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  • 1.
    Johansson, Maria
    et al.
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Tossavainen, Timo
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Faarinen, Ewa-Charlotte
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Tossavainen, Anne
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Student teachers' definitions of the concept “teaching mathematics in preschool”2019In: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) / [ed] Uffe Thomas Jankvist, Marja van den Heuvel-Panhuizen, Michiel Veldhuis, ERME , 2019, p. 2277-2284, article id hal-02414896Conference paper (Other academic)
    Abstract [en]

    This article reports on how a group of preschool and primary student teachers define the concept “teaching mathematics in preschool” in the beginning of their studies. The background for this pilot-study is the recent change in the Swedish curriculum, which means a shift from play-based to more teaching oriented activities, and the actual Swedish debate on the role of teaching in preschool.

  • 2.
    Tossavainen, Anne
    Luleå University of Technology, Department of Health, Education and Technology, Education, Language, and Teaching.
    Characterizing Prospective Elementary Teachers' Mathematical Knowledge for Teaching Fractions2024Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Although research has delved into the challenges faced by mathematics teachers and students across various educational levels when working with fractions, these challenges persist. Fractions are an important but difficult content area in elementary school mathematics, and many future elementary teachers enter teacher education with limited knowledge of fractions. This lack of prior knowledge, combined with diverse experiences and attitudes toward the teaching and learning of mathematics, presents a challenge for teacher education programs aiming at enhancing prospective teachers’ knowledge to enable them to teach fractions effectively. Teacher education is a crucial time to attain a comprehensive pedagogical knowledge of mathematics, and this thesis characterizes prospective elementary teachers’ (n = 61) knowledge for teaching fractions as an outcome of Swedish teacher education. Through four empirical studies, the thesis also addresses the concept of mathematical identity and investigates the topic in light of the Mathematical Knowledge for Teaching framework.

    The findings highlight substantial differences between the participants in the subject matter and pedagogical content knowledge domain of fractions, revealing difficulties in both their procedural and conceptual knowledge. Challenges also arise in analyzing different fraction solutions and combining knowledge of fraction content with knowledge about elementary students, teaching, and the national curriculum document. This difficulty can be a hindrance for the quality teaching of fractions. Moreover, incoherent fraction knowledge occurs across the different knowledge categories included in the Mathematical Knowledge for Teaching framework. The findings also reveal uncertainty in relation to work with fractions and prospective teachers’ mathematical identities. A new framework for the analysis of different aspects of fractions is also presented in the thesis, and the findings are discussed considering the context of Swedish teacher education and the Mathematical Knowledge for Teaching framework. 

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  • 3.
    Tossavainen, Anne
    Luleå University of Technology, Department of Health, Education and Technology, Education, Language, and Teaching.
    Pedagogical content knowledge in prospective elementary teachers’ descriptions of teaching and learning of fractions2024In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170Article in journal (Refereed)
    Abstract [en]

    This study investigates the pedagogical content knowledge identified in six prospective elementary teachers’ written teacher practicum reports. Focusing on the three categories of pedagogical content knowledge included in the Mathematical Knowledge for Teaching framework, the study analyzes the prospective teachers’ descriptions and combines their knowledge of fraction content with knowing about students, teaching, and curriculum. The results indicate that prospective teachers describe teaching and learning of fractions mainly on a general pedagogical level. Moreover, they do not differentiate characteristics for elementary students’ fraction difficulties and misunderstandings as well as fraction core contents in the curriculum. The findings are discussed in relation to the Swedish teacher education context in which the study was conducted. Implications for teacher education are also discussed.

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    fulltext
  • 4.
    Tossavainen, Anne
    Luleå University of Technology, Department of Health, Learning and Technology, Education, Language, and Teaching.
    Student teachers’ common content knowledge for solving routine fraction tasks2022In: LUMAT: International Journal on Math, Science and Technology Education, E-ISSN 2323-7112, Vol. 10, no 2, p. 256-280Article in journal (Refereed)
    Abstract [en]

    This study focuses on the knowledge base that Swedish elementary student teachers demonstrate in their solutions for six routine fraction tasks. The paper investigates the student teachers’ common content knowledge of fractions and discusses the implications of the findings. Fraction knowledge that student teachers bring to teacher education has been rarely investigated in the Swedish context. Thus, this study broadens the international view in the field and gives an opportunity to see some worldwide similarities as well as national challenges in student teachers’ fraction knowledge. The findings in this study reveal uncertainty and wide differences between the student teachers when solving fraction tasks that they were already familiar with; two of the 59 participants solved correctly all tasks, whereas some of them gave only one or not any correct answer. Moreover, the data indicate general limitations in the participants’ basic knowledge in mathematics. For example, many of them make errors in using mathematical symbol writing and different representation forms, and they do not recognize unreasonable answers and incorrect statements. Some participants also seemed to guess at an algorithm to use when they did not remember or understand the correct solution method.

  • 5.
    Tossavainen, Anne
    et al.
    Luleå University of Technology, Department of Health, Education and Technology, Education, Language, and Teaching.
    Helenius, Ola
    University of Gothenburg, Gothenburg, Sweden.
    Student Teachers' Conceptions of Fractions: A Framework for the Analysis of Different Aspects of Fractions2024In: Mathematics Teacher Education and Development, ISSN 1442-3901, Vol. 26, no 1, article id 4Article in journal (Refereed)
    Abstract [en]

    Fractions are core content of elementary school mathematics, and conceptual knowledge of fractions is essential when developing a comprehensive understanding of fractions. Previous research, however, has indicated  limitations in student teachers' fraction knowledge. This study investigated 57 Swedish elementary school student teachers' conceptions of fractions. The data were collected using a paper-and-pencil questionnaire and analysed with an analytical framework building on previous research on four core components of fractions. Using the devised analytical framework, we were able to characterise the conceptual content shown in the student teachers' answers and identify gaps in their fraction knowledge. The most severe gaps were identified in relation to interpretations of fractions, where only the part-whole and the quotient interpretations were identified; the measure, operator, rate, ratio, and number interpretations were missing completely. Aspects of fractions related to representations and procedures were better represented in the participants' conceptions of fractions, but we also illustrate substantial differences between the student teachers. In addition to this quantitative description, we provide qualitative examples. The results raise some questions and implications to be addressed in teacher education programs when developing student teachers' fraction knowledge.

  • 6.
    Tossavainen, Anne
    et al.
    Luleå University of Technology, Department of Health, Education and Technology, Education, Language, and Teaching.
    Johansson, Monica
    Luleå University of Technology, Department of Health, Education and Technology, Education, Language, and Teaching.
    An insight into prospective elementary teachers’ mathematical knowledge for teaching: An example of fraction division2023In: Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) / [ed] Paul Drijvers, Csaba Csapodi, Hanna Palmér, Katalin Gosztonyi & Eszter Kónya, Alfréd Rényi Institute of Mathematics, Budapest, Hungary and ERME , 2023, p. 3303-3310Conference paper (Refereed)
    Abstract [en]

    This study investigates four Swedish prospective elementary mathematics teachers’ mathematical knowledge for teaching fractions. Using narrative inquiry, the study focuses on the prospective teachers’ reflections upon their mathematical identity and their analyses of six different solutions for a fraction division task. The results show that there are substantial differences between the prospective teachers in their mathematical content knowledge, pedagogical content knowledge, and in their attitudes towards mathematics teaching at the time of their graduation. Moreover, the prospective teachers expressed that teacher education did not respond to all their needs in their development as mathematics teachers. Thus, some implications for teacher education are also discussed in this paper.

  • 7.
    Tossavainen, Timo
    et al.
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Johansson, Maria
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Faarinen, Ewa-Charlotte
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Klisinska, Anna
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Tossavainen, Anne
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Swedish Primary and Preprimary Student Teachers' Views Of Using Digital Tools in Preprimary Mathematics Education2018In: Journal of Technology and Information Education, ISSN 1803-537X, Vol. 10, no 2, p. 16-23Article in journal (Refereed)
    Abstract [en]

    Our study surveys Swedish primary and preprimary student teachers' (n=94) views of content and methods of mathematics education in preschool and, especially, of using digital tools in preprimary mathematics education. The views related to digital tools turned out to be clearly positive in general. Students who are strongly for using digital tools are also more sure in saying that mathematics education in preschool should be fun. However, they agree less with the claims such as mathematics lessons should be structured, or that the responsibility for the mathematics education of small children belongs mainly to their parents. Those students who were quite strongly for using digital tools agreed less with the claim that mathematics is one of the most important areas of preprimary education. The willingness to take responsibility for children's mathematical education from the parents was the most significant single factor to explain the participants' opinions about using digital tools.

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