| 1. |
- Bergvall, Ida, 1975-, et al.
(author)
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A model for analysing digital mathematics teaching material from a social semiotic perspective
- 2021
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In: Designs for Learning. - : Stockholm University Press. - 1654-7608 .- 2001-7480. ; 13:1, s. 1-7
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Journal article (peer-reviewed)abstract
- The use of digital teaching materials is increasing in mathematics teaching. The dynamic resources of these materials have great potential, for example to adapt the content to different teaching methods and different students. These materials also provide new opportunities for the increasing distance learning. However, in order to take advantage of this potential and to avoid possible disadvantages, a deepened understanding of the function of these materials is needed. In this article, we describe a social semiotic model for multimodal analysis of digital teaching materials in mathematics. The suggested model is intended as a tool for researchers as well as for teachers, to analyse how affordances by digital technology are utilized to offer mathematical meaning in different teaching materials, by an analysis of networks of information offered regarding central aspects of mathematical concepts.
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| 2. |
- Bergvall, Ida, 1975-, et al.
(author)
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Att utveckla elevers begreppsförmåga : Bildens potential i undervisningen
- 2018
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In: NÄD 2018. - Kristianstad : Högskolan i Kristianstad. ; , s. 10-10
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Conference paper (peer-reviewed)abstract
- Denna studie är ett planerat samarbete mellan aktiva lärare och forskare där syftet är att fördjupa kunskapen om bildens potential att stödja elevers begreppskompetens i matematikämnet. Olika semiotiska resurser såsom naturligt språk, matematisk notation och bilder används som redskap för att stärka elevers begreppskompetens i matematik (Brenner, Herman, Ho och Zimmer, 1999) vilket bland annat är vanligt i läromedel. Förekomsten av bilder som resurser i matematikläromedel har ökat under 2000-talet (Dimmel och Herbst, 2015) och därför behövs en fördjupad kunskap om bilders betydelse för elevers förståelse av matematiken. Bilder i matematiskt ämnesspråk kan vara av olika typ, allt från vardagsnära avbildningar till mer schematiska bilder. Detta har beskrivits som att bilder har olika kodningsorientering (se Kress och van Leeuwen 2006), vilket resulterar i varierande grad av abstraktion.I denna studie analyseras elevers samtal om matematik utifrån bilder med olika kodningsorientering. Studien genomförs i årskurs 5 i grundskolan och årskurs 1 på gymnasiet där elever i grupp löser matematikuppgifter. Inom varje årskurs används samma matematikproblem men typen av bild skiljer sig åt. I gymnasiet studeras elever på ett tekniskt program där syftet med matematikundervisningen är att förbereda eleverna för högre studier. Genom att studera två olika praktiker ges möjlighet till en rik beskrivning av bildens betydelse i två olika kontexter. Analyser genomförs på videoupptagningar av gruppsamtalen, avseende hur och i vilken utsträckning elevernas uttalanden signalerar begreppskompetens såsom definierad av Kilpatrick, Swafford och Findell (2001). Studien avses bidra till ökad kunskap om olika bilders potential att fungera som ett redskap i undervisningen för att stödja utvecklingen av elevers begreppskompetens. Resultaten kan förbättra lärares förutsättningar att göra medvetna didaktiska val av bilder med olika kodningsorientering. Till exempel kan en viss typ av bilder väljas i syfte att skapa förutsättningar för elevsamtal orienterade mot en högre abstraktionsnivå.
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| 3. |
- Bergvall, Ida, 1975-
(author)
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Bokstavligt, bildligt och symboliskt i skolans matematik : – en studie om ämnesspråk i TIMSS
- 2016
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Doctoral thesis (other academic/artistic)abstract
- The overall aim of this thesis is to deepen the understanding of mathematical subject language regarding three semiotic resources, written language, images and mathematical symbols. The theses also investigates high- and low-performingstudents encounter with mathematical subject language.Based on previous research on language and from a theoretical foundation based on systemic functional linguistics (SFL) and social semiotics, four meaning dimensions – packing, precision, personification and presentation – were identified as central in academic language in general and in mathematical subject language. A didactically based reception theoretical perspective has been used for an analysis of high and low achieving students' encounter with the mathematical subject language.The thesis comprises three studies each examining the mathematical subject language in TIMSS 2011 from various angles. The analyzes were conducted on four content areas algebra, statistics, geometry and arithmetic in the Swedish version of the international study Trends in International Mathematics and Science Study 2011 (TIMSS).In a summary, the results showed that the mathematical subject language was used in different ways in the four content areas in TIMSS where colloquial and subject-specific forms of languages had different roles and were expressed in varying degrees by the written language, images and mathematical symbols. Thus each content area was expressed by its own register which means that is not sufficient to talk about mathematical subject language as one single language.The result shows that two forms of language, subject specific and everyday language were used parallel in the TIMSS material. The subject specific forms were most salient in algebra and geometry and the more everyday forms of language were more common in statistics and arithmetic.The results from the correlation analyses indicated that fewer students managed the encounter with tasks in algebra and geometry when they were expressed by subject specific language. In contrast, the results indicated that students were able handle the encounter with the more colloquial expressions of the content areas statistics and arithmetic.
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| 8. |
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| 9. |
- Bergvall, Ida, 1975-, et al.
(author)
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Mediating activities in students’ collaborative work on self-explanation prompts
- 2023
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In: Nordisk matematikkdidaktikk, NOMAD. - : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 28:1-2, s. 31-58
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Journal article (peer-reviewed)abstract
- This study concerns mediating activities in student discussions during collaborative work with self-explanation prompts (SEPs). While the aim of most other tasks, from the students’ perspective, can be perceived as finding the correct answer, discussions supported by SEPs require a different approach, because students must engage in mathematical discussions, and explain their insights into the mathematics at hand. In this study, we explore activities that are fostered by SEPs. The analysis of the activities taking place, reveal five mediating activities to promote in teaching, but also potential hinders for the intended discussion to occur.
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| 10. |
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| 11. |
- Bergvall, Ida, 1975-, et al.
(author)
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Multi-semiotic progression in school mathematics
- 2019
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In: NERA 2019. ; , s. 270-271
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Conference paper (other academic/artistic)abstract
- In mathematical school language, both everyday and technical expressions are commonly used (Barwell, 2013). This means that two discourses, an everyday and a technical discourse, are used together and that students must handle these two discourses simultaneously. In this study, we investigate how images and natural language are used to express these two discourses in Swedish national tests for grade three, six and nine. The aim is to learn more about progression in multisemiotic demands in mathematical subject language.The theoetical base for this study is social semiotics (e.g. Kress & van Leeuwen, 2006), which also forms the framework for the analysis. In a first step of the analysis, the coding orientation (ibid.) in the images was examined, i.e. whether the images express the mathematical content in a naturalistic coding orientation, with a connection to everyday situations, or in a technical coding orientation implicating a subject specific and technical focus in the mathematical content. In the next step, cohesion regarding coding orientation between image and text will be studied, i.e. how participants, processes and circumstances are expressed by an everyday or technically oriented in written natural language and in images and how cohesion is expressed between these two semiotic resources.The analysed materials are the latest released Swedish national tests in mathematics for grade three, six and nine. This means that for grade three and six, the test from 2015 have been studied, while the test for grade nine was from 2013.Preliminary results from the first step of the analysis, show that for a clear majority of the images inthe test for year three and six, the coding-orientation is naturalistic. The images are to a very high degree drawings of people, naturalistic objects or environments. In year nine, the opposite applies and a technical coding orientation is the most common. Exceptions can be found in the problemsolving tasks, with a relatively comprehensive contextual description. In these problem solving tasks, images with a naturalistic coding orientation are used even in grade nine.A tentative conclusion is that there is a rather significant progression towards a more technical language in the multi-semiotic language used in this sample of the Swedish national tests. The results indicate a need to highlight the function of the various multi-semiotic resources used inschool mathematics, in order to support the students’ development of the subject language. These results are relevant for a Swedish, as well as for a Nordic school context and literacy research, since there are great similarities between the school systems in the Nordic countries.
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| 15. |
- Bergvall, Ida, 1975-, et al.
(author)
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The Subject Language Use In Year 8 TIMSS-Test Questions : A Comparison Of Language Uses In Science And Mathematics
- 2018
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In: Network Sessions as ECER 2018.
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Conference paper (peer-reviewed)abstract
- In this study we want to make a contribution by making a comparison between the subject languages in mathematics and science based on linguistic theories about language and language function. Through this theoretical foundation in this present study we also have the opportunity to analyze the language function and thus we can also discuss the language's role in teaching. The aim of this study is to compare and thus gain more knowledge of grammatical features in subject language in science and mathematics and how these grammatical features are used to express meaning. To fulfil this purpose, science and mathematics items from Trends in International Mathematics and Science Study (TIMSS) 2011, grade eight, have been analysed from a functional perspective on language.Empirical studies that compare language use in different subjects are sparsely present (Österholm & Bergqvist, 2013) but there are studies pointing out that how language are used to express meaning varies between different school subjects (e.g. Fang & Schleppegrell, 2008; Schleppegrell, 2004). These linguistic differences have been highlighted as arguments for a more differentiated language-based teaching of subjects, leaning on disciplinary literacy (Shanahan & Shanahan, 2008). In order to conduct such a language-based teaching of subjects, an awareness of the different functions in the language used in various school subject is of great importance. One example of a comparative language study is the corpus study conducted by Ribeck (2015) where the language in Swedish teaching materials in science is analyzed, and compared with teaching materials in social science and with textbooks in mathematics. However, Ribeck does not make a direct analysis of mathematical subject language, her focus is rather on the language used in natural science compared to social science. There are also studies that focuses on the language use within subjects. Here it appears that the subject language is used differently and has different functions in different content areas within school mathematics (e.g. Bergvall, 2016) as well as within the different school science subjects, e.g. biology, physics, chemistry and earth science (e.g. Persson, 2016). This study draws on a social semiotic perspective and systemic functional linguistics (SFL) (Halliday & Matthiessen, 2004). A point of departure is the perspective that different registers of language are used in different social contexts, which in this study is defined as the two school subjects science and mathematics. Grounded in SFL and the three meta-functions ideational, interpersonal and textual function the meaning dimension model of analysis was developed in a previous research project (Bergvall et al., 2016; Persson et al., 2016). Four central meaning dimensions, packing, precision, personification and presentation, were condensed from previous research regarding academic language and language use in the school subjects science and mathematics. The meaning dimensions can be used as measures of how grammatical features are used in various types of texts in order to express meaning. Packing and precision are regarded as aspects of the ideational meta-function. Packing is a measure of the information density in a text and precision is a measure of how and to what extent the given information in the text is specified. Personification, as an aspect of the interpersonal meta-function, is a measure of how personal relations between the reader and the text are expressed. The last meaning dimension, presentation, concerns how the information is structured in the text and is regarded as an aspect of the textual meta-function. In the present study, the four meaning dimensions are used to describe and compare the language and its function in science and mathematics items in TIMSS 2011.MethodBy the use of a quantitative method all items in mathematics and science from the Swedish version of TIMSS 2011, grade eight were analyzed. This material consists of 197 items in science and 217 items in mathematics. The language in these items have been analyzed for word class, word length and number of words per items by a computer based automatic parsing. For this parsing Extensible Markup Language (XML) was used. Some other linguistic features, i.e. passive forms and subordinate clauses, were identified manually. Since the meaning dimensions are used as a base for the linguistic analysis, the results will possibly be generally applicable also for other European languages, although the analysis was conducted on the Swedish version of TIMSS items. Packing was measured by calculating the number of nouns and the number of long words (>6 characters). Precision in the items were provided by words such as adjectives, adverbs, participles and counting words specifying different attributes in the items. Personification was here measured by the number of personal pronouns and proper names and presentation was measured by the presence of subordinate clauses and passive forms. In order to compensate for the varying length of different items, the number of the different linguistic features were divided by the number of words in the particular item. To enable the adding of different features, each feature is normalized by calculating its z-score. An index was then calculated for each meaning dimension based on the linguistic information on each item. From these indices a comparison between the language uses in the two subjects was possible. In the next step of the analysis each subject were separated into content domains: Algebra, Data & chance, Geometry and Numbers for mathematics items and Biology, Chemistry, Earth science and Physics for science items. This enabled variations of language use within the subjects also to be analyzed. The results were compiled in box-plots diagrams which visualized the distribution of the expressions of the four meaning dimensions in the various content domains.Expected OutcomesPreliminary results show that central traits of the academic language as measured by the four meaning dimensions are used in similar ways in both science and mathematics. The levels of packing, precision and presentation are fairly similar when looking at differences between the subjects. Personification shows the largest differences between the subjects, where mathematics as a whole makes more use of personal pronouns and proper names in the items. When separating the subjects into content domains, Statistics shows the highest level of personification. In this domain it can therefore be concluded that human participants are essential, thus emphasizing that this is a domain that this is an area of relevance for people in general or for the student him/herself. This can be interpreted as signaling the possibility to actively participate and interact in similar situations as described by the items context. On the other hand, in domains such as Algebra, Geometry and Earth science where the content is expressed with a low level of personification, the interpretation is that the content of these domains –at least as expressed in TIMSS items- are more separated from peoples’ everyday lives and thus the students’ own reality. Another result that emerges from the analysis relates to the meaning dimension presentation where we see that the written texts, especially in Algebra, but also in Geometry, Numbers and Earth science, mainly contains short sentences without subordinate clauses. In written academic language, subordinate clauses are a common tool for creating information flow and link different parts of the text (Fang, 2006; Schleppegrell, 2004; Veel, 1997). The lack of subordinate clauses in tasks in certain content areas of TIMSS indicates a subject-specific linguistic form that may require a familiarity with this specific form of language use.ReferencesBergvall, I. (2016). Bokstavligt, bildligt och symboliskt i skolans matematik – en studie om ämnesspråk i TIMSS. [Diss.] Uppsala: Acta Universitatis Upsaliensis. Bergvall, I., Wiksten Folkeryd, J., & Liberg, C. (2016). Linguistic features and their function in different mathematical content areas in TIMSS 2011. Nordic Studies in Mathematics Education, 21(2), 45-68. Fang, Z. (2006). The Language Demands of Science Reading in Middle School, International Journal of Science Education, 28(5) 491-520. Fang, Z., & Schleppegrell, M. J. (2008). Reading in secondary content areas: A language-based pedagogy. Ann Arbor: University of Michigan Press. Halliday, M. A. K., & Matthiessen, C. M. I. M. (2004). An introduction to functional grammar (3.th ed.). London: Arnold. Persson, Tomas (2016). De naturvetenskapliga ämnesspråken. De naturvetenskapliga uppgifterna i och elevers resultat från TIMSS 2011 år 8. [Diss.] Uppsala: Acta Universitatis Upsaliensis. Persson, T., af Geijerstam, Å., & Liberg, C. (2016). Features and functions of scientific language(s) in TIMSS 2011. Nordic Studies in Science Education, 12(2), 176-196. Ribeck, Judy (2015). Steg för steg. Naturvetenskapligt ämnesspråk som räknas. [Diss.] Data linguistica. No. 28, Institutionen för svenska språket, Göteborgs universitet. Shanahan, T., & Shanahan, C. (2008). Teaching disciplinary literacy to adolescents: Rethinking content-area literacy. Harvard Educational Review, 78(1), 40–59. Schleppegrell, M. J. (2004). The language of schooling; a functional linguistics perspective. London: Lawrence Erlbaum Associates. Veel, R. (1997). Learning How to Mean-Scientifically Speaking: Apprenticeship into Scientific Discourse in the Secondary School. In. Christie Frances & Jim R. Martin (Eds.), Genre and Institutions: Social Processes in the Workplace and School, s. 161-195. London: Cassell. Österholm, M. & Bergqvist, E. (2013). What is so special about mathematical texts? Analyses of common claims in research literature and of properties of textbooks. ZDM Mathematics education, 45(5) 751-763.
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| 16. |
- Bergvall, Ida, et al.
(author)
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Towards a theoretical understanding of learning with self-explanation prompts
- 2020
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In: Sustainable mathematics in a digitalized world. - Växjö : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 9789198402445 ; , s. 81-90
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Conference paper (peer-reviewed)abstract
- Oral or written requests to students to self-explain important aspects in a task at hand (e.g. self-explanation prompts) has proven to increase learning. Research about such prompts has mainly been implemented with cognitive perspectives focused on the individual. In this paper, we suggest an alternative analytical framework grounded in a sociocultural theory. This framework is valuable because it adapts to the individual learning process as well as to the learning process that takes place in group work. In addition, this framework contributes valuable guidance to the teacher and to authors of teaching materials as well as to researchers in mathematics education. The analytical framework is explained in relation to an example task. An excerpt from student group work is also discussed.
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| 17. |
- Bråting, Kajsa, Docent, 1975-, et al.
(author)
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Exemplifying different methodological approaches of analysing textbooks in mathematics
- 2022
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In: The relation between mathematics education research and teachers' professional development. - Göteborg : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 1651-3274. - 9789198402452 ; 16, s. 125-129, s. 125-129
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Conference paper (peer-reviewed)abstract
- In this symposium, we will discuss different ways of analysing mathematics textbooks from a methodological point of view. The discussion will be based on examples from five separate ongoing analyses of Swedish textbooks divided into two methodological approaches; one where analysis is conducted within an established theoretical framework, and one where analytical tools are constructed through combining aspects of different theories. The symposium will be held at the conference MADIF-13.
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| 18. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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Computer-based assessment in mathematics : Issues about validity
- 2023
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In: LUMAT. - : University of Helsinki; LUMA Centre Finland. - 2323-7112. ; 11:3, s. 49-76
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Journal article (peer-reviewed)abstract
- Computer-based assessments is becoming more and more common in mathematics education, and because the digital media entails other demands than paper-based tests, potential threats against validity must be considered. In this study we investigate how preparatory instructions and digital familiarity, may be of importance for test validity. 77 lower secondary students participated in the study and were divided into two groups that received different instructions about five different types of dynamic and/or interactive functions in digital mathematics items. One group received a verbal and visual instruction, whereas the other group also got the opportunity to try using the functions themselves. The students were monitored using eye-tracking equipment during their work with mathematics items with the five types of functions. The result revealed differences in how the students undertook the dynamic functions due to the students’ preparatory instructions. One conclusion is that students need to be very familiar with dynamic and interactive functions in tests, if validity is to be ensured. The validity also depends on the type of dynamic function used.
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| 19. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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Designing tasks with self-explanation prompts
- 2019
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In: Proceedings of the eleventh congress of the European society for research in mathematics education. - Utrecht : European Society for Research in Mathematics Education (ERME). - 9789073346758 ; , s. 4202-4209
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Conference paper (peer-reviewed)abstract
- This paper presents some results from an ongoing review on self-explanation prompts. An emphasis is laid on design principles based on empirical research. The review is grounded in scaffolding theory, which means that the self-explanation prompts are seen as a temporary support that the student shall learn to manage without. Three themes identified in the review are described and discussed in relation to design and implementation of tasks with self-explanation prompts: prompts with different purposes, the necessity to adapt prompt to students’ prior knowledge, and factors of importance for students’ engagement in the prompts. Examples of tasks with prompts for which these design aspects have been taken into account are given in the paper.
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| 20. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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Digital teaching platforms : the use of dynamic functions to express mathematical content
- 2023
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In: Scandinavian Journal of Educational Research. - : Routledge. - 0031-3831 .- 1470-1170.
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Journal article (peer-reviewed)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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| 22. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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Meeting the needs of today’s society – developing collaborative problem solving skills
- 2019
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In: NERA 2019 Programme. ; , s. 501-502
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Conference paper (peer-reviewed)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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| 23. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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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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In: ECER 2018 Programme.
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Conference paper (peer-reviewed)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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| 24. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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Static, dynamic and interactive elements in digital teaching materials in mathematics : how do they foster interaction, exploration and persistence?
- 2023
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In: LUMAT. - : University of Helsinki. - 2323-7112. ; 11:3, s. 103-131
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Journal article (peer-reviewed)abstract
- Contemporary comprehensive mathematics teaching material covering whole courses has developed substantially from the early versions that roughly were ‘books as pdf’ with some complementary online material. In teaching materials that are offered in online web portals (digital teaching platforms) a variety of dynamic and interactive elements can be utilised, offering new ways to engage with mathematics. Despite this recent development, the variety of affordances of the digital environment are utilised to a surprisingly small extent. The pros and cons with digital teaching materials in mathematics are debated, and publishers advertise with arguments about algorithms that lay out an ideal learning path and about joyful content. Critical for students’ learning while working with teaching materials is however that they find it meaningful to use the materials, a persistence in the interaction with the materials, and furthermore that the willingness to explore mathematics remains. In this study students’ interaction with digital teaching material with various kinds of dynamic and interactive elements supplementing the static parts in the presentation of new content is explored. Differences in students’ attention to mathematical facts, essential in the problem solving, is captured using an eye-tracker. Analyses of differences in attentive behaviour depending on the kind of digital element that are used for presentation reveal that the type of digital element that students attend the least to is static elements. Differences in what is offered to and what is demanded from a reader when mathematical facts are presented using various digital elements is discussed and potential implications from the results are suggested.
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| 25. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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The role of dynamic elements in digital teaching platforms : an investigation of students' reading behaviour
- 2022
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In: Proceedings of the twelfth congress of the European society for research in mathematics education. - : Free University of Bozen-Bolzano; ERME. - 9791221025378 ; , s. 3976-3983
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Conference paper (peer-reviewed)abstract
- The use of digital teaching materials in mathematics education has gained ground since the first introductions of various hard-and software. A distinguishing feature for digital teaching materials is the possibility to offer interactive and dynamic elements. In this study, eye-tracking is used to explore students' reading behaviour when working with mathematics items in a digital environment. In particular, the focus is laid on how students read depending on the extent to which the items offer dynamic elements. Analysis of data from the eye-tracking in combination with students' responses in the interviews provide a broad picture of different types of challenges that students may face in working with dynamic elements. The results also reveal that commonly used dynamic elements as films or feedback on given answers are valuable because users emphasize them as useful and informative.
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| 26. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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Using heat maps from eye tracking in stimulated recall interviews
- 2022
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In: The relation between mathematics education research and teachers’ professional development. - 9789198402452 ; , s. 133-133
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Conference paper (other academic/artistic)abstract
- This presentation discusses students’ interpretations of heat maps from eye tracking. Heat maps are often referred to as ‘just’ eye candy because of their appealing nature and the somewhat ‘hidden’ data. Undoubtedly, there is valuable information in these visualisations and if attention is paid when conclusions are drawn, the data is a useful complement to quantitative measures. We explore pros and cons when using heat maps in stimulated recall interviews and contrast this method to stimulated recall using videos or the use of think aloud protocols. A conclusion is that the heat map can attract attention to what actually happened and thereby evoke valuable references to thought processes, but at the same time it may draw attention to actions instead of to reasoning and thoughts because the image represents the reader’s activity (“I looked at…”).
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| 27. |
- Palm Kaplan, Kristina, et al.
(author)
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Generalizing mathematically through changes in referents
- 2022
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In: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). - : Free University of Bozen-Bolzano and ERME. - 9791221025378
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Conference paper (other academic/artistic)abstract
- In this pilot, opportunities to engage in mathematical generalization were identified in a section of a textbook from year 6. From a social-semiotic perspective, we explored how these opportunities were constructed linguistically. While passive verb forms and nominalizations constructed an independent character of mathematics, logic expansions constructed limitations for the generalizations. Changes in referents constructed opportunities for generalizing actions.
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