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  • 1.
    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.

  • 2.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Theens, Frithjof
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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, p. 125-125Conference paper (Refereed)
  • 3.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 4.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 5.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 6.
    Dyrvold, Anneli
    et al.
    Umeå universitet, Institutionen för matematik och matematisk statistik.
    Bergqvist, Ewa
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 7.
    Edmonds-Wathen, Cris
    et al.
    Umeå universitet, Institutionen för naturvetenskapernas och matematikens didaktik.
    Bergqvist, Ewa
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Institutionen för naturvetenskapernas och matematikens didaktik.
    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, p. 151-151Conference paper (Refereed)
  • 8. Helenius, Ola
    et al.
    Engström, ArneMeaney, TamsinNilsson, PerNorén, EvaSayers, JudyÖsterholm, MagnusUmeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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)
  • 9.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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)
  • 10.
    Österholm, Magnus
    Linköpings universitet, Tillämpad matematik.
    A reading comprehension perspective on problem solving2006In: Developing and researching quality in mathematics teaching and learning : proceedings of MADIF 5 : the 5th Swedish Mathematics Education Research Seminar, Malmö, January 24-25, 2006 / [ed] Christer Bergsten and Barbro Grevholm, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2006, p. 136-145Conference paper (Refereed)
    Abstract [en]

    The purpose of this paper is to discuss the bi-directional relationship between reading comprehension and problem solving, i.e. how reading comprehension can affect and become an integral part of problem solving, and how it can be affected by the mathematical text content or by the mathematical situation when the text is read. Based on theories of reading comprehension and a literature review it is found that the relationship under study is complex and that the reading process can affect as well as act as an integral part of the problem solving process but also that not much research has focused on this relationship.

  • 11.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 12.
    Österholm, Magnus
    Umeå universitet, Institutionen för naturvetenskapernas och matematikens didaktik.
    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.

  • 13.
    Österholm, Magnus
    Linköpings universitet, Tillämpad matematik.
    Characterizing reading comprehension of mathematical texts2006In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 63, no 3, p. 325-346Article in journal (Refereed)
    Abstract [en]

    This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the mathematical texts and the historical text. Before reading the texts, a test of prior knowledge for both mathematics and history was given and after reading each text, a test of reading comprehension was given. The results reveal a similarity in reading comprehension between the mathematical text without symbols and the historical text, and also a difference in reading comprehension between the two mathematical texts. This result suggests that mathematics in itself is not the most dominant aspect affecting the reading comprehension process, but the use of symbols in the text is a more relevant factor. Although the university students had studied more mathematics courses than the upper secondary students, there was only a small and insignificant difference between these groups regarding reading comprehension of the mathematical text with symbols. This finding suggests that there is a need for more explicit teaching of reading comprehension for texts including symbols.

  • 14.
    Österholm, Magnus
    Umeå universitet, Matematik, teknik och naturvetenskap.
    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.

  • 15.
    Österholm, Magnus
    Linköpings universitet, Tillämpad matematik.
    Epistemological beliefs and communication in mathematics education at upper secondary and university levels2009In: Perspectives on mathematical knowledge. Proceedings of MADIF 6, the 6th Swedish Mathematics Education Research Seminar, Stockholm, January 29-30, 2008 / [ed] Christer Bergsten, Barbro Grevholm, Thomas Lingefjärd, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2009, p. 132-134Conference paper (Other academic)
  • 16.
    Österholm, Magnus
    Umeå universitet, Matematik, teknik och naturvetenskap.
    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.

  • 17.
    Österholm, Magnus
    Linköpings universitet.
    Kognitiva och metakognitiva perspektiv på läsförståelse inom matematik2006Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    There seems to exist a general belief that one needs to learn specifically how to read mathematical texts, that is, a need to develop a special kind of reading ability for such texts. However, this belief does not seem to be based on research results since it does not exist much research that focus on reading comprehension in mathematics.

    The main purpose of this dissertation is to examine whether a reader needs special types of knowledge or abilities in order to read mathematical texts. Focus is on students’ reading of different kinds of texts that contain mathematics from introductory university level. The reading of mathematical texts is studied from two different perspectives, on the one hand a cognitive perspective, where reading abilities and content knowledge are studied in relation to reading comprehension, and on the other a metacognitive perspective, where focus is on beliefs and how a reader determines whether a text has been understood or not.

    Three empirical studies together with theoretical discussions, partly based on two literature surveys, are included in this dissertation. The literature surveys deal with properties of mathematical texts and reading in relation to problem solving. The empirical studies compare the reading of different types of texts, partly mathematical texts with texts with content from another domain and partly different types of mathematical texts, where focus is on the use of symbols and texts focusing on conceptual or procedural knowledge. Furthermore, students’ beliefs about their own reading comprehension and about texts and reading in general in mathematics are studied, in particular whether these beliefs are connected to reading comprehension.

    The results from the studies in this dissertation show that the students seem to use a special type of reading ability for mathematical texts; to focus on symbols in a text. For mathematical texts without symbols, a more general reading ability is used, that is, a type of ability also used for texts with content from another domain. The special type of reading ability used for texts including symbols affects the reading comprehension differently depending on whether the text focuses on conceptual or procedural knowledge. Compared to the use of the more general reading ability, the use of the special reading ability creates a worse reading comprehension.

    There seems to exist a need to focus on reading and reading comprehension in mathematics education since results in this dissertation show that courses at the upper secondary level (course E) and at the university level (in algebra and analysis) do not affect the special reading ability. However, the mentioned results show that this focus on reading does not necessarily need to be about learning to read mathematical texts in a special manner but to use an existing, more general, reading ability also for mathematical texts.

    Results from the metacognitive perspective show a difference between conscious aspects, such as regarding beliefs and reflections about comprehension, and unconscious aspects, such as the more automatic processes that make a reader understand a text, where also metacognitive processes are active. In particular, beliefs, which have been examined through a questionnaire, do not have a clear and independent effect on reading comprehension.

    From the texts used in these studies and the participating students, there seems not do be a general need to view the reading of mathematical texts as a special kind of process that demands special types of reading abilities. Instead, the development of a special type of reading ability among students could be caused by a lack of experiences regarding a need to read different types of mathematical texts where similarities with reading in general can be highlighted and used.

  • 18.
    Österholm, Magnus
    Linköpings universitet, Tekniska högskolan.
    Learning mathematics by reading - a study of students interacting with a text2003In: Nordic pre-conference to ICME 10, 2003Conference paper (Other academic)
  • 19.
    Österholm, Magnus
    Linköpings universitet, Tillämpad matematik.
    Learning mathematics by reading - a study of students interacting with a text2003Report (Other academic)
    Abstract [en]

    This study investigates the situation when students on their own read a new mathematical text, and solve problems relevant to the text. The students worked together in pairs on a given text, about the absolute value of real numbers, with a video camera recording their activity. First, the students were instructed to read and discuss the text without any given tasks. Thereafter, the students were given exercises relevant to the text, and they were allowed to keep the text and use it when working with these exercises. Two pairs of students participated, all of them on their last year on the natural science programme at the Swedish upper secondary school. The observations reveal a variety of different activities among the students, and some questions also arise that would be interesting to examine in more detail.

  • 20.
    Österholm, Magnus
    Linköpings universitet.
    Läsa matematiska texter: Förståelse och lärande i läsprocessen2004Licentiate thesis, monograph (Other academic)
    Abstract [sv]

    Denna avhandling behandlar läsning av matematiska texter; hur och vad man förstår och lär sig vid läsningen. Fokus ligger på läsprocessen, det vill säga själva läsandet av texten och vad man förstår efter att läst igenom texten. Huvudsyftet är att studera specifika aspekter i läsandet av just matematiska texter för att testa och utveckla en befintlig, allmän teori kring läsprocessen. Speciellt studeras användningen av symboler i matematiska texter och hur detta kan påverka läsprocessen. Avhandlingen byggs upp av teoretiska diskussioner kring läsning av matematiska texter samt en empirisk studie bland gymnasieelever och universitetsstuderande.

    De teoretiska diskussionerna utgår bland annat från en litteraturstudie kring förekommande påståenden om speciella egenskaper hos matematiska texter, och speciellt diskuteras läsning av symboler och algebraiska uttryck.

    Den empiriska studien (med 106 deltagare) använde tre olika texter; en historietext om ryska revolutionen samt två matematiktexter om gruppteori. Matematiktexterna behandlar samma sak som gruppteori, men skillnaden mellan dem är att den ena använder matematiska symboler i sin presentation medan den andra inte alls använder symboler. Varje deltagare fick läsa en utav matematiktexterna samt historietexterna, och fick efter varje text besvara frågor om textens innehåll.

    Den grupp av personer som läste matematiktexten utan symboler har bättre resultat på frågor om texten än den grupp som läste texten med symboler. Detta verkar kunna bero på oförmåga att artikulera symboler vid läsning av texten samt att avkodningsförmågan inte verkar kunna utnyttjas på samma sätt för texten med symboler. Läsning av matematiska texter med symboler är alltså ganska speciellt och man kan behöva lära sig hur man läser sådana texter. Däremot verkar det finnas många likheter med läsning av matematiska texter utan symboler och historietexten. Det matematiska innehållet verkar alltså inte i någon större omfattning påverka läsprocessen, utan hur detta innehåll presenteras är en viktig aspekt.

    I de teoretiska diskussionerna ges förslag på hur läsning av matematiska symboler kan infogas i den allmänna teorin för läsprocessen. Överlag finns dock ingen anledning att se läsning av matematiska texter som någon speciell typ av process som skiljer sig från läsning av andra texter. Den allmänna teorin för läsprocessen kan därmed fungera som teoretisk grund även för läsförståelse av matematiska texter, möjligen med föreslaget tillägg om matematiska symboler.

  • 21.
    Österholm, Magnus
    Umeå universitet, Matematik, teknik och naturvetenskap.
    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.

  • 22.
    Österholm, Magnus
    Linköpings universitet, Tillämpad matematik.
    Metacognition and reading - criteria for comprehension of mathematics texts2006In: Proceedings of the 30th conference of the International group for the psychology of mathematics education / [ed] J. Novotná, H. Moraová, M. Krátká and N. Stehlíková, Prague: The International Group for the Psychology of Mathematics Education , 2006, p. 289-296Conference paper (Other academic)
    Abstract [en]

    This study uses categories of comprehension criteria to examine students’ reasons for stating that they do, or do not, understand a given mathematics text. Nine student teachers were individually interviewed, where they read a text and commented on their comprehension, in particular, why they felt they did, or did not, understand the text. The students had some difficulties commenting on their comprehension in this manner, something that can be due to that much of comprehension monitoring, when criteria for comprehension are used, might be operating at an unconscious cognitive level. Some specific aspects of mathematics texts are examined, such as the symbolic language and conceptual and procedural understanding.

  • 23.
    Österholm, Magnus
    Linköpings universitet, Tekniska högskolan.
    Reading mathematical texts: cognitive processes and mental representations2004Conference paper (Refereed)
  • 24.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 25.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 26.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 27.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 28.
    Österholm, Magnus
    Umeå universitet, Institutionen för naturvetenskapernas och matematikens didaktik.
    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.

  • 29.
    Österholm, Magnus
    Umeå universitet, Matematik, teknik och naturvetenskap.
    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.

  • 30.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 31.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 32.
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 33.
    Österholm, Magnus
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Bergqvist, Ewa
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 34.
    Österholm, Magnus
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Bergqvist, Ewa
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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.

  • 35.
    Österholm, Magnus
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Bergqvist, Ewa
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    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).

  • 36.
    Österholm, Magnus
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Bergqvist, Tomas
    Umeå universitet, Institutionen för tillämpad utbildningsvetenskap.
    Liljekvist, Yvonne
    Karlstads universitet & Uppsala universitet.
    van Bommel, Jorryt
    Karlstads universitet.
    Utvärdering av Matematiklyftets resultat: slutrapport2016Report (Other (popular science, discussion, etc.))
1 - 36 of 36
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