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  • 201.
    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.

  • 202.
    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.

  • 203.
    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)
  • 204.
    Van Steenbrugge, H.
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lesage, E.
    Valcke, M.
    Desoete, A.
    Preservice elementary school teachers' knowledge of fractions: a mirror of students' knowledge?2014In: Journal of Curriculum Studies, ISSN 0022-0272, E-ISSN 1366-5839, Vol. 46, no 1, p. 138-161Article in journal (Refereed)
    Abstract [en]

    This research analyses preservice teachers' knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students' knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students' understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers' knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning.

  • 205.
    Van Steenbrugge, Hendrik
    et al.
    Mälardalens högskola.
    Bergqvist, Tomas
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Social Sciences, Department of applied educational science.
    Mathematics Curriculum Programs as Tools for Design: An Analysis of the Forms of Address2014In: AERA Online Paper Repository, 2014Conference paper (Refereed)
    Abstract [en]

    This paper studies how elementary mathematics curriculum programs can be designed to accommodate a flexible use by a range of teachers. We do so by analyzing three design principles: the provision of multiple entry points, the adoption of a resource-centric material design, and the allowance for flexibility across lessons and units that group lessons. These design principles are examined by describing three forms of address: the look, voice and structure of the curriculum programs. The analysis relates to six curriculum programs from three countries that vary in a number of ways. As such, we aim to provide useful instances that add to our knowledge of designing curriculum programs as tools for the design of teaching. 

  • 206.
    Van Steenbrugge, Hendrik
    et al.
    Mälardalens Högskola.
    Norqvist, Mathias
    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).
    Unraveling students’ reasoning: analyzing small-group discussions during task solvingManuscript (preprint) (Other academic)
    Abstract [en]

    The aim of this study is to examine students’ mathematical reasoning, suggested by Lithner (2008), to see how reasoning sequences will unfold in actual classroom situations. We visited two classrooms in an upper secondary school and observed two student groups in each classroom for the time it took them to complete a task, constructed and presented to them by their teacher. Initial analysis showed that there were two interesting dimensions to regard, group characteristics (i.e., motivation and persistence) and task design (i.e., reasoning promoted by the task). We recorded conversations between the students and after transcribing we utilized Lithner’s (2008) framework of mathematical reasoning to analyze students’ reasoning. We classified the moments (vertices) when the students’ reasoning took a new trajectory and characterized the segment (edge) between two such vertices according to the students’ reasoning (i.e., either creative mathematically founded reasoning or algorithmic reasoning). We then visualized the students’ reasoning in graphs (see Figure 10) and analyzed the patterns, the progress and types of reasoning, as well as how the group characteristics and task design would influence reasoning and progress. The result showed that task design is important for which reasoning the students will use. Although an algorithmic-task does not exclude creative reasoning, it only occurs in our data if the students have difficulties and strive to handle them by themselves. We also observed that group characteristics were important for the chosen reasoning type. 

  • 207.
    Vennberg, Helena
    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).
    Norqvist, Mathias
    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.
    Counting on: Long Term Effects of an Early Intervention Programme2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L., Umeå: PME , 2018, Vol. 4, p. 355-362Conference paper (Refereed)
    Abstract [en]

    This paper reports the long-term results of an intervention study with 134 six-year-old students from seven preschool-classes in northern Sweden to evaluate whether the Think, Reason and Count in Preschool-class programme (TRC) could prevent at-risk students from becoming low-performing students in mathematics. Whereas the pre-test score revealed that the intervention and the control group preformed equally, scores on the delayed follow-up-test in Grade 3 showed that the intervention group performed better than the control group and that at-risk students had closed the performance gap between themselves and their not-at-risk peers.

  • 208.
    Viholainen, Antti
    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.
    Critical features of formal and informal reasoning in the case of the concept of derivative2011In: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education: Vol. 4: developing mathematical thinking / [ed] Ubuz, Behiye, 2011, p. 305-312Conference paper (Refereed)
    Abstract [en]

    Mathematical reasoning can be categorised into formal and informal ones on the basis of the type of used arguments. Both types of reasoning are needed in mathematics, but students usually tend to restrict their reasoning either to formal or informal mode only. Three examples collected and re-analysed from earlier studies reveal some critical features of this kind of restricted reasoning: A formal reasoning may easily become dependent on memory or authoritative references or it may become superficial imitation of algorithms. Informal reasoning, for one, may easily be based on intuitive conceptions, and its validity may be difficult to evaluate.

  • 209.
    Viholainen, Antti
    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.
    Finnish mathematics teacher students' skills and tendencies to use informal and formal reasoning in the case of derivative2010In: Ajankohtaista matemaattisten aineiden opetuksen ja oppimisen tutkimuksessa (About the actual research in teaching and learning of mathematical subjects): Matematiikan ja luonnontieteiden opetuksen tutkimuspäivät Joensuussa 22.-23.10.2009 (Symposium of the Finnish Mathematics and Science Education Research Association, Joensuu, October 22-23, 2009) / [ed] M. Asikainen, P. Hirvonen & K. Sormunen, Joensuu: University of Eastern Finland , 2010, p. 87-102Conference paper (Refereed)
    Abstract [en]

    The arguments constructed in mathematical reasoning may be either formal or informal: They may be based either on definitions, axioms and previously proven theorems or on concrete interpretations of mathematical concepts and situations. In addition, arguments may be superficial or deep. Results shared in this paper are from three different studies in which both students’ skills to produce informal and formal arguments and their tendencies to choose between informal and formal reasoning in problem solving situations were studied. The students in all these studies were Finnish high school pre-service mathematics teachers, and the data was collected by using a written test and videotaped interviews. The tasks used were about the concept of derivative. Results of the studies indicated that the students’ skills to produce informal and formal arguments were dependent on each other. The difference between the levels of these skills was not significant, but several students had a tendency to avoid the use of the formal definition of derivative, which led to difficulties in problem solving situations. However, this tendency could not be explained by the students’ inadequate skills to handle the definition of derivative

  • 210.
    Viholainen, Antti
    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.
    Lisää luovuutta matematiikkaan (More creativity into mathematics)2010In: Dimensio, ISSN 0782-6648, no 6, p. 70-72Article in journal (Other (popular science, discussion, etc.))
  • 211.
    Viholainen, Antti
    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.
    Hemmi, Kirsti
    Mälardalen universitet.
    Lepik, Madis
    Tallinn university.
    Upper secondary school teachers' views of proof and proving: an explorative cross-cultural study2010In: Proceedings of the 16th Conference of Mathematical Views (MAVI16), 2010Conference paper (Refereed)
    Abstract [en]

    This paper reports the results of initial explorations about teachers’ views of proofand proving in upper secondary school context in Sweden, Estonia and Finland. Thestudy was carried out in order to develop a questionnaire for a cross-culturalcomparative survey in Baltic countries and Nordic countries with respect of theculture of proof in school mathematics (NorBa Proof Project). The data consistsmainly of teachers’ written responses to some open questions concerning their viewsof proof and the meaning of dealing with proof in upper secondary school context.

  • 212.
    Vingsle, Charlotta
    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).
    Formativ bedömning och självreglerat lärande: vad behöver vi för att få det att hända?2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Previous research has shown that substantial learning gains are possible when formative assessment and support for students’ development of self-regulated learning skills are implemented in classroom practice. Such implementation is not straightforward and there is a need for both further understanding of the knowledge and skills teachers require to practice formative assessment, and further insights into how different characteristics of ordinary teaching practices support students’ in becoming proficient self-regulated learners. This doctoral thesis includes a licentiate thesis and two articles. In the licentiate thesis, classroom observations are used to investigate the knowledge and skills used by a teacher engaged in a comprehensive formative classroom practice. The results show that the teacher's practice is complex and requires advanced knowledge and skills that are often used simultaneously and under time pressure. For example, the teacher, sometimes in a matter of seconds, handles new (to her) mathematics, makes inferences from students’ responses to their understanding, and based on these inferences makes decisions about her teaching. The first article is a literature review focusing on the effects of formative assessment on student achievement in mathematics since there is a lack of knowledge of the effects of formative assessment on student achievement, in particular for subject areas such as mathematics. In the review, a systematic literature search is made for articles studying the effects of both teacher-centered approaches and approaches emphasizing student involvement in the formative assessment processes. The latter type of approaches includes teacher practices that support students’ development of aspects of self-regulated learning competence. The results show that all approaches included in the review have significant positive effects on student achievement in mathematics. The second article examines in what ways learning situations in authentic classroom practices provide opportunities for the students to develop self-regulated learning skills, and how students experience these opportunities. The analysis is based on data from classroom observations of three teachers’ mathematics lessons, and on interviews with their students. The results show that instruction in self-regulated learning skills mostly occurred implicitly, and the opportunities to develop the skills were mainly provided and experienced at the observational level.

  • 213.
    Vingsle, Charlotta
    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).
    Formative assessment: teacher knowledge and skills to make it happen2014Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Several studies have demonstrated that substantial learning gains are possible when teachers use formative assessment in their classroom practice. At the heart of most definitions of formative assessment lies the idea of collecting evidence of students’ thinking and learning, and based on this information modifying teaching to better meet students’ needs. Such regulation of learning processes would require skills to elicit the thinking underlying students’ oral and written responses, and the capacity to make suitable instructional decisions based on this thinking. When the continuation of the teaching is contingent on the information that appears in such assessments additional knowledge and skills are required compared with a more traditional approach to teaching.

    Today, sufficient knowledge about how to help in-service teachers and pre-service teachers develop their formative classroom practice is lacking. In the pursuit of gathering research evidence about the specific content and design of professional development programs and teacher education courses in formative assessment, it is important that we know what kinds of skills and knowledge teachers need to successfully orchestrate a formative classroom practice.

    The aim of this study is to identify activities and characterize the knowledge and skills that a teacher of mathematics uses in her formative assessment practice during whole-class lessons.

    The study is a case study of a teacher’s formative assessment practice during mathematics lessons in year 5. The data were analysed by identifying a) the formative assessment practice b) the teacher’s activities during the formative assessment practice and c) the teacher knowledge and skills used during the activities.

    The main result of the study shows that the formative assessment practice is a very complex, demanding and difficult task for the teacher in several ways. For example, during short term minute-by-minute formative assessment practice the teacher uses knowledge and skills to eliciting, interpreting and use the elicited information to modify instruction to better meet student learning needs. She also helps students’ to engage in common learning activities and take co-responsibility of their learning. In the minute-by-minute formative assessment practice the teacher also handles new mathematics (to her), unpredictable situations and makes decisions about teaching and learning situations in a matter of seconds. 

     

  • 214.
    Vingsle, Charlotta
    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.
    How hard can it be? What knowledge and skills does a teacher practicing formative assessment use?2014Conference paper (Other academic)
    Abstract [en]

    This case study investigates a teacher ́s use and need of knowledge and skills during interaction in whole-class is using formative assessment. This practice includes eliciting information about student learning, interpreting the responses, and modifying teaching and learning activities based on the given information. The teacher has participated in a professional development program and teaches grade 5 in mathematics. The results of the study will be presented at the conference.

  • 215.
    Vingsle, Charlotta
    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).
    Opportunities to develop emerging self-regulating skills: Teacher instruction and student experiences during mathematics lessonsManuscript (preprint) (Other academic)
    Abstract [en]

    The ability to self-regulate one’s learning has been associated with academic success, and recognized as an important component in successful life-long learning. But studies on how characteristics of ordinary classroom practices provide or impair opportunities for students to develop self-regulate learning skills are rare. This study examines in what ways learning situations in authentic classroom practices provide opportunities for the students to develop self-regulated learning skills, and how students experience these opportunities. The analysis is based on data from classroom observations of three teachers’ mathematics lessons, and on interviews with their students. The results show that the opportunities for students to develop self-regulated learning skills were mainly provided by learning situations in which the teacher modeled the skills, and most often the students did not recognize these situations as opportunities to develop the skills. However, they did so more often when they had an active role in the learning situations.

  • 216.
    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)
  • 217.
    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.

  • 218.
    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.

  • 219.
    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.

  • 220.
    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.

  • 221.
    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.

  • 222.
    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.

  • 223.
    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.

  • 224.
    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.

  • 225.
    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.

  • 226.
    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.

  • 227.
    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.

  • 228.
    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.

  • 229.
    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.

  • 230.
    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.

  • 231.
    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.

  • 232.
    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.

  • 233.
    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.

  • 234.
    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).

  • 235.
    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.

  • 236.
    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.))
2345 201 - 236 of 236
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