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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.

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. 

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 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.

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…”).

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.

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.

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.

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. 

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.