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All texts are characterized by cohesive relations (see e.g., Halliday & Matthiessen,2014). In mathematical texts a facet of cohesion is networks of information between the various semiotic resources. A network is anchored by a central aspect introducing a theme relevant throughout an entire section of text. This anchoring expression isfollowed by different types of expansions of a concept, creating a cohesive network throughout the text. In this study, we focus on logical expansions as they express mathematical connections, and interpreting those are central to understandingmathematics. A logical expansion is expressed when a previously introduced centralaspect is justified, by a reason, condition, or comparison in another instance. The theoretical understanding of expansions has been developed from van Leeuwen’s (2005) work. When dynamic functions are introduced, new ways of representation are also introduced, which means that new ways to express logical expansions inmathematics may appear. On this basis, our aim is to explore how meaning is offeredto students via logical expansions in static and dynamic texts.

Mathematics text is multisemiotic and reading such texts is typically not linear due to the interrelation between the resources natural language, symbols and images (O’Halloran, 2015). The current research explores timeline analysis of student readingas a method to investigate how students connect different resources in the mathematical text, and thus which information is gained. The focus is laid on reading central aspects of mathematical concepts, expressed in different semiotic resources, and how the meaning is expanded throughout the text (e.g. see, van Leeuwen 2005). 

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.

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.

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.

Digital media offer new opportunities to visualise mathematics and to engage students in interactive activities. The launching of digital teaching platforms in mathematics has, however, been met with some hesitation, and printed textbooks still play a substantial role in classrooms. This study addresses questions about how affordances of the digital media are utilised in contemporary digital teaching platforms in mathematics. An analysis using a typology capturing variation in interactivity and dynamics reveals substantial influence from textbooks on the design of digital teaching platforms. Static features and lecture-like films are mainly used when new concepts are introduced; whereas interactive activities are most common in tasks. When it comes to mathematical processes, there is a tendency to use a combination of different types of elements when relations between mathematical objects are in focus, as opposed to when the focus is on “doing”, which indicates that digital features are utilised where most needed. The sparse use of dynamic and interactive features is discussed, and some suggestions are made for the development of digital teaching platforms.

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.