| 1. |
- Bergvall, Ida, 1975-, et al.
(författare)
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A model for analysing digital mathematics teaching material from a social semiotic perspective
- 2021
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Ingår i: Designs for Learning. - : Stockholm University Press. - 1654-7608 .- 2001-7480. ; 13:1, s. 1-7
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Tidskriftsartikel (refereegranskat)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.
(författare)
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Att utveckla elevers begreppsförmåga : Bildens potential i undervisningen
- 2018
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Ingår i: NÄD 2018. - Kristianstad : Högskolan i Kristianstad. ; , s. 10-10
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Konferensbidrag (refereegranskat)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-, et al.
(författare)
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Mediating activities in students’ collaborative work on self-explanation prompts
- 2023
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Ingår i: Nordisk matematikkdidaktikk, NOMAD. - : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 28:1-2, s. 31-58
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Tidskriftsartikel (refereegranskat)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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| 4. |
- Bergvall, Ida, 1975-, et al.
(författare)
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Multi-semiotic progression in school mathematics
- 2019
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Ingår i: NERA 2019. ; , s. 270-271
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)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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| 5. |
- Bergvall, Ida, et al.
(författare)
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Towards a theoretical understanding of learning with self-explanation prompts
- 2020
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Ingår i: Sustainable mathematics in a digitalized world. - Växjö : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 9789198402445 ; , s. 81-90
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Konferensbidrag (refereegranskat)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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| 6. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Computer-based assessment in mathematics : Issues about validity
- 2023
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Ingår i: LUMAT. - : University of Helsinki; LUMA Centre Finland. - 2323-7112. ; 11:3, s. 49-76
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Tidskriftsartikel (refereegranskat)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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| 7. |
- 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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| 8. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Designing tasks with self-explanation prompts
- 2019
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Ingår i: 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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Konferensbidrag (refereegranskat)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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| 9. |
- Dyrvold, Anneli, 1970-
(författare)
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Difficult to read or difficult to solve? : The role of natural language and other semiotic resources in mathematics tasks
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- When students solve mathematics tasks, the tasks are commonly given as written text, usually consisting of natural language, mathematical notation and different types of images. This is one reason why reading and interpreting such texts are important parts of being mathematically proficient, at least within the school context. The ability utilized when dealing with aspects of mathematical text is denoted in this thesis as a mathematical reading ability; this ability is useful when reading mathematical language, for example, in task text. There is, however, a lack of knowledge of what characterizes this mathematical language, what students need to learn regarding the mathematical language, and exactly which mathematical language that tests should preferably assess. Therefore, the purpose of this thesis is to contribute to the knowledge of aspects of difficulty related to textual features in mathematics tasks. In particular, one aim is to distinguish between a difficulty that has to do with a mathematical ability and another that has not. Different types of text analyses are utilized to capture textural features that might be demanding for the students when reading and solving mathematics tasks. Aspects regarding vocabulary are investigated both in a literature review and in a study where corpora are used to analyse word commonness. Other textual analyses focus on textual features that concern mathematical notation and images, besides natural language. Statistical methods are used to analyse potential relations between the textual features of interest and both task difficulty and task demand on reading ability. The results from the research review are sparse regarding difficult vocabulary, since few of the reviewed studies analyses word aspects separately. Several of the analysed textual features are related to aspects of difficulty. The results show that tasks with more words that are uncommon both in a mathematical context and in an everyday context, may favour students with good reading ability rather than students with good mathematical ability. Another textual feature that is likely to be demanding for students, is if the task texts contains many meaning relations, for example, when several words refer to the same or similar object. These results have implications for the school practice both regarding textual features that are important from an educational perspective and regarding the construction of tests. The research does also contribute to an understanding of what characterizes a mathematical language.
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| 10. |
- 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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| 11. |
- 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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| 12. |
- 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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| 13. |
- Dyrvold, Anneli, 1970-
(författare)
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Läsa matematik eller matematisk läsning?
- 2017
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Ingår i: Dyslexi. - Stockholm : Svenska Dyslexiföreningen. - 1401-2480. ; 22:3, s. 18-23
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Artikeln belyser olika aspekter av förhållandet mellan matematik och språk. En viktig poäng är att dessa båda inte bör ses som åtskilda. Att behärska ämnet matematik innebär även att behärska ämnets språk. Således utgår artikeln från en förståelse av ämnesspråket som en del av matematiken, inte enbart som ett verktyg för att kommunicera matematik.
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| 14. |
- 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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| 15. |
- 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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| 16. |
- Dyrvold, Anneli, 1970-
(författare)
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Relations between various semiotic resources in mathematics tasks : a source of students’ difficulties
- 2020
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Ingår i: Research in Mathematics Education. - : Routledge. - 1479-4802 .- 1754-0178. ; 22:3, s. 265-283
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Tidskriftsartikel (refereegranskat)abstract
- Tackling mathematics tasks often involves reading and interpreting different semiotic resources such as natural language (words), mathematical notation, and images. This study aims to enhance knowledge of how meaning relations, in the form of “cohesive ties” between and within different semiotic resources, are related to how difficult it is to read and solve mathematics tasks. Using 133 tasks from PISA mathematics tests and 354 tasks from the annual Swedish National Test in mathematics, statistical analyses found relations between the presence of different types of cohesive ties and measures of how difficult the tasks were to read and solve. The results reveal a difficulty aspect related to the extent to which a task has cohesive ties, of any kind, and that non-mathematics-specific reading demand is not part of this difficulty aspect. An implication is that mathematics teaching should also focus on the identification of cohesive relations in the text of tasks.
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| 17. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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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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Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 11:3, s. 103-131
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Tidskriftsartikel (refereegranskat)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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| 18. |
- Dyrvold, Anneli, 1970-
(författare)
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The mathematics in the taskstext
- 2017
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Ingår i: PME 41. Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education. - Singapore. - 9789811137426 ; , s. 2-289-2-296
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Konferensbidrag (refereegranskat)abstract
- This study focuses on textual features that can be demanding in the reading of mathematics tasks. Two types of qualitative analyses are conducted on a few tasks to explore and evaluate what some previous statistical relations between particular textual features and the tasks reading demand stand for. First, the type of progression between the content represented as natural language is analysed. Second, the interaction between all semiotic resources of the text (i.e. natural language, mathematical notation, and images) is analysed. Preliminary results indicate that a reading demand that is unwanted in mathematics tasks seems to be related to features of the natural language but not to interaction between words and images or mathematical notation.
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| 19. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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The role of dynamic elements in digital teaching platforms : an investigation of students' reading behaviour
- 2022
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Ingår i: 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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Konferensbidrag (refereegranskat)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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| 20. |
- Dyrvold, Anneli, 1970-
(författare)
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The role of semiotic resources when reading and solving mathematics tasks
- 2016
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Ingår i: Nordisk matematikkdidaktikk, NOMAD. - Gothenburg : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 21:3, s. 51-72
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Tidskriftsartikel (refereegranskat)abstract
- One part of being proficient in mathematics is to be able to read and solve mathematics tasks where mathematics is represented using different semiotic resources (i.e. natural language, mathematical notation, and different types of images). In the current study, statistical methods are used to investigate the potential meaning that the presence and co-occurrences of semiotic resources have for how demanding a mathematical task is to read and solve. The results reveal that the number of different semiotic resources in a mathematical task is not related to difficulty, but that difficulty is related to the particular combinations of semiotic resources where pictorial images are one of the resources. The results also indicate that the difficulty related to these semiotic characteristics is not related to an unnecessary reading demand.
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| 21. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Uncommon vocabulary in mathematical tasks in relation to demand of reading ability and solution frequency
- 2015
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Ingår i: Nordisk matematikkdidaktikk. - Göteborg : NMC Nationellt centrum för matematikutbildning. - 1104-2176. ; 20:1, s. 101-128
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Tidskriftsartikel (refereegranskat)abstract
- This study reports on the relation between commonness of the vocabulary used in mathematics tasks and aspects of students’ reading and solving of the tasks. The vocabulary in PISA tasks is analyzed according to how common the words are in a mathematical and an everyday context. The study examines correlations between different aspects of task difficulty and the presence of different types of uncommon vocabulary. The results show that the amount of words that are uncommon in both contexts are most important in relation to the reading and solving of the tasks. These words are not connected to the solution frequency of the task but to the demand of reading ability when solving the task.
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| 22. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Using heat maps from eye tracking in stimulated recall interviews
- 2022
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Ingår i: The relation between mathematics education research and teachers’ professional development. - 9789198402452 ; , s. 133-133
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)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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| 23. |
- Dyrvold, Anneli, 1970-
(författare)
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Which textual features are difficult when reading and solving mathematical tasks? : Questions of Theme and Rheme
- 2016
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Ingår i: Proceedings of the 40th Conference of the International Group for the psychology of Mathematics Education. - : International Group for the Psychology of Mathematics Education. - 9781365455063 ; , s. 150-150
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Konferensbidrag (refereegranskat)abstract
- In this study a combination of statistical and qualitative methods are used to explore the potential role the presence of, and interaction between, different semiotic resources have for how difficult mathematics tasks are to read and solve. The semiotic resources of interest are natural language, mathematical notation, and different types of images. Two different dependent variables are used: one that explains a general task difficulty and one that explains the tasks demand on a general reading ability. T-tests have revealed that tasks with four particular combinations of semiotic resources are solved to a significantly lower frequency than other tasks. Moreover, chi-square tests reveal that the same tasks are overrepresented in the group of tasks for which a general reading ability is not beneficial to use in the solving process. The results of those statistical tests do however only contribute an understanding of what presence of and cooccurrences of particular semiotic resources mean for the reading and solving of mathematics tasks.The second step in this study is therefore a qualitative analysis of a few tasks from two particular groups of tasks identified in the statistical analyses, namely i) tasks that are more difficult to solve and for which a general reading ability is not beneficial to use, and ii) tasks for which a general reading ability is highly beneficial to use in the solving process. The purpose of the qualitative analysis is to explore relations within and between the semiotic resources in tasks that are identified as extremes in the statistical tests (the ones mentioned above). Therefore the method for the qualitative analyses is based on theory about texture (Liu & O'Halloran, 2009) and Kress’ concepts translation and transduction (Kress, 2010). The results will contribute to an understanding of the role that multisemiotic features in task text have for aspects of task difficulty.
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| 24. |
- Dyrvold, Anneli, 1970-
(författare)
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Which textual features are difficult when reading and solving mathematics tasks?
- 2017
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Ingår i: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10). - Dublin : Dublin City University. - 9781873769737 ; , s. 1412-1413
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Konferensbidrag (refereegranskat)abstract
- Despite the digital revolution much of the mathematics practiced in schools is still tightly bound to two-dimensional texts. This emphasis on text is neither surprising, nor inadequate, since mathematics has developed through a long history with the use of written text, consisting of natural language, mathematical notation and images. Natural language is our native language consisting of letters and words (see e.g., www.oed.com). Different features of the mathematics text are also important in written tests, since reading the text is part of the assessment. If the text is hard to read, that difficulty can be relevant as part of assessing the communicative competence in mathematics. Crucial is, however, whether potentially difficult textual features are part of what the assessment aims at. This issue is investigated in the current study, using a synthesis of statistical results and qualitative analyses of task text.
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| 25. |
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| 26. |
- Ribeck, Judy, 1982-, et al.
(författare)
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Subject Language in mathematics textbooks : Verbal text fragments supplemented by other semiotic resources
- 2019
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Ingår i: ECER 2019 Conference Programme.
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Konferensbidrag (refereegranskat)abstract
- Different subjects have developed their own ways to construe meaning. To be able to convey the message, specific linguistic means are used in particular ways depending on the subject. The subject language in mathematics is characterized by the utilization of verbal language together with the semiotic resources mathematical notation and images. Each semiotic resource contribute to different functions of language and one resource can modulate the meaning made by another resource. Thus, adding one semiotic resource enhances the affordances of the other, a phenomenon referred to as meaning multiplication(e.g., Lemke, 1998). The intricacy of how the semiotic resources can be used together is indeed an asset, but at the same time this intricacy increases the demand on the reader. There are several reasons why students of mathematics must appropriate the subject language and learn to read mathematics. For example, language not only determines what is possible to communicate within a subject, but also modulates the way we think (e.g., Pederson, Danziger, Wilkins, Levinson, Kita, & Senft, 1998). In addition, texts with multiple semiotic resources are an important means to enhance students’ conceptual knowledge (e.g., Kilpatrick, Swafford, & Findell, 2001). Important contributions have been made to characterize the subject language in mathematics (e.g., Morgan & Tang, 2016; O'Halloran, 2005), but much is still unknown or needs further analysis. There are also features about the subject language in mathematics that are taken for true, but for which the empirical evidence is weak (Österholm, & Bergqvist, 2013). Since knowledge about the particular features of a subject language is a prerequisite for teaching the subject, there is a need to develop our understanding about how we communicate in mathematics to solidify the basis on which language-conscious mathematics teaching must be built. One distinguishing feature of printed mathematics texts is the mixture of mathematical notation and words, even in short fragments of text (Ribeck, 2015). In this study, we aim at characterizing the subject language in mathematics by linguistically analysing such verbal text fragments(hereafter referred to as VTFs), sorting out how the totality of semiotic resources interact to make the message complete. The categories taken into account in the analysis concern information structure (i.e. Theme and Rheme) and semantic roles (i.e. Participant, Process and Circumstance). In line with this focus, the following research questions are posed: RQ 1) What characterizes VTFsin mathematics textbooks regarding their linguistic content?RQ 2) What role do VTFs and the semiotic resources mathematical notationand imagestake in relation to each other to make the message complete?The analysis of relations between the different semiotic resources is based on a functional perspective on language, with a particular focus on means that are used to create a mental representation of reality. Royce’s (2007) framework for intersemiotic complementarity between the semantic categories Process, Participantand Circumstance is used. Intersemiotic complementarity is a concept that catches how the means of different semiotic resources in a text interact to provide a coherent message. Since mathematical notation is an important resource in mathematics texts the framework is modified to include also mathematical notation (cf. Dyrvold, 2016). In addition, we use the notion of Theme and Rheme (Halliday 1994), which is seen as crucial to the organisation and construal of meaning from a reader’s perspective.MethodThe data used in this study builds upon previous results from Ribeck (2015), where VTFs are automatically extracted from a corpus of 5.2 million words originating from Swedish secondary and upper secondary textbooks. For every word in the VTFs, a parser has added information about part of speech and syntactic function. In the current study these VTFs are analysed quantitatively and qualitatively. Two different analyses are conducted, each relating to one research question. The first step aims at identifying the most common types of VTFs. Here, the VTFs are coded and analysed for their linguistic characteristics. This quantitative analysis will reveal patterns among the VTFs as to what information they convey. In the next step, the common VTFs that have been identified are analysed in relation to the other semiotic resources. The focus is laid on how meaning is construed around Themes and Rhemes and the means used to obtain cohesion between Participants, Processes and Circumstances represented by the different semiotic resources. In the analysis of the thematic progression between Themes and Rhemes (see e.g., Danes, 1974) the role of the VTFs is taken as the starting point for the message that is construed in the text. Thereafter, the roles of all semiotic resources are included in the analysis to describe the information structure throughout the text. The analysis of cohesion between Participants, Processes and Circumstances is bidirectional; first potential cohesive relations to other semiotic resources indicated by the VTFs are analysed, second the content represented by the other semiotic resources are analysed in relation to the VTFs.Expected OutcomesThis study is expected to contribute knowledge about a particular feature that distinguishes the mathematical subject language from other subject languages in natural and social sciences, namely its substantial share of VTFs (cf. Ribeck, 2015). The utilization of two different analyses enables us to elucidate the subject language of mathematics from different point of views. It may be argued that verbal language in multimodal texts only makes sense in their context, and consequently is not meaningful to analyse separately. However, the VTFs are present in the textbooks and the reader needs an understanding of their textual function. Thus, we argue that a deepened understanding of the separate semiotic resources is a necessary first step towards understanding the intricacy in how they together construe subject-specific meaning. The analysis of the role of the VTFs in relation to the other semiotic resources is expected to offer a rich understanding of a crucial characteristic of the subject language in mathematics, namely how the semiotic resources complement each other. The combination of resources may either be necessary for a particular message or redundant to each other, something that will be highlighted by the bidirectional analysis. The results will contribute to characterize the subject language in mathematics, which is necessary to plan and implement teaching that strengthen students’ language competence.ReferencesDanes, F. (1974). Functional Sentence Perspective and the organization of the text. In F. Danes (ed.). Papers on Functional Sentence Perspective, (pp.106-28). The Hague: Mouton. Dyrvold, A. (submitted and preprint). Relations between various semiotic resources in mathematics tasks – a possible source of students’ difficulties. In Dyrvold, A. (2016). Difficult to read or difficult to solve? The role of natural language and other semiotic resources in mathematics tasks. Diss. Umeå universitet: institutionen för matematik och matematisk statistik. Halliday, M.A.K. (1994) An introduction to functional grammar. 2nd ed. London: Edward Arnold. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Lemke, J. L. (1998). Multiplying Meaning: Visual and verbal semiotics in scientific text In J. R. Martin & R. Veel (Eds.), Reading Science (pp. 87-113). London: Routledge Morgan, C. & Tang, S. (2016). To what extent are students expected to participate in specialised mathematical discourse? Change over time in school mathematics in England, Research in Mathematics Education, 18:2, 142-164, doi: 10.1080/14794802.2016.1174145 O'Halloran, K. (2005). Mathematical Discourse: Language, symbolism and visual images. London: Continuum. Pederson, E., Danziger, E. Wilkins, D., Levinson, S., Kita, S., & Senft, G. (1998). Semantic typology and spatial conceptualization. Language, Vol. 74, No. 3 (Sep., 1998), pp. 557-589 Published by: Linguistic Society of America. Royce, T.D. (2007). Intersemiotic Complementarity: A framework for multimodal discourse analysis. In Royce, T. & W. Bowcher, New Directions in the Analysis of Multimodal Discourse, New York: Routledge, 2007, pp. 63-109 Ribeck, J. (2015). Step by step. A computational analysis of Swedish textbook language. Diss. University of Gothenburg: Department of Swedish. 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 ‐ The International Journal on Mathematics Education, 45 (5), 751‐763.
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| 27. |
- Teledahl, Anna, 1972-, et al.
(författare)
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Support in relation to problem solving – building a common knowledge base?
- 2022
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Ingår i: The relation between mathematics education research and teachers’ professional development. - 9789198402452 ; , s. 117-120
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Konferensbidrag (refereegranskat)abstract
- We present three closely related projects concerned with supporting students’ mathe-matical problem solving. The projects build on the assumption that problem solving activities are beneficial to students’ learning but challenging for teachers to organise. Teachers must find ways to support students’ progress in problem solving without removing necessary challenges. The projects deal with this support in different ways, something we intend to use to illustrate the risk that mathematics education research becomes fragmented, making it more difficult for teachers to access and use research results in their professional development. We welcome participants to discuss how closely related research projects like ours can collaborate and complement each other to contribute to a knowledge base that is accessible and useful to teachers.
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| 28. |
- Österholm, Magnus, et al.
(författare)
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The study of difficult vocabulary in mathematics tasks : a framework and a literature review
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The purpose of this study is to contribute to the methodology of research on difficult vocabulary in mathematics tasks. The contribution consists of a framework for the study of difficult vocabulary in mathematics tasks and a literature review of empirical research in the area. The framework includes five main aspects of word difficulty that have been examined in empirical studies and discuss these in the light of theories on reading comprehension. In addition, methodological issues are presented in relation to each main aspect. The literature review examines both methodological aspects of 36 reviewed articles, and synthesizes results on difficult vocabulary. The literature review shows that a commonly used method—to study several word aspects together—is very unfortunate from the perspective of building accumulative knowledge about difficult vocabulary in mathematics tasks. The only well-supported conclusion possible to draw from the synthesis of results from the empirical studies, is that some word aspects are not related to task difficulty.
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