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- Bergqvist, Ewa, Docent, et al.
(författare)
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How mathematical symbols and natural language are integrated in textbooks
- 2020
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In mathematical text and talk, natural language is a constant companion to mathematical symbols. The purpose of this study is to identify different types of relations between natural language and symbolic language in mathematics textbooks. Here we focus on the level of integration. We have identified examples of high integration (e.g., when symbols are part of a sentence), medium integration (e.g., when the shifts between natural and symbolic language occurs when switching to a new line), and low integration (e.g., when symbols and written words are connected by the layout).
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| 4. |
- Theens, Frithjof, 1969-
(författare)
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Does language matter? : sources of inequivalence and demand of reading ability of mathematics tasks in different languages
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Practicing mathematics is not possible without the use of language. To communicate mathematical content, not only words in natural language are used but also non-verbal forms of communication such as mathematical symbols, graphs, and diagrams. All these forms of communication can be seen as part of the language used when doing mathematics. When mathematics tasks are used to assess mathematical competence, it is important to know how language can affect students’ possibility to solve the task. In this thesis, two different but related aspects of the relation between language and mathematics tasks are investigated. The first aspect concerns linguistic features of written mathematics task that can make the task more difficult to read and/or to solve. These features may result in unnecessary and unwanted reading demands, that is, the task then partially assesses students’ reading ability instead of their mathematical ability. The second aspect concerns differences between different language versions of mathematics tasks used in multilanguage assessments. These differences may cause inequivalence between the language versions, that is, the task may be more difficult to solve for students of one language group than students of another. Therefore, the purpose of this thesis is to investigate some of the effects that language can have on written mathematics tasks, in particular, on the validity of mathematics assessments. The thesis focuses on unnecessary reading demands and inequivalence in multilanguage assessments. The data in this thesis are obtained from tasks of the Programme for International Student Assessment (PISA) 2012. The task texts and the student results on these tasks are analyzed quantitatively to identify the occurrence and possible sources of unnecessary reading demands and inequivalence. Think-aloud-protocols and task-based interviews of students who had worked with some of the tasks, serve to qualitatively identify possible sources of reading demands and inequivalence, respectively.The results showed both unnecessary reading demands and inequivalence in some of the tasks. Some linguistic features were identified as possible sources of these reading demands, while others were not related to them. For example, sentence length was not related to reading demands of tasks in Swedish, whereas sentence structure was identified as a possible source of unnecessary reading demands. Some linguistic differences between different language versions of mathematics tasks were also identified as possible sources of inequivalence, and in addition there were curricular differences that were such potential sources. The findings of this thesis have implications for designing mathematics tasks both in one language and in multilingual settings. They may help to ensure validity of mathematics assessments, but also to make mathematics texts easier to understand for students in general.
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| 5. |
- Vingsle, Lotta, 1959-
(författare)
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Formative assessment : Teacher knowledge and skills to make it happen
- 2015
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Ingår i: Proceedings of the Ninth Conference of the European Society for Reseach in Mathematics Education (CERME9). - : European Society for Research in Mathematics Education. - 9788072908448 ; , s. 3172-3173
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Konferensbidrag (refereegranskat)abstract
- The study investigates a teacher's use of activities, knowledge and skills when conducting formative assessment during interaction in whole-class. This formative assessment practice includes eliciting information about student learning, interpreting the responses, and modifying teaching and learning activities based on elicited information. Results show that the teacher used activities that help students to engage in common learning activities and take co-responsibility for their learning. Furthermore, while orchestrating the activities the teacher used knowledge and skills that are complex, demanding and difficult.
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| 6. |
- Wikström Hultdin, Ulrika, et al.
(författare)
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Applying a new framework of connections between mathematical symbols and natural language
- 2023
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Ingår i: Journal of Mathematical Behavior. - : Elsevier. - 0732-3123 .- 1873-8028. ; 72
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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