. (2000). Multimedia literacy demands of the scientific curriculum. Linguistics and Education, 10 (3), 247–271.O'Halloran, K. (2005). Mathematical Discourse: Language, symbolism and visual images. London: Continuum. O’Halloran, K. (2007). Systemic functional multimodal discourse analysis (SF–MDA) approach to mathematics, grammar and literacy. In A. McCabe, M. O’Donnell, and R. Whittaker (Eds). Advances in Language and Education. London: Continuum. O’Halloran, K. (2011). Multimodal Discourse Analysis. In K. Hyland and B. Paltridge (Eds). Companion to Discourse. London and New York: Continuum. Royce, T. (2007). Intersemiotic complementarity: a framework for multimodal discourse analysis. In
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