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  • 1.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    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, Interactive Media and Learning (IML).
    Boesen, Jesper
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Helenius, Ola
    Örebro universitet.
    Lithner, Johan
    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.
    Palm, Torulf
    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.
    Palmberg, Björn
    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.
    Matematikutbildningens mål och undervisningens ändamålsenlighet: grundskolan våren 20092009Report (Other academic)
  • 2.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    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, Interactive Media and Learning (IML).
    Boesen, Jesper
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Helenius, Ola
    Örebro universitet.
    Lithner, Johan
    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.
    Palm, Torulf
    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.
    Palmberg, Björn
    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.
    Matematikutbildningens mål och undervisningens ändamålsenlighet: gymnasiet hösten 20092010Report (Other academic)
  • 3.
    Bergqvist, Tomas
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Hudson, Brian
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lindwall, Krister
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Podcasting in School2008Report (Other academic)
    Abstract [en]

    Podcasting is a new phenomenon in Swedish schools. This pa- per describes a project where the main goal is to analyze if the students’ interest in mathematics is affected if the mathematics is made accessible via podcasts and iPods. Teachers at eleven schools were encouraged to produce podcasts as a part of their mathematics teaching in school year eight. The results indicate an increased interest in mathematics and the learning of mathematics among the students. We also found that the tech- nical difficulties for the teachers were underestimated in the project, and that teachers had difficulties in finding time for the production of podcasts.

     

  • 4.
    Bergqvist, Tomas
    et al.
    Umeå University, Faculty of Social Sciences, Department of Interactive Media and Learning (IML). Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Hudson, Brian
    Umeå University, Faculty of Social Sciences, Department of Interactive Media and Learning (IML). Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lithner, Johan
    Umeå University, Faculty of Teacher Education, Mathematics, Technology and Science Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lindwall, Krister
    Umeå University, Faculty of Social Sciences, Department of Interactive Media and Learning (IML).
    Podcasting in school2009In: Sixth Research Seminar of the Swedish Society for Research in Mathematics Education (MADIF 6), In press, 2009Conference paper (Refereed)
    Abstract [en]

    Podcasting is a new phenomenon in Swedish schools. This paper describes a project where the main goal is to analyze if the students’ interest in mathematics is affected if the mathematics is made accessible via podcasts and ipods. Teachers at eleven schools were encouraged to produce podcasts as a part of their mathematics teaching in school-year eight. The results indicate an increased interest in mathematics and the learning of mathematics among the students. We also found that the technical difficulties for the teachers were underestimated in the project, and that teachers had difficulties in finding time for the production of podcasts.

  • 5.
    Bergqvist, Tomas
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Social Sciences, Department of applied educational science, Interactive Media and Learning (IML).
    Lithner, Johan
    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.
    Mathematical reasoning in teachers' presentations2012In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 31, no 2, p. 31p. 252-269Article in journal (Refereed)
    Abstract [en]

    This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers’ ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on available algorithms, often without arguments that justify the reasoning, which may lead to rote learning. The students are given some opportunities to see aspects of creative reasoning, such as reflection and arguments that are anchored in the mathematical properties of the task components, but in relatively modest ways.

  • 6.
    Bergqvist, Tomas
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Social Sciences, Department of applied educational science.
    Lithner, Johan
    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.
    Why is learning via creative reasoning effective?2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged: PME , 2016Conference paper (Refereed)
  • 7.
    Bergqvist, Tomas
    et al.
    Umeå University, Faculty of Teacher Education, Department of Interactive Media and Learning. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lithner, Johan
    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).
    Sumpter, Lovisa
    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).
    Upper secondary students’ task reasoning2008In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, Vol. 39, no 1Article in journal (Refereed)
    Abstract [en]

    Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and guided reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer.

  • 8. Björkqvist, Ole
    et al.
    Gjone, GunnarJohansson, BengtKristjánsdóttir, AnnaLithner, JohanUmeå 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).Wallin, HansUmeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Preparation of researchers in mathematics education: Nordic symposium Umeå, August 17-20, 19951996Conference proceedings (editor) (Other academic)
  • 9.
    Boesen, Jesper
    et al.
    Göteborgs universitet.
    Helenius, Ola
    Göteborgs universitet och Örebro universitet.
    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).
    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.
    Lithner, Johan
    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).
    Palm, Torulf
    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).
    Palmberg, Björn
    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).
    Developing mathematical competence: from the intended to the enacted curriculum2014In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 33, p. 72-87Article in journal (Refereed)
    Abstract [en]

    This study investigates the impact of a national reform in Sweden introducing mathematical competency goals. Data were gathered through interviews, classroom observations, and online surveys with nearly 200 teachers. Contrasting to most studies of this size, qualitative analyses were conducted. The results show that teachers are positive to the message, but the combination of using national curriculum documents and national tests to convey the reform message has not been sufficient for teachers to identify the meaning of the message. Thus, the teachers have not acquired the functional knowledge of the competence message required to modify their teaching in alignment with the reform. The results indicate that for complex reform messages, such as the competency message, to have intended impact on classroom practice, special attention needs to be put on the clarity of the message. To have high-stakes tests, for example, does not alone seem to be sufficient. 

  • 10. Boesen, Jesper
    et al.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Palm, Torulf
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Assessing mathematical competencies: an analysis of Swedish national mathematics tests2018In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 62, no 1, p. 109-124Article in journal (Refereed)
    Abstract [en]

    Internationally, education reform has been directed towards describing educational goals that go beyond topic and content descriptions. The idea of mathematical competencies describes such goals. National tests have been seen as one way of communicating these goals and influence teaching. The present study analyses Swedish national tests in mathematics, and seeks evidence about the extent to which they represent these competencies and may play a role in reforming teaching. The results show that the national tests assess all competencies. However, the study also shows a limited focus on the competencies’ interpretation and evaluation aspects. Thus, the tests do not fully capture the complex nature of the competencies. This may cloud the reform message and restrict the possibilities for the tests to function as levers for reform.

  • 11.
    Boesen, Jesper
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lithner, Johan
    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).
    Palm, Torulf
    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 types of assessment tasks and the mathematical reasoning students use2010In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 75, no 1, p. 89-105Article in journal (Refereed)
    Abstract [en]

    The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative mathematically founded reasoning. In addition, most successful solutions to such tasks were based on this type of reasoning.

  • 12.
    Jonsson, Bert
    et al.
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Karlsson, Linnea
    Umeå University, Faculty of Medicine, Department of Integrative Medical Biology (IMB). Umeå University, Faculty of Medicine, Umeå Centre for Functional Brain Imaging (UFBI).
    Lithner, Johan
    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.
    Liljekvist, Yvonne
    Karlstad University.
    Norqvist, Mathias
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Nyberg, Lars
    Umeå University, Faculty of Medicine, Department of Integrative Medical Biology (IMB), Physiology. Umeå University, Faculty of Medicine, Umeå Centre for Functional Brain Imaging (UFBI). Umeå University, Faculty of Medicine, Department of Radiation Sciences, Diagnostic Radiology.
    Mathematical Teaching Method affects Performance and Brain Activity2012Conference paper (Refereed)
  • 13.
    Jonsson, Bert
    et al.
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Kulaksiz, Yagmur C.
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Lithner, Johan
    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).
    Creative and algorithmic mathematical reasoning: effects of transfer-appropriate processing and effortful struggle2016In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 47, no 8, p. 1206-1225Article in journal (Refereed)
    Abstract [en]

    Two separate studies, Jonsson et al. (J. Math Behav. 2014;36: 20–32)and KarlssonWirebring et al. (Trends Neurosci Educ. 2015;4(1–2):6–14),showed that learning mathematics using creative mathematical reasoningand constructing their own solution methods can be moreefficient than if students use algorithmic reasoning and are giventhe solution procedures. It was argued that effortful struggle was thekey that explained this difference. It was also argued that the resultscould not be explained by the effects of transfer-appropriate processing,although this was not empirically investigated. This studyevaluated the hypotheses of transfer-appropriate processing andeffortful struggle in relation to the specific characteristics associatedwith algorithmic reasoning task and creativemathematical reasoningtask. In a between-subjects design, upper-secondary students werematched according to their working memory capacity.The main finding was that the superior performance associated withpracticing creative mathematical reasoning was mainly supportedby effortful struggle, however, there was also an effect of transferappropriateprocessing. It is argued that students need to strugglewith important mathematics that in turn facilitates the constructionof knowledge. It is further argued that the way we construct mathematicaltasks have consequences for how much effort students allocateto their task-solving attempt.

  • 14.
    Jonsson, Bert
    et al.
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    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).
    Liljekvist, Yvonne
    Department of Mathematics and Computer Science, Karlstad University, Sweden ; The Centre of Science, Mathematics and Engineering Education Research, Karlstad University, Sweden.
    Lithner, Johan
    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.
    Learning mathematics through algorithmic and creative reasoning2014In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, no 36, p. 20-32Article in journal (Refereed)
    Abstract [en]

    There are extensive concerns pertaining to the idea that students do not develop sufficient mathematical competence. This problem is at least partially related to the teaching of procedure-based learning. Although better teaching methods are proposed, there are very limited research insights as to why some methods work better than others, and the conditions under which these methods are applied. The present paper evaluates a model based on students’ own creation of knowledge, denoted creative mathematically founded reasoning (CMR), and compare this to a procedure-based model of teaching that is similar to what is commonly found in schools, denoted algorithmic reasoning (AR). In the present study, CMR was found to outperform AR. It was also found cognitive proficiency was significantly associated to test task performance. However the analysis also showed that the effect was more pronounced for the AR group.

  • 15.
    Jäder, Jonas
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). School of Education, Health and Social Studies, Dalarna University, Falun, Sweden.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Sidenvall, Johan
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Mathematical problem solving in textbooks from twelve countries2019In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed)
    Abstract [en]

    A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by mimicking available templates or whether a solution had to be constructed without guidance from the textbook. There were similarities between the twelve textbooks in the sense that most tasks could be solved using a template as guidance. A significantly lower proportion of the tasks required a solution to be constructed. This was especially striking in the initial sets of tasks. Textbook descriptions indicating problem solving did not guarantee that a task solution had to be constructed without the support of an available template.

  • 16.
    Karlsson Wirebring, Linnea
    et al.
    Umeå University, Faculty of Social Sciences, Department of Psychology. Umeå University, Faculty of Medicine, Department of Integrative Medical Biology (IMB). Umeå University, Faculty of Medicine, Umeå Centre for Functional Brain Imaging (UFBI).
    Lithner, Johan
    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).
    Jonsson, Bert
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Liljekvist, Yvonne
    Karlstad, Sweden.
    Norqvist, Mathias
    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.
    Nyberg, Lars
    Umeå University, Faculty of Medicine, Umeå Centre for Functional Brain Imaging (UFBI). Umeå University, Faculty of Medicine, Department of Radiation Sciences, Diagnostic Radiology. Umeå University, Faculty of Medicine, Department of Integrative Medical Biology (IMB).
    Learning mathematics without a suggested solution method: durable effects on performance and brain activity2015In: Trends in Neuroscience and Education, ISSN 2211-9493, Vol. 4, no 1-2, p. 6-14Article in journal (Refereed)
    Abstract [en]

    A dominant mathematics teaching method is to present a solution method and let pupils repeatedly practice it. An alternative method is to let pupils create a solution method themselves. The current study compared these two approaches in terms of lasting effects on performance and brain activity. Seventythree participants practiced mathematics according to one of the two approaches. One week later, participants underwent fMRI while being tested on the practice tasks. Participants who had created the solution method themselves performed better at the test questions. In both conditions, participants engaged a fronto-parietal network more when solving test questions compared to a baseline task. Importantly, participants who had created the solution method themselves showed relatively lower brain activity in angular gyrus, possibly reflecting reduced demands on verbal memory. These results indicate that there might be advantages to creating the solution method oneself, and thus have implications for the design of teaching methods.

  • 17.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A framework for analysing qualities of mathematical reasoning: version 32005Report (Other academic)
    Abstract [en]

    The purpose of this paper is to propose an empirically grounded and relatively well-specified framework for analysing creative problem solving reasoning and rote algorithmic reasoning. This is motivated by i) the persistent focus by students and by mathematics teachers, textbooks, and tests on rote learnt algorithms, ii) this algorithmic focus as a main cause behind learning difficulties, and iii) the lack of frameworks that can further help us to understand, analyse, and communicate the relevant phenomena.

  • 18.
    Lithner, Johan
    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).
    A research framework for creative and imitative reasoning2008In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 67, no 3, p. 255-267Article in journal (Refereed)
    Abstract [en]

    This conceptual research framework addresses the problem of rote learn- ing by characterising key aspects of the dominating imitative reasoning and the lack of creative mathematical reasoning found in empirical data. By relating reasoning to thinking processes, student competencies, and the learning milieu it explains origins and consequences of different reasoning types

     

  • 19.
    Lithner, Johan
    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).
    An emerging research framework for analyzing creative and imitative reasoning in problem solving2009In: Problem solving in mathematics education / [ed] Lars Burman, 2009, p. 23-37Conference paper (Refereed)
    Abstract [en]

    A central problem in mathematics education is that we want students to become problem solvers, but even after 20 years of research and reform many students still do rote thinking. This thinking is a main factor behind learning and achievement difficulties and has been analysed in a series of empirical studies. This presentation will summarise these studies, with a particular focus on the roles of creative and imitative reasoning.

  • 20.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Comparing two versions of Markov's inequality on compact sets1994In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 77, no 2, p. 202-211Article in journal (Refereed)
    Abstract [en]

    We compare a local and a global version of Markov's inequality defined on compact subsets of C. As a main result we show that the local version implies the global one. The same result was also obtained independently by A. Volberg.

  • 21.
    Lithner, Johan
    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.
    Learning mathematics by imitative and creative reasoning: plenary lecture2015In: Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education, Hobart: UniPrint, University of Tasmania , 2015, Vol. 1, p. 35-50Conference paper (Refereed)
    Abstract [en]

    This paper presents an interdisciplinary research program carried out in collaboration between researchers from mathematics education, psychology and neuroscience. A large body of research has shown that imitative models of mathematics teaching and learning are both common and largely ineffective. The purpose of the program is to explore if and how teaching, including task design, based on students‘ creative task solution reasoning may be more effective. 

  • 22.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Learning mathematics by imitative or creative reasoning2015In: Selected regular lectures from the 12th international congress on mathematical education / [ed] Sung Je Cho, Springer, 2015, p. 487-506Chapter in book (Refereed)
  • 23.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Lusten att Lära, Luleå kommun: Nationella kvalitetsgranskningar 2001/20022002Report (Other (popular science, discussion, etc.))
  • 24.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Lusten att Lära, Osby kommun: Nationella kvalitetsgranskningar 2001/20022002Report (Other (popular science, discussion, etc.))
  • 25.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Mathematical reasoning and familiar procedures1998Report (Other academic)
  • 26.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Mathematical reasoning and familiar procedures2000In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 31, no 1, p. 83-95Article in journal (Refereed)
    Abstract [en]

    Four first-year undergraduate students are working with two tasks. The underlying question treated is "what are the characteristics and background causes of their difficulties when trying to solve these tasks?" The purpose is to give a general survey of their main difficulties, rather than to go deeply into details. It seems like one of the common characteristics is that the students are more focused on what is familiar and remembered, than on (even elementary) mathematical reasoning and accuracy.

  • 27.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Mathematical reasoning in calculus textbook exercises2000Report (Other academic)
  • 28.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Mathematical reasoning in calculus textbook exercises2004In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 23, no 4, p. 405-427Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to study some of the strategies that are possible to use in order to solve the exercises in undergraduate calculus textbooks. It is described in detail how most exercises may be solved by mathematically superficial strategies, often without actually considering the core mathematics of the book section in question.

  • 29.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology. Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Mathematical reasoning in task solving1999Report (Other academic)
  • 30.
    Lithner, Johan
    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).
    Principles for designing mathematical tasks that enhance imitative and creative reasoning2017In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 49, no 6, p. 937-949Article in journal (Refereed)
    Abstract [en]

    The design research programme Learning by Imitative and Creative Reasoning (LICR) studies whether, how and why tasks and teaching that enhance creative reasoning lead to a more productive struggle and more efficient learning than the common but inefficient task designs based on imitating given solution procedures. The purpose of this paper is to synthesise the research outcomes determined to date by providing the following: a conceptual framework for key concepts and relationships among teaching, tasks, student activities and learning; a theoretical basis for analyses of causal effects between task/teaching design and learning outcomes; a design research methodology for transforming initial design ideas, through cycles of evaluation and revision, into firmer design principles; and an application of this theory and methodology to empirical studies carried out to date, in order to propose task-design principles related to imitative and creative reasoning.

  • 31.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology. Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Students’ mathematical reasoning in textbook exercise solving2000Report (Other academic)
  • 32.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Students’ mathematical reasoning in university textbook exercises2003In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 52, no 1, p. 29-55Article in journal (Refereed)
    Abstract [en]

    Video recordings of three undergraduate students’ textbook-based home- work are analysed. A focus is on the ways their exercise reasoning is mathematically well- founded or superficial. Most strategy choices and implementations are carried out without considering the intrinsic mathematical properties of the components involved in their work. It is essential in their strategies to find procedures to mimick and few constructive reasoning attempts are made.

     

  • 33.
    Lithner, Johan
    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 Exercises in Calculus Textbooks2003Report (Other academic)
    Abstract [en]

    This paper studies the discrepancy between the rich goals and the limited outcome in terms of reasoning required to do exercises.

  • 34.
    Lithner, Johan
    Institut for Studiet af Matematik og Fysik samt deres Funktioner i Undervisning, Forskning og Anvendelser, Roskilde universitetscenter, Danmark.
    Undergraduate learning difficulties and mathematical reasoning2001Doctoral thesis, comprehensive summary (Other academic)
  • 35.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Undergraduate learning difficulties and mathematical reasoning: a literature survey and project overview2001Report (Other academic)
  • 36.
    Lithner, Johan
    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).
    University mathematics students’ learning difficulties2011In: Education Inquiry, ISSN 2000-4508, E-ISSN 2000-4508, Vol. 2, no 2, p. 289-303Article in journal (Refereed)
    Abstract [en]

    The processes of learning mathematics are immensely complex and we do to large extents lack insights in these processes. This is especially problematic when it comes to tertiary mathematics education, which has been much less researched than primary and secondary mathematics education. Thus it is far from possible to clarify all relevant issues related to university mathematics learning difficulties. This paper will discuss the notion of learning difficulties and some related insights.

  • 37.
    Lithner, Johan
    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 Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    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).
    Boesen, Jesper
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Palm, Torulf
    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).
    Palmberg, Björn
    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).
    Mathematical competencies: A research framework2010In: Mathematics and mathematics education: Cultural and social dimensions / [ed] Bergsten, Jablonka & Wedege, Linköping, Sweden: Svensk förening för matematikdidaktisk forskning, SMDF , 2010, p. 157-167Conference paper (Refereed)
  • 38.
    Lithner, Johan
    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.
    Palm, Torulf
    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).
    Learning difficulties and mathematical reasoning2010In: The first sourcebook on nordic research in mathematics education: Norway, Sweden, Iceland, Denmark and contributions from Finland / [ed] Sriraman, B., Bergsten, C., Goodchild, S., Palsdottir, G., Dahl Sondergaard, B., & Haapasalo, L., Charlotte, NC: Information Age Publishing, 2010, p. 283-298Chapter in book (Refereed)
  • 39.
    Lithner, Johan
    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).
    Wallin, HansUmeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Matematikdidaktisk forskning: nordisk forskarworkshop; Umeå, 21-25 augusti 19961997Conference proceedings (editor) (Other academic)
  • 40.
    Lithner, Johan
    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).
    Wallin, HansUmeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nordic research workshop: problem driven research in matematics education2000Conference proceedings (editor) (Other academic)
  • 41.
    Lithner, Johan
    et al.
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Woijcik, Adam
    University of Krakow.
    A Note on Bernstein's Theorems1995In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 81, no 3, p. 316-322Article in journal (Refereed)
    Abstract [en]

    There is given a completion to Theorem 3.3 of [11] by showing that on compact subsets of R N (or C N) preserving Markov′s inequality, some speed of polynomial approximation leads to Lipschitz- and Zygmund-type classes of functions.

  • 42.
    Norqvist, Mathias
    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.
    Jonsson, Bert
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Eye-tracking data and mathematical tasks with focus on mathematical reasoning2019In: Data in Brief, E-ISSN 2352-3409, Vol. 25, article id 104216Article in journal (Refereed)
    Abstract [en]

    This data article contains eye-tracking data (i.e., dwell time and fixations), Z-transformed cognitive data (i.e., Raven's Advanced Progressive Matrices and Operation span), and practice and test scores from a study in mathematics education. This data is provided in a supplementary file. The method section describes the mathematics tasks used in the study. These mathematics tasks are of two kinds, with and without solution templates, to induce different types of mathematical reasoning.

  • 43.
    Norqvist, Mathias
    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.
    Jonsson, Bert
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Lithner, Johan
    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).
    Qwillbard, Tony
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Holm, Linus
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Investigating algorithmic and creative reasoning strategies by eye tracking2019In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 55, article id 100701Article in journal (Refereed)
    Abstract [en]

    Imitative teaching and learning approaches have been dominating in mathematics education. Although more creative approaches (e.g. problem-based learning) have been proposed and implemented, a main challenge of mathematics education research is to document robust links between teaching, tasks, student activities and learning. This study investigates one aspect of such links, by contrasting tasks providing algorithmic solution templates with tasks requiring students’ constructions of solutions and relating this to students’ learning processes and outcomes. Information about students’ task solving strategies are gathered by corneal eye-tracking, which is related to subsequent post-test performances and individual variation in cognitive proficiency. Results show that students practicing by creative tasks outperform students practicing by imitative algorithmic tasks in the post-test, but also that students that perform less well on creative tasks tend to try ineffective imitative strategies.

  • 44.
    Norqvist, Mathias
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Liljekvist, Yvonne
    Karlstads universitet.
    Jonsson, Bert
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Lithner, Johan
    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).
    Increased efficiency when engaging in creative mathematical founded reasoning2013In: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 5. / [ed] Lindmeier, A. M. & Heinze, A., Kiel, Germany: PME , 2013, p. 136-136Conference paper (Refereed)
  • 45.
    Norqvist, Mathias
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lithner, Johan
    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).
    Jonsson, Bert
    Umeå University, Faculty of Social Sciences, Department of Psychology.
    Liljekvist, Yvonne
    Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap..
    Creative Reasoning More Beneficial For Cognitively Weaker Students2015In: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, Prague: Charles University , 2015, p. 502-503Conference paper (Refereed)
    Abstract [en]

    In a study with 91 upper-secondary students the efficiency of two different types of mathematical practice tasks, procedural based algorithmic tasks and creative reasoning tasks, were studied. It was found that although the algorithmic group outperformed the creative group during practice the latter performed significantly better on a follow-up test. Closer inspection revealed that the difference in test performance was, contrary to common beliefs, driven by the cognitively weaker students.

  • 46.
    Palm, Torulf
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Boesen, Jesper
    National Center for Mathematics Education, University of Gothenburg.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Mathematical reasoning requirements in Swedish upper secondary level assessments2011In: Mathematical Thinking and Learning, ISSN 1098-6065, E-ISSN 1532-7833, Vol. 13, no 3, p. 221-246Article in journal (Refereed)
    Abstract [en]

    We investigate the mathematical reasoning required to solve the tasks in the Swedish national tests and a random selection of Swedish teacher-made tests. The results show that only a small proportion of the tasks in the teacher-made tests require the students to produce new reasoning and to consider the intrinsic mathematical properties involved in the tasks. In contrast, the national tests include a large proportion of tasks for which memorization of facts and procedures are not sufficient. The conditions and constraints under which the test development takes place indicate some of the reasons for this discrepancy and difference in alignment with the reform documents.

  • 47.
    Sidenvall, Johan
    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).
    Granberg, Carina
    Umeå University, Faculty of Social Sciences, Department of applied educational science, Interactive Media and Learning (IML). Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lithner, Johan
    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.
    Palmberg, Björn
    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.
    Supporting Teachers to Support Students’ Problem-solvingManuscript (preprint) (Other academic)
    Abstract [en]

    The purpose of this intervention study was to develop, test, and evaluate a teacher guide structured in line with central tenets of formative assessment in a real classroom setting. The teacher-guide was designed to support teachers’ diagnosis of student difficulties and their choice of feedback to help students to continue the construction of solution methods during problem- solving if they become stuck. By using an approach inspired by design research, five teachers used the teacher guide for two plus two weeks in 12 mathematics courses in upper secondary school with revisions of the teacher guide in between the iterations. Ninety-six teacher-student interactions were observed, and teacher interviews were conducted. The results showed that the teacher guide supported the teachers in providing less algorithmic information and instead focusing on the problem-solving process, and by that helping the students to themselves construct solutions during their problem-solving activity. The use of the teacher guide was sometimes constrained by the type of tasks the students were working on, by difficulties in making reasonable diagnoses of students’ difficulties, and by students’ insufficient ability and/or willingness to communicate.

  • 48. Sidenvall, Johan
    et al.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Jader, Jonas
    Students' reasoning in mathematics textbook task-solving2015In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 46, no 4, p. 533-552Article in journal (Refereed)
    Abstract [en]

    This study reports on an analysis of students' textbook task-solving in Swedish upper secondary school. The relation between types of mathematical reasoning required, used, and the rate of correct task solutions were studied. Rote learning and superficial reasoning were common, and 80% of all attempted tasks were correctly solved using such imitative strategies. In the few cases where mathematically founded reasoning was used, all tasks were correctly solved. The study suggests that student collaboration and dialogue does not automatically lead to mathematically founded reasoning and deeper learning. In particular, in the often common case where the student simply copies a solution from another student without receiving or asking for mathematical justification, it may even be a disadvantage for learning to collaborate. The results also show that textbooks' worked examples and theory sections are not used as an aid by the student in task-solving.

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