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  • 1.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Bergqvist, Tomas
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Social Sciences, Department of applied educational science.
    Vingsle, Lotta
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Wikström Hultdin, Ulrika
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    How mathematical symbols and natural language are integrated in textbooks2020Conference paper (Other academic)
    Abstract [en]

    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).

  • 2.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Bergqvist, Tomas
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Social Sciences, Department of applied educational science.
    Vingsle, Lotta
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Wikström Hultdin, Ulrika
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    How mathematical symbols and natural language are used in teachers’ presentations2020Conference paper (Other academic)
    Abstract [en]

    In this study, we examine how the use of natural language varies, considering the symbolic language in procedural and conceptual aspects of mathematics.

  • 3.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Dyrvold, Anneli
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Relating vocabulary in mathematical tasks to aspects of reading and solving2012In: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar, Umeå, January 24-25, 2012 / [ed] Christer Bergsten, Eva Jablonka & Manya Raman, Linköping: SMDF , 2012, p. 61-70Conference paper (Refereed)
    Abstract [en]

    This paper focuses on relationships between vocabulary in mathematical tasks and aspects of reading and solving these tasks. The paper contains a framework that highlights a number of different aspects of word difficulty as well as many issues to consider when planning and implementing empirical studies concerning vocabulary in tasks, where the aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.

  • 4.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Dyrvold, Anneli
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Relating vocabulary in mathematical tasks to aspects of reading and solving2012In: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar, Umeå, January 24-25, 2012 / [ed] Christer Bergsten, Eva Jablonka & Manya Raman, Linköping: SMDF , 2012, p. 61-70Conference paper (Refereed)
    Abstract [en]

    This paper focuses on relationships between vocabulary in mathematical tasks and aspects of reading and solving these tasks. The paper contains a framework that highlights a number of different aspects of word difficulty as well as many issues to consider when planning and implementing empirical studies concerning vocabulary in tasks, where the aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.

  • 5.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Jonsson, Bert
    Umeå University, Faculty of Social Sciences, Department of applied educational science. Umeå University, Faculty of Social Sciences, Department of Psychology.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    The processing of mathematical symbols in working memory2020Conference paper (Other academic)
    Abstract [en]

    This empirical study examines how different types of symbols, familiar and unfamiliar, are processed in working memory; phonologically and/or visuo-spatially.

  • 6.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Theens, Frithjof
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Linguistic properties of PISA mathematics tasks in different languages2016In: ICT in mathematics education: the future and the realities: Proceedings of MADIF 10: the tenth research seminar of the Swedish Society for Research in Mathematics Education Karlstad, January 26–27, 2016 / [ed] Häggström, Johan; Norén, Eva; van Bommel, Jorryt; Sayers, Judy; Helenius, Ola; Liljekvist, Yvonne, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2016, p. 147-147Conference paper (Refereed)
    Abstract [en]

    The mathematics PISA tasks are primarily supposed to measure mathematical ability and not reading ability, so it is important to avoid unnecessary demands of reading ability in the tasks. Many readability formulas are using both word length and sentence length as indicators of text difficulty. In this study, we examine differences and similarities between English, German, and Swedish mathematics PISA tasks regarding word length and sentence length. We analyze 146 mathematics PISA tasks from 2000–2013, in English, German, and Swedish. For each task we create measures of mean word and sentence length. To analyze if there are any differences between the three language versions of the tasks, we use t-tests to compare the three languages pairwise. We found that in average, the German versions have the longest words, followed by Swedish and then English. Average sentence length was highest for English, followed by German and then Swedish.

  • 7.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Theens, Frithjof
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Relations between linguistic features and difficulty of PISA tasks in different languages2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged, Hungary: PME , 2016, Vol. 1, p. 125-125Conference paper (Refereed)
  • 8.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Theens, Frithjof
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Department of Mathematics and Science Education, Mid Sweden University, SE-85170, Sundsvall, Sweden.
    The role of linguistic features when reading and solving mathematics tasks in different languages2018In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 51, p. 41-55Article in journal (Refereed)
    Abstract [en]

    The purpose of this study is to deepen the understanding of the relation between the language used in mathematics tasks and the difficulty in reading and solving the tasks. We examine issues of language both through linguistic features of tasks (word length, sentence length, task length, and information density) and through different natural languages used to formulate the tasks (English, German, and Swedish). Analyses of 83 PISA mathematics tasks reveal that tasks in German, when compared with English and Swedish, show stronger connections between the examined linguistic features of tasks and difficulty in reading and solving the tasks. We discuss if and how this result can be explained by general differences between the three languages.

  • 9.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    A theoretical model of the connection between the process of reading and the process of solving mathematical tasks2010In: Mathematics and mathematics education: Cultural and social dimensions. Proceedings of MADIF 7 / [ed] C. Bergsten, E. Jablonka & T. Wedege, Linköping, Sweden: Svensk förening för matematikdidaktisk forskning, SMDF , 2010, p. 47-57Conference paper (Refereed)
    Abstract [en]

    In this paper we suggest a theoretical model of the connection between the process of reading and the process of solving mathematical tasks. The model takes into consideration different types of previous research about the relationship between reading and solving mathematical tasks, including research about traits of mathematical tasks (a linguistic perspective), about the reading process (a psychological perspective), and about behavior and reasoning when solving tasks (a mathematics education perspective). In contrast to other models, our model is not linear but cyclic, and considers behavior such as re-reading the task.

  • 10.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Monash University, Australia.
    Communicating mathematics or mathematical communication?: An analysis of competence frameworks2012In: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education: Vol. 2: opportunities to learn in mathematics education / [ed] Tai-Yih Tso, 2012, p. 67-74Conference paper (Refereed)
    Abstract [en]

    In this study we analyse the communication competence included in two different frameworks of mathematical knowledge. The main purpose is to find out if mathematical communication is primarily described as communication of or about mathematics or if it is (also) described as a special type of communication. The results show that aspects of mathematics are mostly included as the content of communication in the frameworks but the use of different forms of representation is highlighted both in the frameworks and also in prior research as a potential cause for characterising mathematical communication differently than "ordinary" communication.

  • 11.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Språkbrukets roll i matematikundervisningen2014In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 2014, no 1, p. 27-31Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Det språk vi använder oss av i matematikklassrummet kan fokuseras på många olika sätt. Språket är också nödvändigt att förhålla sig till vid utvecklingen av sitt matematiska tänkande. Författarna diskuterar här relationer mellan språk och lärande.

  • 12.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Variation of explicit argumentation in mathematics textbooks2017In: Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education / [ed] Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H., 2017, Vol. 1, p. 170-170Conference paper (Refereed)
  • 13.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Österholm, MagnusUmeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).Granberg, CarinaUmeå University, Faculty of Social Sciences, Department of applied educational science, Interactive Media and Learning (IML). Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).Sumpter, LovisaStockholms universitet.
    Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education2018Conference proceedings (editor) (Refereed)
  • 14.
    Bergqvist, Tomas
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Social Sciences, Department of applied educational science.
    Liljekvist, Yvonne
    Karlstads universitet.
    van Bommel, Jorryt
    Karlstads universitet.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Evaluation of a large scale professional development program: Vol 22017In: Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education / [ed] Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H., Singapore: The International Group for the Psychology of Mathematics Education , 2017, Vol. 2, p. 153-160Conference paper (Refereed)
    Abstract [en]

    This paper reports on a par of an evaluation of the professional development program (PDP) Boost for Mathematics in Sweden. Around 200 mathematics lessons were observed, and the teachers were interviewed after each lesson. The findings indicate that the PDP has had a significant impact on the teachers’ knowledge about the mathematical competencies as they are presented in the national curriculum documents, and that the teaching practice had improved and now gives the students better possibilities to develop the competencies. The results also show that these improvements are still present one year after the program had ended. 

  • 15.
    Dyrvold, Anneli
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Uncommon vocabulary in mathematical tasks in relation to demand of reading ability and solution frequency2015In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 20, no 1, p. 5-31Article in journal (Refereed)
    Abstract [en]

    This study reports on the relation between commonness of the vocabulary used in mathematics tasks and aspects of students’ reading and solving of the tasks. The vocabulary in PISA tasks is analyzed according to how common the words are in a mathematical and an everyday context. The study examines correlations between different aspects of task difficulty and the presence of different types of uncommon vocabulary. The results show that the amount of words that are uncommon in both contexts are most important in relation to the reading and solving of the tasks. These words are not connected to the solution frequency of the task but to the demand of reading ability when solving the task.

  • 16.
    Edmonds-Wathen, Cris
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Comparing mathematics tasks in different languages2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged, Hungary: PME , 2016, Vol. 1, p. 151-151Conference paper (Refereed)
  • 17.
    Edmonds-Wathen, Cris
    et al.
    Umeå University.
    Bergqvist, Ewa
    Umeå University.
    Österholm, Magnus
    Umeå University.
    Framework of linguistic properties to compare mathematics tasks in different languages2016In: ICT in mathematics education: the future and the realities: Proceedings of MADIF 10 The tenth research seminar of the Swedish Society for Research in Mathematics Education Karlstad, January 26–27, 2016 / [ed] Johan Häggström, Eva Norén, Jorryt van Bommel, Judy Sayers, Ola Helenius, Yvonne Liljekvist, Göteborgs universitet , 2016, p. 146-146Conference paper (Other academic)
    Abstract [en]

    This study aims to construct a framework of linguistic properties of mathematical tasks that can be used to compare versions of mathematics test tasks in different natural languages. The framework will be useful when trying to explain statistical differences between different language versions of mathematical tasks, for example, differences in item functioning (DIF) that are due to inherent properties of different languages. Earlier research suggests that different languages might have different inherent properties when it comes to expressing mathematics. We have begun with a list of linguistic properties for which there are indications that they might affect the difficulty of a task. We are conducting a structured literature review looking for evidence of connections between linguistic properties and difficulty. The framework should include information about each property including methods used to measure the property, empirical and/or theoretical connections to aspects of difficulty, and relevance for mathematical tasks.

  • 18. Helenius, Ola
    et al.
    Engström, ArneMeaney, TamsinNilsson, PerNorén, EvaSayers, JudyÖsterholm, MagnusUmeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Development of Mathematics Teaching: Design, Scale, Effects: Proceedings from Madif9: The Ninth Swedish Mathematics Education Research Seminar, Umeå, February 4-5, 20142015Conference proceedings (editor) (Refereed)
  • 19.
    Johansson, Helena
    et al.
    Department of Mathematics and Science Education, Mid Sweden University, Sundsvall, Sweden.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Department of Mathematics and Science Education, Mid Sweden University, Sundsvall, Sweden.
    Objectification of upper-secondary teachers’ verbal discourse in relation to symbolic expressions2019In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 56, article id 100722Article in journal (Refereed)
    Abstract [en]

    Research literature points to the importance of objectification when learning mathematics, and thereby in the discourse of mathematics. To increase the field’s understanding of aspects and degrees of objectification in various mathematical discourses, our study uses the combination of two sub-processes of objectification in order to analyse upper-secondary teachers’ word use in relation to any type of mathematical symbols. Our results show that the verbal discourse around symbols is very objectified. This can put high demands on students understanding of their teacher, since it might be needed that the students have reached a certain degree of objectification in their own thinking in order to be able to participate in a more objectified discourse. The results also show that there exist patterns in the variation of the degree of objectification, in particular that the discourse tends to be more objectified when more familiar symbols are used. This exploratory study also reveals several phenomena that could be the focus of more in-depth analyses in future studies.

  • 20.
    Sullivan Hellgren, Jenny
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Argumentation in university textbooks: comparing biology, chemistry and mathematics2017Conference paper (Refereed)
  • 21.
    Theens, Frithjof
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Linguistic features as possible sources for inequivalence of mathematics PISA tasks2018In: Perspectives on professional development of mathematics teachers: Proceedings of MADIF 11, The eleventh research seminar of the Swedish Society for Research in Mathematics Education, Karlstad, January 23–24, 2018 / [ed] Johan Häggström, Yvonne Liljekvist, Jonas Bergman Ärlebäck, Maria Fahlgren, Oduor Olande, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF , 2018, Vol. 13, no 13, p. 226-226Conference paper (Refereed)
    Abstract [en]

    When mathematics tasks are translated to different languages, there is a risk that the different language versions are not equivalent and display differential item functioning (DIF). In this study, we aimed to identify possible sources of DIF. We investigated whether differences in some linguistic features are related to DIF between the English (USA), German, and Swedish versions of mathematics tasks of the PISA 2012 assessment. The linguistic features chosen in this study are grammatical person, voice (active/passive), and sentence structure. We analyzed the three different language versions of 83 mathematics PISA tasks in three steps. First, we calculated the amount of differences in the three linguistic features between the language versions. Then, we calculated DIF, using the Mantel-Haenszel procedure pairwise for two language versions at a time. Finally, we searched for correlations between the amount of linguistic differences and DIF between the versions. The analysis showed that differences in linguistic features occurred between the language versions – differences in voice were most common – and that several items displayed intermediate or large level of DIF. Still, there were no statistical significant correlations between differences in linguistic features and DIF between the language versions, that is, there must be other sources of DIF.

  • 22.
    Theens, Frithjof
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Linguistic features in mathematics PISA tasks in different languages2017Conference paper (Refereed)
    Abstract [en]

    When the results of international comparative studies such as PISA or TIMSS get published, they are discussed broadly in media and are used to influence politics and public opinion. To solve mathematics PISA tasks, students have to read and understand the task text. Still, since the mathematics tasks are primarily supposed to measure mathematical ability and not reading ability, it is important to avoid unnecessary demands of reading ability in the tasks. In addition, the different language versions of a task used in PISA might vary in reading difficulty. Such differences can result in differential item functioning (DIF), that is, that students with the same mathematical ability but from different countries have a different probability of answering the item correctly. One reason for DIF between language versions is that linguistic features can differ between language versions. In this study we focus on four different linguistic features that in earlier studies have shown connections to the difficulty of solving mathematics tasks (e.g., Abedi, Lord, & Plummer, 1997).

    • Grammatical person, that is, if the text is written in first, second, or third person.
    • Voice, that is, if active or passive voice is used in the text.
    • Sentence structure, that is, how the sentences are built of main and subordinate clauses.
    • Word order, that is, the order of subject, finite verb, and object in the sentence.

    This study is part of a larger project examining the relation between the language used in mathematics tasks and both the tasks’ difficulty and demand of reading ability. The research questions in this study are: Which differences in the four linguistic features investigated occur between PISA tasks in English, German, and Swedish? Which of these differences are related to DIF between the task versions? The English (USA), German, and Swedish language versions of 83 mathematics tasks of the PISA 2012 assessment are analyzed. The first step of the analysis was to search for differences in the four linguistic features between the different language versions of the tasks. The next steps will be quantitative analyses of the differences, a statistical analysis to detect DIF between the versions, and then statistical analyses to investigate possible relations between the differences and DIF. The first step showed that some differences occur sporadically, for example, the use of third person (he/she/it) in one language version and second person (you) in another language version. Other differences occur much more frequently. For example, differences in word order are quite common, in particular since the finite verb always is at the last position in subordinate clauses in German but not in English and Swedish. The next steps of the analysis are at present (January 2017) ongoing.

  • 23.
    Theens, Frithjof
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    The relation between linguistic features and DIF in multilanguage mathematics assessmentsManuscript (preprint) (Other academic)
  • 24.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    A framework for studying differences between process- and object-oriented discourses2011In: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, vol 1: Developing mathematical thinking / [ed] Behiye Ubuz, 2011, p. 367-367Conference paper (Other academic)
  • 25.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Beliefs: A theoretically unnecessary construct?2010In: Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon, France / [ed] V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello, Lyon: Institut National de Recherche Pédagogique , 2010, p. 154-163Conference paper (Refereed)
    Abstract [en]

    In this paper I analyze different existing definitions of the term beliefs, focusing on relations between beliefs and knowledge. Through this analysis I note several problems with different types of definitions. In particular, when defining beliefs through a distinction between belief and knowledge systems, this creates an idealized view of knowledge, seen as something more pure (less affective, less episodic, and more logical). In addition, attention is generally not given to from what point of perspective a definition is made; if the distinction between beliefs and knowledge is seen as being either individual/psychological or social. These two perspectives are also sometimes mixed, which results in a messy construct. Based on the performed analysis, a conceptualization of beliefs is suggested.

  • 26.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Characterizing mathematics education research discourse on belief2011In: Current state of research on mathematical beliefs XVI: Proceedings of the MAVI-16 Conference, June 26-29, 2010, Tallinn, Estonia / [ed] Kirsti Kislenko, Tallinn, Estonia: Institute of Mathematics and Natural Sciences, Tallinn University , 2011, p. 200-217Conference paper (Refereed)
    Abstract [en]

    The discursive use of ‘belief’ in research articles are analyzed as a contribution to the reflexive activity in belief-research, in particular regarding theoretical aspects of the notion of belief. The purpose of this paper is to create an explicitly described procedure for such an analysis, from the selection of data to categorizations of the smallest unit of analysis. The method of analysis builds on some linguistic structures, focusing in this paper on the use of adjectives and verbs in relation to ‘belief’. From the analysis of the use of ‘belief’ in eight articles a set of categories is created describing different uses of the notion of belief.

  • 27.
    Österholm, Magnus
    Umeå University, Faculty of Teacher Education, Mathematics, Technology and Science Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Do students need to learn how to use their mathematics textbooks?: The case of reading comprehension2008In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 13, no 3, p. 53-73Article in journal (Refereed)
    Abstract [en]

    The main question discussed in this paper is whether students need to learn how to read mathematical texts. I describe and analyze the results from different types of studies about mathematical texts; studies about properties of mathematical texts, about the reading of mathematical tasks, and about the reading of mathematical expository texts. These studies show that students seem to develop special reading strategies for mathematical texts that are not desirable. It has not been possible to find clear evidence for the need of a specific ”mathematical reading ability”. However, there is still a need to focus more on reading in mathematics teaching since students seem to develop the non-desirable reading strategies.

  • 28.
    Österholm, Magnus
    Umeå University, Faculty of Teacher Education, Mathematics, Technology and Science Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Kan vi separera läsning från matematikämnet?2009In: Dyslexi, ISSN 1401-2480, Vol. 14, no 3, p. 18-21Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    För uppgifter som man använder i undervisning eller prov i matematik så vill man i första hand utveckla eller testa kunskaper i matematik och inte elevernas läsförmåga. Om undervisning i matematik bygger mycket på läsning så verkar det finnas större risk att elever som har svårigheter med läsning också kommer få svårigheter med matematikämnet. En tanke kan därför vara att man vill separera läsning från matematikämnet, för att på så sätt undvika dessa potentiella problem. Mitt syfte med denna artikel är att analysera vissa aspekter av relationer mellan läsning och matematik, för att på detta sätt se om och hur en sådan separering kan göras.

  • 29.
    Österholm, Magnus
    Umeå University, Faculty of Teacher Education, Mathematics, Technology and Science Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Läsförståelsens roll inom matematikutbildning2009In: Matematikdidaktiska frågor: Resultat från en forskarskola / [ed] Gerd Brandell, Göteborg: Nationellt centrum för matematikutbildning (NCM), Göteborgs universitet , 2009, 1, p. 154-165Chapter in book (Other (popular science, discussion, etc.))
    Abstract [sv]

    Denna artikel beskriver undersökningar kring hur universitetsstudenter och skolelever läser olika typer av texter. Frågor jag vill besvara är hur man bör förhålla sig till läsning inom matematikutbildning och om man behöver behandla läsförståelse som en del av undervisning inom matematik. I artikeln behandlar jag undersökningar kring läsning av uppgiftstexter samt undersökningar kring läsning av förklarande texter. Därefter jämför jag dessa olika typer av lässituationer och noterar då vissa likheter mellan lässtrategier som elever använder sig av i de olika situationerna. Bland annat noterar jag att texter som innehåller symboler tycks aktivera en speciell lässtrategi hos elever. Denna strategi verkar handla om att fokusera på symboler och andra typer av nyckelord i texten, vilket resulterar i en sämre läsförståelse. En slutsats är därför att det finns behov av att behandla läsning i matematikundervisning eftersom elever på egen hand tenderar att utveckla bristfälliga lässtrategier. Jag diskuterar också förslag på hur man kan göra detta. Som avslutning i artikeln diskuterar jag även hur resultaten om läsning kan ses i relation till andra forskningsresultat.

  • 30.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Relationships between epistemological beliefs and properties of discourse: Some empirical explorations2010In: Mathematics and mathematics education: Cultural and social dimensions. Proceedings of MADIF 7 / [ed] C. Bergsten, E. Jablonka & T. Wedege, Linköping: Svensk förening för matematikdidaktisk forskning, SMDF , 2010, p. 241-250Conference paper (Refereed)
    Abstract [en]

    In this paper I investigate what types of epistemologies are conveyed through properties of mathematical discourse in two lectures. A main purpose is to develop and explore methods for a type of analysis for this investigation. The analysis focuses on the types of statements and types of arguments used in explicit argumentations in the lectures. This type of analysis proves to be useful when characterizing epistemological aspects of lectures. However, some limitations are also noted, in particular that it was common to use more implicit types of argumentations in the lectures, which was not included as data in the present analysis.

  • 31.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Students' summaries of mathematical lectures: Comparing the discourse of students with the discourse of lectures2012In: Mathematics Education: Expanding Horizons. Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia / [ed] J. Dindyal, L. P. Cheng & S. F. Ng, Singapore: MERGA , 2012, p. 578-585Conference paper (Refereed)
    Abstract [en]

    This study focuses on a distinction between process- and object-oriented discourses when characterising the discourse of university students' summaries of lectures and examining connections between students' discourse and the discourse of lectures. Results show that students' discourse in general tends to be process-oriented, by their use of active verbs and little use of nominalisations. Students' summaries of process-oriented lectures also tend to be more process-oriented, but the differences between individual students are larger than differences caused by variations of the discourse in the lectures.

  • 32.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    The ontology of beliefs from a cognitive perspective2010In: Proceedings of the conference MAVI-15: Ongoing research on beliefs in mathematics education, September 8-11, 2009, Genoa, Italy / [ed] F. Furinghetti & F. Morselli, Genoa: Department of Mathematics, University of Genoa , 2010, p. 35-46Conference paper (Refereed)
    Abstract [en]

    In order to refine existing theories of beliefs, attention is given to the ontology of beliefs, in particular how a belief can be seen as a mental object or a mental process. The analysis focuses on some central aspects of beliefs; unconsciousness, context­ualization, and creation and change of beliefs, but also relates to research metho­dology. Through the analysis, the creation of belief is highlighted as a central aspect for more in-depth theories of beliefs. The outline of a theoretical framework is described – a framework that has the benefit of creating a coherent integration of all different aspects discussed, and which can also be used as a framework when designing and analyzing methods for empirical research.

  • 33.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    The role of mathematical competencies in curriculum documents in different countries2018In: Perspectives on professional development of mathematics teachers: Proceedings of MADIF 11, The eleventh research seminar of the Swedish Society for Research in Mathematics Education, Karlstad, January 23–24, 2018 / [ed] Johan Häggström, Yvonne Liljekvist, Jonas Bergman Ärlebäck, Maria Fahlgren, Oduor Olande, Karlstad: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018, p. 131-140Conference paper (Refereed)
    Abstract [en]

    The inclusion of competencies in curriculum documents can be seen as an international reform movement in mathematics education. The purpose of this study is to understand which role mathematical competencies have in curriculum documents in different countries, with a focus on the relationship between competencies and content. Curriculum documents from 11 different countries were analysed. The results reveal three different themes of variation, concerning if the competencies are specific to mathematics, if competencies are described as learning goals, and if such learning goals are differentiated between grade levels.

  • 34.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    The role of theory when studying epistemological characterizations of mathematics lecture(r)s2012In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 9, no 3, p. 431-464Article in journal (Refereed)
    Abstract [en]

    The study presented in this paper is a contribution to the scientific discussion about the role and use of theory in mathematics education research. In particular, focus is here on the use of and comparison between different types of theories and frameworks, which is discussed primarily through the example of an empirical study examining what types of messages about mathematics are conveyed in lectures. The main purpose of this paper is to examine how different types of theories and frameworks can affect different parts of the research process.

  • 35.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    The roles of prior knowledge when students interpret mathematical texts2010In: The first sourcebook on nordic research in mathematics education: Norway, Sweden, Iceland, Denmark and contributions from Finland / [ed] Bharath Sriraman, Christer Bergsten, Simon Goodchild, Gudbjorg Palsdottir, Bettina Dahl Søndergaard & Lenni Haapasalo, Charlotte, NC, USA: Information Age Publishing, 2010, p. 431-440Chapter in book (Refereed)
    Abstract [en]

    In this chapter I examine what roles different types of prior knowledge have in the comprehension process when reading mathematical texts. Through theoretical analyses, three central aspects are highlighted; cognitive structure, cognitive process, and metacognition. For all these three aspects, questions arise regarding relationships between general and content-specific types of prior knowledge. Some empirical studies are described that study these questions.

  • 36.
    Österholm, Magnus
    Umeå University, Faculty of Teacher Education, Mathematics, Technology and Science Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Theories of epistemological beliefs and communication: A unifying attempt2009In: Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, 2009, p. 4-257-4-264Conference paper (Refereed)
    Abstract [en]

    In order to develop more detailed knowledge about possible effects of beliefs in mathematics education, it is suggested that we look more in-depth at more general types of theories. In particular, the study of relations between epistemological beliefs and communication is put forward as a good starting point in this endeavor. Theories of the constructs of epistemological beliefs and communication are analyzed in order to try to create a coherent theoretical foundation for the study of relations between the two constructs. Although some contradictions between theories are found, a type of unification is suggested, building on the theories of episte­mological resources and discursive psychology.

  • 37.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    To translate between different perspectives in belief research: a comparison between two studies2011In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 16, no 1-2, p. 57-76Article in journal (Refereed)
    Abstract [en]

    A common problem in belief research seems to be a missing link between aspects of theory and empirical analyses and results. This issue highlights a question of how dependent empirical studies about beliefs actually are on the theoretical perspective described in the study. In this paper, I examine relationships between two different perspectives. One perspective focuses on belief change, and seems to rely on a type of cognitive perspective, where beliefs can be characterized as mental objects. The other perspective argues for moving away from such cognitive perspective and instead to adopt a participatory perspective in the analysis of mathematics teaching. The results show that the study about belief change is not dependent on seeing beliefs as mental objects, but that this study could as well have been located within a participatory perspective.

  • 38.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    What aspects of quality do students focus on when evaluating oral and written mathematical presentations?2011In: Mathematics: Traditions and [New] Practices. Proceedings of the AAMT–MERGA conference held in Alice Springs, 3–7 July 2011 / [ed] J. Clark, B. Kissane, J. Mousley, T. Spencer & S. Thornton, Adelaide, Australia: AAMT and MERGA , 2011, p. 590-598Conference paper (Refereed)
    Abstract [en]

    University students' evaluations of mathematical presentations are examined in this paper, which reports on part of a pilot study about different types of presentations, regarding different topics, formats (oral or written), and discourses (process- or object-oriented). In this paper focus is on different formats; oral lectures and written texts. Students’ written comments about what is good or bad about given presentations are analysed in order to examine what students focus on when evaluating the quality of presentations. In addition, evaluations given about written and oral presentations are compared in order to examine if/how format affects students’ evaluations regarding quality.

  • 39.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    What is the basis for self-assessment of comprehension when reading mathematical expository texts?2015In: Reading Psychology, ISSN 0270-2711, E-ISSN 1521-0685, Vol. 36, no 8, p. 673-699Article in journal (Refereed)
    Abstract [en]

    The purpose of this study was to characterize students’ self-assessments when reading mathematical texts, in particular regarding what students use as a basis for evaluations of their own reading comprehension. A total of 91 students read two mathematical texts, and for each text they performed a self-assessment of their comprehension and completed a test of reading comprehension. Students’ self-assessments were to a less degree based on their comprehension of the specific text read, but more based on prior experiences. However, the study also produced different results for different types of texts and when focusing on different aspects of reading comprehension.

  • 40.
    Österholm, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Methodological issues when studying the relationship between reading and solving mathematical tasks2012In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 17, no 1, p. 5-30Article in journal (Refereed)
    Abstract [en]

    In this paper we examine four statistical methods used for characterizing mathematical test items regarding their demands of reading ability. These methods rely on data of students' performance on test items regarding mathematics and reading and include the use of regression analysis, factor analysis and different uses of correlation coefficients. Our investigation of these methods focuses on aspects of validity and reliability, using data from PISA 2003 and 2006. The results show that the method using factor analysis has the best properties when taking into account aspects of both validity and reliability.

  • 41.
    Österholm, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    What is so special about mathematical texts?: Analyses of common claims in research literature and of properties of textbooks2013In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 45, no 5, p. 751-763Article in journal (Refereed)
    Abstract [en]

    This study surveys claims in research articles regarding linguistic properties of mathematical texts, focusing on claims supported by empirical or logical arguments. It also performs a linguistic analysis to determine whether some of these claims are valid for school textbooks in mathematics and history. The result of the survey shows many and varying claims that mainly describe mathematical texts as highly compact, precise, complex, and containing technical vocabulary. However, very few studies present empirical support for their claims, and the few empirical studies that do exist contradict the most common, and unsupported, claims, since no empirical study has shown mathematical texts to be more complex than texts from other subjects, and any significant differences rather indicate the opposite. The linguistic analysis in this study is in line with previous empirical studies and stands in contrast to the more common opinion in the unsupported claims. For example, the mathematics textbooks have significantly shorter sentences than the history textbooks.

  • 42.
    Österholm, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    What mathematical task properties can cause an unnecessary demand of reading ability?2012In: Proceedings of Norma 11, The Sixth Nordic Conference on Mathematics Education in Reykjavík, May 11-14, 2011 / [ed] G. H. Gunnarsdóttir, F. Hreinsdóttir, G. Pálsdóttir, M. Hannula, M. Hannula-Sormunen, E. Jablonka, U. T. Jankvist, A. Ryve, P. Valero & K. Wæge, Reykjavík, Iceland: University of Iceland Press, 2012, p. 661-670Conference paper (Refereed)
    Abstract [en]

    In this study we utilize results from Swedish students in PISA 2003 and 2006 to examine what types of task properties predict the demand of reading ability of a task. In particular, readability properties (sentence length, word length, common words, and information density) and task type properties (content, competence, and format) are examined. The results show that it is primarily readability properties of a task that predict the task’s demand of reading ability, in particular word length and to some extent information density (measured through the noun-verb quotient).

  • 43.
    Österholm, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Dyrvold, Anneli
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    The study of difficult vocabulary in mathematics tasks: a framework and a literature reviewManuscript (preprint) (Other academic)
    Abstract [en]

    The purpose of this study is to contribute to the methodology of research on difficult vocabulary in mathematics tasks. The contribution consists of a framework for the study of difficult vocabulary in mathematics tasks and a literature review of empirical research in the area. The framework includes five main aspects of word difficulty that have been examined in empirical studies and discuss these in the light of theories on reading comprehension. In addition, methodological issues are presented in relation to each main aspect. The literature review examines both methodological aspects of 36 reviewed articles, and synthesizes results on difficult vocabulary. The literature review shows that a commonly used method—to study several word aspects together—is very unfortunate from the perspective of building accumulative knowledge about difficult vocabulary in mathematics tasks. The only well-supported conclusion possible to draw from the synthesis of results from the empirical studies, is that some word aspects are not related to task difficulty.

  • 44.
    Österholm, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Mittuniversitetet.
    Bergqvist, Tomas
    Umeå University, Faculty of Social Sciences, Department of applied educational science. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Liljekvist, Yvonne
    Karlstads universitet & Uppsala universitet.
    van Bommel, Jorryt
    Karlstads universitet.
    Utvärdering av Matematiklyftets resultat: slutrapport2016Report (Other (popular science, discussion, etc.))
  • 45.
    Österholm, Magnus
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Bergqvist, Tomas
    Umeå universitet, Institutionen för tillämpad utbildningsvetenskap.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Uppsala universitet.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Utvärdering av Matematiklyftets resultat: slutrapport2016Report (Other (popular science, discussion, etc.))
    Abstract [sv]

    Matematiklyftet är en fortbildning för alla lärare i Sverige som undervisar i matematik. Den genomfördes 2012-2016. Kärnan i fortbildningen var det kollegiala lärandet. Lärare arbetade tillsammans med olika moduler som var och en bestod av didaktiskt material att använda vid planering, diskuss-ioner och genomförande av matematikundervisning, samt vid kollegiala reflektioner och diskussioner. Genom modulerna belystes primärt fyra olika didaktiska perspektiv: (1) att undervisa matematik utifrån förmågorna, (2) bedömning för lärande och undervisning i matematik, dvs. formativ bedömning, (3) rutiner/interaktioner i klassrummet och (4) klassrumsnormer/sociomatematiska normer.

    Denna rapport presenterar en utvärdering av Matematiklyftets resultat där det undersökts i vilken utsträckning Matematiklyftet har bidragit till att utveckla en bestående undervisningskultur och en bestående fortbildningskultur. Utvärderingen syftar också till att identifiera faktorer som gynnar eller missgynnar Matematiklyftets resultat och ska även fungera både formativt och summativt. Det innebär att både slutsatser om hur Matematiklyftet har uppnått målen att utveckla undervisnings- och fortbildningskulturen och slutsatser om hur stöd till planeringar och genomförande av liknande fort-bildningssatsningar formuleras. Urvalet i utvärderingen består av 35 grund-och gymnasieskolor. På varje skola har tre lärare slumpmässigt valts ut att ingå i utvärderingen, dvs. totalt 105 lärare. I utvärderingen ingår också varje skolas rektor och representant för skolhuvudman. Skolorna har besökts vid två tillfällen för att kunna undersöka förändring i undervisnings- och fortbildningskultur. Datamaterialet består av observationer av matematiklektioner och av kollegiala samtal, intervjuer och enkäter med lärare och rektorer, samt intervjuer med representanter för skolhuvudmän. I datamaterialet ingår även insamlade dokument (t.ex. fortbildningsplaner och kopior av undervisningsmaterial) och bakgrundsinformation om de besökta skolorna (från externa databaser). Denna rapport utgör slutrapporten för utvärderingen av Matematiklyftets resultat. Nedan redovisas utvärderingens huvudsakliga resultat tillsammans med rekommendationer inför framtida fortbildningssatsningar av samma typ som Matematiklyftet.

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