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Tossavainen, A. (2024). Characterizing Prospective Elementary Teachers' Mathematical Knowledge for Teaching Fractions. (Doctoral dissertation). Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Characterizing Prospective Elementary Teachers' Mathematical Knowledge for Teaching Fractions
2024 (English)Doctoral 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. 

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2024
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
Keywords
elementary teacher education, fractions, mathematical identity, mathematical knowledge for teaching, prospective elementary teacher
National Category
Pedagogy
Research subject
Mathematics and Science Education
Identifiers
urn:nbn:se:ltu:diva-105152 (URN)978-91-8048-544-9 (ISBN)978-91-8048-545-6 (ISBN)
Public defence
2024-06-20, A109, Luleå University of Technology, Luleå, 10:00 (English)
Opponent
Supervisors
Available from: 2024-04-19 Created: 2024-04-19 Last updated: 2024-05-30Bibliographically approved
Tossavainen, A. (2024). Pedagogical content knowledge in prospective elementary teachers’ descriptions of teaching and learning of fractions. Scandinavian Journal of Educational Research
Open this publication in new window or tab >>Pedagogical content knowledge in prospective elementary teachers’ descriptions of teaching and learning of fractions
2024 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170Article in journal (Refereed) Epub ahead of print
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.

Place, publisher, year, edition, pages
Taylor & Francis, 2024
Keywords
fractions, mathematical knowledge for teaching, pedagogical content knowledge, prospective elementary teacher, teacher education
National Category
Pedagogy
Research subject
Mathematics and Science Education
Identifiers
urn:nbn:se:ltu:diva-105146 (URN)10.1080/00313831.2024.2362928 (DOI)
Note

Full text: CC BY License;

This article has previously appeared as a manuscript in a thesis.

Available from: 2024-04-18 Created: 2024-04-18 Last updated: 2024-06-05
Tossavainen, A. & Helenius, O. (2024). Student Teachers' Conceptions of Fractions: A Framework for the Analysis of Different Aspects of Fractions. Mathematics Teacher Education and Development, 26(1), Article ID 4.
Open this publication in new window or tab >>Student Teachers' Conceptions of Fractions: A Framework for the Analysis of Different Aspects of Fractions
2024 (English)In: Mathematics Teacher Education and Development, ISSN 1442-3901, Vol. 26, no 1, article id 4Article in journal (Refereed) Published
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.

Keywords
conceptions of fractions, conceptual knowledge, elementary school, student teachers, teacher education
National Category
Didactics
Research subject
Mathematics and Science Education
Identifiers
urn:nbn:se:ltu:diva-104465 (URN)2-s2.0-85184913890 (Scopus ID)
Note

Validerad;2024;Nivå 1;2024-03-06 (signyg)

Available from: 2024-03-06 Created: 2024-03-06 Last updated: 2024-04-19Bibliographically approved
Tossavainen, A. & Johansson, M. (2023). An insight into prospective elementary teachers’ mathematical knowledge for teaching: An example of fraction division. In: Paul Drijvers, Csaba Csapodi, Hanna Palmér, Katalin Gosztonyi & Eszter Kónya (Ed.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13): . Paper presented at 13th Congress of the European Society for Research in Mathematics Education (CERME13), Budapest, Hungary, July 10-14, 2023. (pp. 3303-3310). Alfréd Rényi Institute of Mathematics, Budapest, Hungary and ERME
Open this publication in new window or tab >>An insight into prospective elementary teachers’ mathematical knowledge for teaching: An example of fraction division
2023 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
Alfréd Rényi Institute of Mathematics, Budapest, Hungary and ERME, 2023
Keywords
fraction division, mathematical identity, mathematical knowledge for teaching, prospective teacher, teacher education
National Category
Didactics
Research subject
Mathematics and Science Education
Identifiers
urn:nbn:se:ltu:diva-104471 (URN)
Conference
13th Congress of the European Society for Research in Mathematics Education (CERME13), Budapest, Hungary, July 10-14, 2023.
Note

ISBN for host publication: 978-963-7031-04-5

Available from: 2024-03-06 Created: 2024-03-06 Last updated: 2024-04-19Bibliographically approved
Tossavainen, A. (2022). Student teachers’ common content knowledge for solving routine fraction tasks. LUMAT: International Journal on Math, Science and Technology Education, 10(2), 256-280
Open this publication in new window or tab >>Student teachers’ common content knowledge for solving routine fraction tasks
2022 (English)In: LUMAT: International Journal on Math, Science and Technology Education, E-ISSN 2323-7112, Vol. 10, no 2, p. 256-280Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
University of Helsinki, 2022
Keywords
common content knowledge, elementary school, fractions, student teacher, teacher education
National Category
Pedagogy
Research subject
Mathematics Education
Identifiers
urn:nbn:se:ltu:diva-92163 (URN)10.31129/lumat.10.2.1656 (DOI)2-s2.0-85135486064 (Scopus ID)
Note

Validerad;2022;Nivå 1;2022-07-14 (sofila)

Available from: 2022-07-14 Created: 2022-07-14 Last updated: 2024-04-19Bibliographically approved
Johansson, M., Tossavainen, T., Faarinen, E.-C. & Tossavainen, A. (2019). Student teachers' definitions of the concept “teaching mathematics in preschool”. In: Uffe Thomas Jankvist, Marja van den Heuvel-Panhuizen, Michiel Veldhuis (Ed.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11): . Paper presented at Eleventh Congress of the European Society for Research in Mathematics Education (CERME11), 6-10 February, 2019, Utrecht, The Netherlands (pp. 2277-2284). ERME, Article ID hal-02414896.
Open this publication in new window or tab >>Student teachers' definitions of the concept “teaching mathematics in preschool”
2019 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
ERME, 2019
Keywords
Young children, Teaching, Learning, Mathematics, student teachers, preschool
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:ltu:diva-78217 (URN)
Conference
Eleventh Congress of the European Society for Research in Mathematics Education (CERME11), 6-10 February, 2019, Utrecht, The Netherlands
Note

ISBN för värdpublikation: 978-90-73346-75-8

Available from: 2020-03-26 Created: 2020-03-26 Last updated: 2023-09-04Bibliographically approved
Tossavainen, T., Johansson, M., Faarinen, E.-C., Klisinska, A. & Tossavainen, A. (2018). Swedish Primary and Preprimary Student Teachers' Views Of Using Digital Tools in Preprimary Mathematics Education. Journal of Technology and Information Education, 10(2), 16-23
Open this publication in new window or tab >>Swedish Primary and Preprimary Student Teachers' Views Of Using Digital Tools in Preprimary Mathematics Education
Show others...
2018 (English)In: Journal of Technology and Information Education, ISSN 1803-537X, Vol. 10, no 2, p. 16-23Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Palacky University Olomouc, 2018
Keywords
a digital tool, ICT, mathematics education, preprimary, primary, view
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:ltu:diva-70617 (URN)10.5507/jtie.2018.007 (DOI)
Available from: 2018-08-28 Created: 2018-08-28 Last updated: 2023-09-04Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-0429-243X

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