Mid Sweden University

Användningen av olika uttrycksformer är en central del inom matematik. I denna artikel beskriver författarna hur kontraster mellan uttrycksformer kan bli ett verktyg för bättre matematiklärande.

The use of different modes (e.g., words, mathematical symbols, images) is central to encounter different perspectives of the same mathematical idea, and a combination of different modes generally contribute to a deeper understanding, than each mode separately (O'Halloran, 2005). At the same time, research has shown that combinations of modes, e.g., in mathematical textbooks, are challenging for students to interpret (Norberg, 2019). This on-going study contributes to the fields understanding of the complexity of interplay between modes by using Engebretsen’s (2012) theory of the necessity of balance between cohesion and tension to analyse how modes are used when introducing new mathematical ideas in textbooks.We have delimited our analysis to the introduction of equality and of subtraction in three commonly used textbooks for first grade students. Figure 1 shows an example of an introduction of equality. In this example, we identified one type of cohesion between the use of circles (images) in two groups, the numerals with an equal sign between (symbols), and the words “equal numbers” and “is equal to” in the yellow box. These modes address the same objects in the same way, that is, there is cohesion. At the same time, there are no symbols present in the exercise below. Students should only circle an equal number of objects found in the picture. Thus, there is a type of tension between the yellow box and the exercise since the different modes do not have the same role in these different parts. Further analysis will identify different types of cohesion and tension between modes, before examining how these are handled by students.

This study aims to describe and analyze the literacy events that occur in school-age educare practice. Literacy in this article is seen as the social practice where people use reading, writing, meaning-making and communicative expressions in interaction with others, in particular in the informal context of everyday life. With the after-school activities as a context, many opportunities are provided for conversation and functional language use, thus creating good conditions for multilingual students’ language development. Observations were made of school-age educare teacher students in 68 after-school centres, and their reflections were collected. The article authors carried out the analysis of observation protocols and reflection protocols through thematic analysis. The results show a significant variation between the different school-age educare practices concerning literacy activities and access to books, in particular few books in languages other than Swedish. Furthermore, it turned out that both educators and children had a schooled view of reading and writing activities. We conclude that school-age educare centres have the potential as a literacy arena that can be utilized much more than this study has shown, especially to arouse students’ desire to read.

Syftet med denna studie är att beskriva och analysera de literacyaktiviteter som förekommer i fritidshemmets praktik. Literacy ses i denna artikel som den sociala praktik där människor använder läsning, skrivande, meningsskapande och kommunikativa uttryck i samspel med andra, särskilt i vardagens informella sammanhang. Med fritidshemmets aktiviteter som kontext ges många möjligheter för samtal, funktionell språkanvändning och sålunda även goda förutsättningar för flerspråkiga elevers språkutveckling. Observationer gjordes av fritidshemslärarstudenter i 68 fritidshem och deras reflektioner samlades in. Analys av observationsprotokoll och reflektionsprotokoll genomfördes av artikelförfattarna genom tematisk analys, där de öppna svaren intog en viktig roll. Resultatet visar på en stor variation mellan de olika fritidshemmen avseende förekomst av literacyaktiviteter och tillgång till böcker, främst gällande böcker på andra språk än svenska. Vidare framgår att både pedagoger och barn hade en skolifierad syn på läs- och skrivaktiviteter. Vår slutsats är att fritidshemmet har en potential som literacyarena som kan utnyttjas i långt högre grad än vad denna studie visat, framför allt för att väcka elevers läslust.

This article focuses on students' meaning-making when working with mathematics textbooks from a multimodal approach that encompasses all resources for communication, which is an under researched area. Central to this study are the designed meanings of the textbooks and the affordances discovered by students when working with the textbooks. Video transcripts from 18 Year 1 (ages 7–8) students working with seven textbook pages were analysed. The results show that the designs of exercises are complex, that the students use different approaches when working with the textbook – from one exercise to another as well as within the same exercise – and that they sometimes discover content other than what the textbook was designed to offer. Conclusions drawn from this are that textbooks can be improved as learning tools – multimodal aspects of this are highlighted – and that more awareness of multimodality in mathematics teaching could support students' mathematical learning.

There is an increasing use of digital learning resources in mathematics education,which provides potential for multimodal approaches and new ways for students to meet and learn mathematics, but the outcome depends on the design and the implementation of the digital resources (Hoyles, 2018). This on-going study contributes by examining affordances of combinations of different modes in relation to number sense. We use Halliday’s social semiotic theory (Halliday & Matthiessen, 2013) and McIntosh et al.(1992) number sense framework for analysing a specific app, Vektor. We analysed the two exercises in the app that relate to aspects of number sense, Number pals and Number line. Each round in respective exercise was analysed with respect to Halliday’s three metafunctions: ideational, interpersonal, and textual. For the ideational function, McIntosh et al.’s framework was used to characterise the mathematical content. As an example, figure 1 illustrates the second and third rounds in Numberpals. In these rounds, both coloured rectangles and numerals are used to present the mathematics, and the main aspect of number sense in focus is identified as Multiple representations for numbers, for example, two red + three green = one red + four green, and 2+3=1+4. In the first round there were no numerals in the bars, only rectangles, and in the later rounds there were only numerals in the bars.Preliminary results, concerning the ideational metafunction, show that the mathematical object in focus may be perceived in different ways; either as just rectangles that should be combined (in a visual/geometrical sense), or as numbers of rectangles, or as numbers (and relations between numerals). This can impact students’ development of number sense. Further analyses will include all metafunctions and a focus on progression in the exercises. 

Denna rapport utgör ett resultat från projektet ”Matematik-app för elever och lärare”, som var en samverkan mellan Mittuniversitetet och Örnsköldsviks kommun. I detta projekt genomfördes en utvärdering av matematikappen Vektor, både ur elevperspektiv och lärarperspektiv. Det övergripande syftet med projektet var att bidra till en utveckling av matematikundervisningen för yngre elever, från förskoleklass till årskurs 3 (F-3). Analyser genomfördes som fokuserade på hur appen kan användas som stöd för elevers lärande kring tallinjen och taluppfattning samt hur appen kan användas som stöd för lärares arbete med planering och utveckling av undervisningen kring detta matematikinnehåll. Resultaten påvisar flera möjligheter till att använda appen i matematikundervisningen men att det också finns vissa spänningar mellan appens egenskaper och lärares behov. Detta leder till att lärarna inte använder appen utifrån instruktionerna som anges av appens tillverkare, utan de gör visst motstånd och anpassar användningen.

Denna rapport har granskats och diskuterats på ett högre seminarium inom Nätverk för Ämnesdidaktisk forskning i Matematik och Naturvetenskap (NÄMN) vid Mittuniversitetet.

This article focuses on how Swedish Year One students (age 7–8) make meaning when working with images in mathematics textbooks. Images include textbook images, but also students’ self-drawn images used as support for calculation. The focus was (1) what the images in the exercises were designed to offer (the designed affordance), and (2) what the students discovered when working with them. The data material consisted of video transcripts of 18 students working with subtraction exercises from mathematics textbooks. The results showed that the students sometimes discovered the designed affordance and sometimes did not. The students who discovered the designed affordance sometimes used the image when performing the calculations, while others did not. Some students expressed that images in mathematics textbooks are for those who find mathematics difficult, and that completing exercises without using the images was desired. The students’ approaches to images were discussed in two specific cases: First, the students’ desire to use mathematical symbols rather than images may lead to students not discovering the mathematics content that the exercise is designed to offer. Second, the use of mathematical symbols rather than images may lead to students not discovering themselves as mathematical individuals.

Mathematics textbooks are teaching tools used by most students studying mathematics worldwide. In this descriptive textbook analysis, all Swedish mathematics textbooks for Year 1, both digital and printed, were mapped out according to the resources used for communication. For delimitation, a focus on subtraction as an arithmetic operation was chosen. The result shows large differences between the 17 textbook series, concerning both the type of subtraction exercises offered and the use of different resources for communication and learning, such as writing, images, and mathematical symbols. Digital textbooks were largely similar to the printed textbooks, except for one tablet-based textbook. Altogether, the study shows that the choice of mathematics textbooks affects how subtraction is presented to students and, by extension, the learning situations students encounter when working with mathematics textbooks.