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Between symbols and words: structural connections in mathematics texts and their effect on reading
Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.ORCID iD: 0000-0003-4777-7629
2024 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Mellan symboler och ord : om strukturella kopplingar i matematiktexter och hur dessa kan påverka läsningen (Swedish)
Abstract [en]

While students progress through their school years, they are expected to develop reading skills in all academic subjects, including mathematics. Mathematics texts, being multisemiotic, require readers to make meaning not only from written language but also from mathematical symbols and visualizations. Integrating content presented through different sign systems is essential for creating coherence. Thus, the organizational structure of these texts becomes critically important when designing texts for learning. The purpose of this thesis is to build knowledge of the organization of mathematical symbols and written language, and to achieve better understanding of how this organization influences the reading of mathematics texts. 

First, the structural connections between mathematical symbols and written language in mathematics texts designed for students are characterized. Five distinct categories of such connections—Interwoven, Chunked, Marked, Adjoined, and Referenced—are identified, ranging from connections in which mathematical symbols are integrated into sentences (Interwoven), to those based solely on the proximity between two text sequences (Adjoined). The prevalence of these connection categories in textbooks from different school levels is also investigated. The results indicate a progression in the use of structural connections, with a shift from reliance on proximity in early school years towards a preference for symbols interwoven in sentences between years 2 and 5, suggesting that all students eventually need to navigate texts with interwoven symbols. Additionally, changes can be seen in how symbols are being connected to more detailed meanings. Second, the reading of mathematics texts employing two distinct text designs inspired by the new framework is compared: one design features only sentences with interwoven symbols, whereas the other uses a graphic to highlight key connections between symbols and words. The reading processes and experiences of students are investigated by analyzing gaze measurements and interviews. The results indicate that the two designs have different advantages depending on the situation. While the graphic design can facilitate reading and interpretation by drawing attention to the connections between symbols and words, enabling quicker content matching, the symbols interwoven in sentences might provide better access to details or allow more efficient reading in other contexts. Moreover, individual differences in processing and experiences were noted: while some readers benefitted from the graphic design, others did not. Yet, as reading becomes more complex, the graphic is increasingly appreciated. It is concluded that while readers generally prefer text designs that enhance readability, the optimal design varies based on the reader and the context. The discussion includes what text design benefits whom and under what circumstances. 

Place, publisher, year, edition, pages
Umeå: Umeå University, 2024. , p. 117
Series
Umeå Studies in the Educational Science, ISSN 2004-8890, E-ISSN 2004-8661 ; 68
Keywords [en]
text organization, reading mathematics, multimodality, semiotic resources, text design, textbooks, diciplinary literacy, inter-semiotic connections, sign systems
Keywords [sv]
matematikläroböcker, teckensystem, semiotiska resurser, multimodalitet, intersemiotiska kopplingar
National Category
Didactics Mathematics
Research subject
didactics of mathematics
Identifiers
URN: urn:nbn:se:umu:diva-223461ISBN: 9789180703796 (print)ISBN: 9789180703802 (electronic)OAI: oai:DiVA.org:umu-223461DiVA, id: diva2:1852181
Public defence
2024-05-16, Hörsal NAT.D.320, Naturvetarhuset, Umeå, 09:00 (English)
Opponent
Supervisors
Available from: 2024-04-25 Created: 2024-04-17 Last updated: 2024-05-06Bibliographically approved
List of papers
1. Applying a new framework of connections between mathematical symbols and natural language
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2023 (English)In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 72, article id 101097Article in journal (Refereed) Published
Abstract [en]

A reader of mathematical text must often switch between reading mathematical symbols and reading words. In this study, five different categories of structural connections between symbols and language, which invite such switches, are presented in a framework. The framework was applied in a study of Swedish mathematics textbooks, where 180 randomly selected pages from different educational stages were analyzed. The results showed a significant change in communication patterns as students progress through school. From a predomination of connections based on proximity found in year two, there is a gradual change to a predomination of symbols interwoven in sentences in year eight. Furthermore, more qualitative investigations of the different connections complemented the quantification, both through further explanations of the quantitative results, and through more examples of differences in communication patterns. The implications for readers of mathematics texts are discussed.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Inter-semiotic connections, Mathematical communication, Mathematical notation, Multimodal communication, Semiotic resources, Spatial connections
National Category
Didactics Other Mathematics
Identifiers
urn:nbn:se:umu:diva-214590 (URN)10.1016/j.jmathb.2023.101097 (DOI)2-s2.0-85170711454 (Scopus ID)
Funder
Swedish Research Council, 2017-03577
Available from: 2023-09-28 Created: 2023-09-28 Last updated: 2024-04-17Bibliographically approved
2. How words are used in textbooks to specify referents for mathematical symbols
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(English)Manuscript (preprint) (Other academic)
National Category
Didactics
Identifiers
urn:nbn:se:umu:diva-223527 (URN)
Available from: 2024-04-18 Created: 2024-04-18 Last updated: 2024-04-18Bibliographically approved
3. How the organization of mathematical symbols and written language affect reading and learning: students’ perceptions and preferences
Open this publication in new window or tab >>How the organization of mathematical symbols and written language affect reading and learning: students’ perceptions and preferences
(English)Manuscript (preprint) (Other academic)
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:umu:diva-223528 (URN)
Available from: 2024-04-18 Created: 2024-04-18 Last updated: 2024-04-19
4. Students’ reception of two alternative arrangements of mathematical symbols and words in task texts
Open this publication in new window or tab >>Students’ reception of two alternative arrangements of mathematical symbols and words in task texts
(English)In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028Article in journal (Refereed) Accepted
Place, publisher, year, edition, pages
Elsevier
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:umu:diva-223529 (URN)
Available from: 2024-04-18 Created: 2024-04-18 Last updated: 2024-04-19

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Wikström Hultdin, Ulrika

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