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Från design till meningsskapande: En multimodal studie om elevers arbete med matematikläroböcker i årskurs 1
Mid Sweden University, Faculty of Human Sciences, Department of Education.ORCID iD: 0000-0003-3009-3159
2020 (Swedish)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis examines students’ work with mathematics textbooks in Year 1 (students aged 7–8 years) of Swedish elementary school. The aim of this thesis was to contribute knowledge about and an understanding of how students make meaning in their work with mathematics textbooks. Central to the thesis was the textbook’s designed meaning potentials, or the meaning potential needed to solve the exercise as designed, as well as the students’ meaning-making when working with the textbooks. With regard to the students’ meaning-making, interest is directed first, to the students’ specific meaning-making in the work with the textbook and second, to the students’ opportunities to take agency in the work with the textbook. This thesis was delimited to the area of subtraction in both printed and digital mathematics textbooks. The theoretical point of departure for this thesis was a design-oriented multimodal perspective (Selander & Kress, 2010). Interest was directed to the various resources for communication, or modes (e.g. Kress, 2010), in the mathematics textbook, such as images, mathematical symbols, moving images, writing and speech. Two studies were conducted: Study 1, Multimodal textbook analysis and Study 2, Students’ meaning-making. Two analyses were made in Study 1. The first was a descriptive textbook analysis mapping out the modes and subtraction in all Swedish Year 1 textbooks, totaling 17 textbook series, both digital and printed, and approximately 1,700 pages. That analysis was followed by a multimodal qualitative textbook analysis of 2–4 exercises from each textbook series according to its designed meaning potential. Study 2 examined the students’ work with mathematics textbooks. The data that formed the basis for the analysis were textbook pages, the teacher’s guides to the used mathematics textbook series, video material of 18 Year 1students’ work with these pages and representations in the form of studentresponses. The analysis involved a multimodal approach focusing on what mathematical content the exercises were designed to offer and what the stu-dents discovered when working with the mathematics textbook.Two articles were written based on Study 1 (Articles I and II), and two were written based on Study 2 (Articles III and IV). In addition to this, the data from Study 1 and the results from Study 2 were also analyzed using the concept of agency to further deepen the understanding of students’ meaning-making when working with mathematics textbooks. The results showed large differences between mathematics textbooks for Year1 in Sweden, regarding both how different modes are used and how subtraction is presented. The results also showed that the students’ work with mathematics textbooks differed. The students’ meaning-making was sometimes based on the designed meaning potential but sometimes not. Regarding images, the results showed that images could be particularly challenging for the students to interpret and that several students expressed that it was desirable to solve the exercises without using the images. The analysis using the concept of agency showed that exercises in which students could choose their working methods made it possible to take agency and that the students’ possibility for agency is affected by the prevailing notion that successful mathematics students do not use images but base their meaning-making on mathematical symbols. All in all, three conclusions were drawn. First, the mathematics textbook as a teaching resource could be developed, both printed and digital mathematics textbooks. Complexities can be detected more easily through greater awareness of modes as various forms of expression for the textbooks’ mathematics content. Second, the complexity of the students’ individual work with the mathematics textbook was highlighted. The students’ individual work should start from the basis of the exercise’s design, so that the students’ meaning-making can be directed to the designed meaning potentials. Third, for younger students to discover themselves as mathematical individuals, one must question the notions that mathematical symbols are the most important mode for young learners and that images are for those who find mathematics difficult. Based on these conclusions, questions can be raised concerning students’ potential for discovering themselves as mathematical individuals and whether the students’ self-discovery as mathematical individuals would differ if the mathematics textbooks more fully recognized students’ meaning-making using various modes. One question raised in relation to the students’ possibilities to take agency when working with mathematics textbooks concerned what knowledge is recognized in Year 1 mathematics textbooks. The results indicated that mathematical symbols already occupy a special position in Year 1. If modes other than mathematical symbols are more widely recognized as knowledge, then more young students will discover themselves as mathematical individuals.

Place, publisher, year, edition, pages
Sundsvall: Mittuniversitetet , 2020. , p. 126
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 317
Keywords [en]
Mathematics textbooks, Students’ Meaning-making, Multimodality, Meaning potential, Agency, Year 1, Subtraction
National Category
Pedagogical Work
Identifiers
URN: urn:nbn:se:miun:diva-38970ISBN: 978-91-88947-42-0 (print)OAI: oai:DiVA.org:miun-38970DiVA, id: diva2:1427593
Public defence
2020-05-29, Fälldinsalen, Sundsvall, 10:00 (Swedish)
Opponent
Supervisors
Note

Vid tidpunkten för disputationen var följande delarbeten opublicerade: delarbete I, III och IV (manuskript).

At the time of the doctoral defence the following papers was unpublished: paper I, III, and IV (manuscript).

Available from: 2020-05-08 Created: 2020-04-30 Last updated: 2020-05-08Bibliographically approved
List of papers
1. Exercise design in mathematics textbooks: The case of subtraction - A descriptive textbook analysis mapping out Swedish Year 1 textbooks
Open this publication in new window or tab >>Exercise design in mathematics textbooks: The case of subtraction - A descriptive textbook analysis mapping out Swedish Year 1 textbooks
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Mathematics textbooks are widely used teaching tools and are used by most students whostudy mathematics worldwide. In this descriptive textbook analysis, all Swedishmathematics textbooks for Year 1, both digital and printed, were mapped out according towhat resources for communication that are used. For delimitation, a focus on subtractionas an arithmetic operation was chosen. The result shows large differences between the 17textbook series, concerning both the type of subtraction exercise offered and the use ofdifferent resources for communication and learning such as writing, images, andmathematical symbols. Digital textbooks were largely similar to the printed textbooks,except for a tablet-based textbook. Altogether, subtraction is presented differently indifferent textbook series, and therefore, the choice of mathematics textbooks affects howsubtraction is offered.

National Category
Pedagogy
Identifiers
urn:nbn:se:miun:diva-38974 (URN)
Available from: 2020-04-30 Created: 2020-04-30 Last updated: 2020-05-04Bibliographically approved
2. Potential for Meaning Making in Mathematics Textbooks: A Multimodal Analysis of Subtraction in Swedish Year 1
Open this publication in new window or tab >>Potential for Meaning Making in Mathematics Textbooks: A Multimodal Analysis of Subtraction in Swedish Year 1
2019 (English)In: Designs for Learning, ISSN 1654-7608, Vol. 11, no 1, p. 52-62Article in journal (Refereed) Published
Abstract [en]

Textbooks are a common teaching tool widely used in children’s mathematical education. Comparativestudies of textbooks have focused on different aspects, such as content, mathematical symbols and so on.However, a multimodal approach to textbook research—that is, studying how writing, images, mathematicalsymbols, etc. interact—is sparse. This study analyses 40 exercises from 17 Swedish Year 1 (children7–8 years) textbooks using a multimodal approach with a focus on subtraction as an arithmetic operation.The aim was to describe and analyse how subtraction in Swedish Year 1 mathematics textbooks can beunderstood using a multimodal approach. The results show that it is sometimes possible to solve an exercisewithout focusing on the mathematical content that the exercise is designed to offer. Writing, images,mathematical symbols, speech and moving images are used differently within the same textbook andbetween textbooks. The results also show that there are considerable similarities between the exercisesin printed and digital textbooks, with some exceptions. The examples in the study indicate that three differentapproaches are needed when working with these exercises, which implies great complexity in children’smeaning making in their work with mathematics textbooks. This could negatively impact children’saccess to beneficial learning situations. Therefore, this study could contribute to a larger awareness ofthe complexity in question, which, by extension, may contribute to the development of beneficial learningsituations in mathematics education, especially regarding subtraction.

Keywords
meaning potential; modes; designs for learning; multimodality; mathematics textbooks; digital textbooks; printed textbooks; primary school; early years; subtraction
National Category
Pedagogy
Identifiers
urn:nbn:se:miun:diva-36236 (URN)10.16993/dfl.123 (DOI)
Available from: 2019-05-30 Created: 2019-05-30 Last updated: 2020-04-30Bibliographically approved
3. Children's meaning-making when working with mathematics textbooks: A multimodal study focusing on the designed and the discovered
Open this publication in new window or tab >>Children's meaning-making when working with mathematics textbooks: A multimodal study focusing on the designed and the discovered
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This article focuses on children’s meaning-making when working withmathematics textbooks. Central to this study is the space between what thetextbook is designed to offer and what is discovered by the child when workingwith the textbook. Using a multimodal approach, video transcripts from 18 Year 1(7-8 years) children working with seven different pages from their textbookswere analysed together with the children’s solutions to the exercises. The resultsshow that children use different approaches when working with the textbook, bothbetween exercises and also within the same exercise, and sometimes discover othercontent than the textbook was designed to offer. Sometimes, the design of anexercise, and the child’s meaning-making when working with the exercise, do notmatch. This mismatch between the designed and the discovered may deny childrenaccess to beneficial learning situations, unless children receive more support whenworking with mathematics textbooks.

Keywords
meaning-making, design, affordance
National Category
Pedagogical Work
Identifiers
urn:nbn:se:miun:diva-38975 (URN)
Available from: 2020-04-30 Created: 2020-04-30 Last updated: 2020-05-04Bibliographically approved
4. Communicating Mathematics through Images: A multimodal study of year 1 children's meaning-making when working with mathematics textbooks
Open this publication in new window or tab >>Communicating Mathematics through Images: A multimodal study of year 1 children's meaning-making when working with mathematics textbooks
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This article focuses on how children make meaning when working with images inmathematics textbooks in Swedish Year 1 (7–8 years). Images include the textbook images,but also children’s self-drawn images used as support for calculation. Focus was aimed at(1) what the images in the exercises were designed to offer and (2) what the childrendiscovered when working with them. The data material consisted of video transcripts of 18children’s work with exercises from mathematics textbooks dealing with subtraction. Theresults showed that the children sometimes discovered the designed affordance andsometimes did not. The children who discovered the designed affordance sometimes usedthe image when performing the calculations, while others did not. Some of the childrenexpressed that images in mathematics textbooks are for those who find mathematicsdifficult and that completing exercises without using the images was desired. Thechildren’s approaches to images were discussed in two specific cases: First, the children’sdesire to use mathematical symbols rather than images may lead to children not discoveringthe mathematics content that the exercise is designed to offer. Second, the use ofmathematical symbols rather than images may lead to children not discovering themselvesas mathematical individuals.

Keywords
meaning-making, design, affordance, images, mathematics textbooks
National Category
Pedagogical Work
Identifiers
urn:nbn:se:miun:diva-38976 (URN)
Available from: 2020-04-30 Created: 2020-04-30 Last updated: 2020-05-04Bibliographically approved

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