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  • 1.
    Gerhardt, Karin
    et al.
    Sveriges lantbruksuniversitet, Sverige.
    Wolrath Söderberg, Maria
    Södertörn University, School of Culture and Education, Rhetoric.
    Lindblad, Inger
    Södertörn University, School of Social Sciences, Social Work.
    Diderichsen, Öjvind
    Södertörn University, Teacher Education, Teacher Education and Aesthetic Learning Processes.
    Gullström, Martin
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Dahlin, Maria
    Södertörn University, School of Culture and Education, Rhetoric.
    Köping Olsson, Ann-Sofie
    Södertörn University, School of Social Sciences, Business Studies.
    Lehtilä, Kari
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Rasoal, Chato
    Södertörn University, School of Police Studies.
    Dobers, Peter
    Södertörn University, School of Social Sciences, Business Studies.
    Johansson, Johanna
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Berndt, Kurt D.
    Södertörn University, Teacher Education, Mathematics Education.
    Karlholm, Dan
    Södertörn University, School of Culture and Education, History and Theory of Art.
    Kjellqvist, Tomas
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Lalander, Rickard
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Vallström, Maria
    Södertörn University, School of Historical and Contemporary Studies, Ethnology.
    Alvarsson-Hjort, Jesper
    Södertörn University, School of Social Sciences, Psychology.
    Sjöholm, Cecilia
    Södertörn University, School of Culture and Education, Aesthetics.
    Lönngren, Ann-Sofie
    Södertörn University, School of Culture and Education, Comparative Literature.
    Bydler, Charlotte
    Södertörn University, School of Culture and Education, History and Theory of Art.
    Färjsjö, Eva
    Södertörn University, Teacher Education, Mathematics Education.
    Porseryd, Tove
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Sio, Miriam
    Södertörn University, Teacher Education, Teacher Education and Aesthetic Learning Processes.
    Yazdanpanah, Soheyla
    Södertörn University, School of Culture and Education, Gender Studies.
    Pihl Skoog, Emma
    Södertörn University, School of Historical and Contemporary Studies, Archive Studies.
    Sörbom, Adrienne
    Södertörn University, School of Social Sciences, Sociology.
    Gallardo Fernández, Gloria L.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Wadstein MacLeod, Katarina
    Södertörn University, School of Culture and Education, History and Theory of Art.
    Garrison, Julie
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Andrén, Elinor
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Svärd, Veronica
    Södertörn University, School of Social Sciences, Social Work.
    Hajighasemi, Ali
    Södertörn University, School of Social Sciences, Social Work.
    Spånberger Weitz, Ylva
    Södertörn University, School of Social Sciences, Social Work.
    Elmersjö, Magdalena
    Södertörn University, School of Social Sciences, Social Work.
    Persson, Sara
    Södertörn University, School of Social Sciences, Business Studies.
    Borevi, Karin
    Södertörn University, School of Social Sciences, Political Science.
    Carlsson, Nina
    Södertörn University, School of Social Sciences, Political Science.
    Löfgren, Isabel
    Södertörn University, School of Culture and Education, Media and Communication Studies.
    Ghose, Sheila
    Södertörn University, School of Culture and Education, English language.
    Bonow, Madeleine
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Bornemark, Jonna
    Södertörn University, School of Culture and Education, Centre for Studies in Practical Knowledge.
    Podolian, Olena
    Södertörn University, School of Social Sciences, Political Science.
    Grahn, Mats
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Environmental Science.
    Gunnarsson Payne, Jenny
    Södertörn University, School of Historical and Contemporary Studies, Ethnology.
    Kaun, Anne
    Södertörn University, School of Culture and Education, Media and Communication Studies.
    Faber, Hugo
    Södertörn University, School of Social Sciences, Political Science.
    Cederberg, Carl
    Södertörn University, School of Culture and Education, Centre for Studies in Practical Knowledge.
    Gradén, Mattias
    Högskolan Dalarna, Sverige.
    Nog nu, politiker – ta klimatkrisen på allvar2022In: Aftonbladet, no 2022-08-25Article in journal (Other (popular science, discussion, etc.))
  • 2.
    Karlsson, Natalia
    et al.
    Södertörn University, Teacher Education, Mathematics Education.
    Kilborn, Wiggo
    University of Gothenburg, Sweden.
    Arithmetic and algebraic knowledge in student learning of concepts2023In: Education and New Development 2023: Volume 1 / [ed] Mafalda Carmo, World Institute for Advanced Research and Science (WIARS), Portugal, Lisboa, Portugal: inSciencePress , 2023, Vol. 1, p. 3-7Conference paper (Refereed)
    Abstract [en]

    Current research deals with students’ arithmetical and algebraical knowledge, with focus on a conceptual connection, and the relationship between two aspects of knowledge. The content in question is rational numbers, rational equations and problem-solving about proportion and ratio in grades 7, 8 and 9. The method contains three tests given to 400 students in grades 7–9. Tools for analysis were theories of generalizing arithmetic into algebra (Kieran, 2004) and the relationship between arithmetic and algebra in a conceptual context (Kaput, 2008). 

    Current research shows that students’ knowledge of algebra and arithmetic often has a limited conceptual connection and a weak relationship. Their knowledge of arithmetic operations and solving rational equations use to be just procedural and rely on formulas learnt in a procedural way and often mixed up. The study also shows that students’ procedural strategies in finding formulas suitable for solving the equations, as well as carrying out the corresponding calculations, were often insufficient.  

    The study pays attention to shortcomings in students' conceptualization of arithmetic operations with rational numbers and how to apply them solving rational equations. One reason for this is lack of continuity in instruction and learning.  

  • 3.
    Karlsson, Natalia
    et al.
    Södertörn University, Teacher Education, Mathematics Education.
    Kilborn, Wiggo
    Matematikens didaktik och undervisningens innehåll i årskurs 1-6: guidat lärande med praktiska exempel2023 (ed. 1)Book (Other academic)
    Abstract [sv]

    Den första delen av boken handlar om matematikens didaktik innebörd som är ett tvärvetenskapligt forskningsfält, där möts olika vetenskaper. I boken reder författarna ut  individualiserings-och konkretiseringsprocesser samt vad diagnostisering och kontinuiteten i undervisningen kan innebära. I andra delen av boken beskrivs om hur matematiskt innehåll inom olika områden i skolans matematik för årskurs 1-6 kan utformas och hur undervisningen inom dessa områden kan gå i klassrumspraktiken. 

  • 4.
    Karlsson, Natalia
    et al.
    Södertörn University, Teacher Education, Mathematics Education.
    Kilborn, Wiggo
    University of Gothenburg, Sweden.
    Pre-service teacher' knowledge of mathematics: A framework for sustainable development of student knowledge2023In: Education and New Developments 2023: Volume 1 / [ed] Mafalda Carmo, Lisboa, Portugal: inSciencePress , 2023, Vol. 1, p. 196-200Conference paper (Refereed)
    Abstract [en]

    The purpose of this article is to draw attention to, analyze and discuss the following issues: (1) What mathematics should teacher education include, in order for student teachers to gain knowledge of a teaching practice that ensures the progression in students' mathematics development, and (2) How can the subject-specific content in an algebra course for student teachers be designed through an interaction between formal concepts in mathematics and the content of practical mathematics teaching with focus on algebra. An analysis of these issues is carried out within a theoretical framework of didactics of mathematics, related to a research context.

    This article is based on two research projects, MIL (Mathematics in teacher education) and SKUM (Student teachers’ knowledge and perceptions of mathematics) as well as ongoing research work with a focus on the quality of student teacher education in mathematics and the didactics of mathematics in the K–3 and 4–6 programs at Södertörn University. 

  • 5.
    Karlsson, Natalia
    et al.
    Södertörn University, Teacher Education, Mathematics Education.
    Kilborn, Wiggo
    University of Gothenburg, Sweden.
    Teachers' mathematical content knowledge and students' progression in learning of fraction and proportion2022In: Education and New Developments 2022: Volyme 1 / [ed] Mafalda Carmo, Lisboa: inScience Press, 2022, Vol. 1, p. 7-11Conference paper (Refereed)
    Abstract [en]

    Proportional reasoning causes considerable difficulty for students. One reason for this is, that a lack of basic understanding of fractions in earlier years, causes difficulties in the middle years. Moreover, learning of fractions and proportion is a long-term process and students encounter it continuously from grade 1 to 9. It is also difficult to teach, and teachers’ mathematical content knowledge plays a crucial role in students’ learning of mathematics. The purpose of this study is to analyse the effects of teaching, and the influence of teachers’ mathematical content knowledge about fractions and proportion on students learning in progression from grade 4 and 5 to grade 8. The method contains pre- and post-tests for 86 students, classroom observations, checking students’ written solutions and interviews of 35 selected students after the post-test. The intervention includes construction of educational materials (EM), teachers participating in seminars-training related to EM and teacher’s implementation of EM. The EM contains tasks for students and a teachers’ guide with aims and goals for teaching and a theoretical background. Tools for analysis were a methodological design, Variation theory, and a theoretical approach, Mathematical Content Knowledge for Teaching. In focus of the analysis was students learning in progression, related to variation and crucial aspects of learning. Findings from this study shows that teachers’ mathematical content knowledge and their ability to identify the objects of learning and apply this in teaching is very important for students’ learning and progression in their learning. Most students showed an ability to learn, but their performance was intimately linked to teachers’ perception of the crucial aspects in teaching, and variation. Moreover, anomalies in students’ perceptions of basic concepts caused obstacles in their learning. Some anomalies seem to have followed students from middle School to grade 8. Finally, the study illustrated how anomalies arise if misconceptions are not noticed by teachers. The outcome of the study can explain more about crucial steps in teaching and learning of fraction and proportion. The study pay attention to challenges in mathematics teaching.

  • 6.
    Karlsson, Natalia
    et al.
    Södertörn University, Teacher Education, Mathematics Education.
    Kilborn, Wiggo
    University of Gothenburg, Sweden.
    Teaching and learning the multiplication table by using multiplicative structures: Variation and crutial patterns2022In: Education and New Developments 2022: Volyme 1 / [ed] Mafalda Carmo, Lisboa: inScience Press, 2022, Vol. 1, p. 45-49Conference paper (Refereed)
    Abstract [en]

    This paper examines and analyzes how students learn multiplication tables, specifically the role of multiplicative structures and how these are used as students learn to master the tables. The analysis is performed in the context of the generalization process related to the teaching activity focusing students’ perception of concepts. The theoretical approach applies Davydov’s concept of theoretical generalization as perception-conception-elementary concept (PCE model) and Vergnaud’s theory of multiplicative structures in three classes: mapping rule (MR), multiplicative comparison (MC), and Cartesian product (CP). For the methodological design, Marton’s variation theory has been chosen.

    This study includes two teachers and 40 students in two Year 3 classes, followed two years later by one teacher and 25 students in one Year 5 class. The analysis of the outcome is based on documented classroom observations, one-on-one interviews with students and teachers’ reflections on students’ learning outcomes. The conclusion of the study is that the generalization of multiplication is a difficult process for students, especially in the classes MC and PC, and one that sometimes results in challenges to identifying multiplicative situations and relating these to the multiplication tables. This illustrates that teaching activities and teachers’ support are necessary conditions for students’ learning. The study also shows that multiplicative structures can help students to find and systematize crucial patterns in the multiplication table, allowing them to learn the multiplication table in a more efficient and structured manner. During the one-on-one interviews, students actively searched for and found structures and solutions that did not come up during lessons. This shows that multiplicative structures are a suitable didactic tool for identifying patterns in multiplication tables, thereby facilitating learning other than by rote.

  • 7.
    Karlsson, Natalia
    et al.
    Södertörn University, Teacher Education, Mathematics Education.
    Kilborn, Wiggo
    University of Gothenburg, Sweden.
    The impact of teachers' matter knowledge on students' learning of rational numbers and proportion2023In: Education Applications & Developments VIII: Advances in Education and Educational Trends / [ed] Mafalda Carmo World Institute for Advanced Research and Science, WIARS, Portugal, Lisboa, Portugal: inSciencePress , 2023, p. 13-24Chapter in book (Refereed)
    Abstract [en]

    This study examines the impact of teachers’ subject matter knowledge on students’learning. The mathematical content deals with rational number as fractions andproportion. The study includes pre- and post-tests from 99 students, classroomobservations, students’ written solutions and interviews with 48 selected studentsafter the post-tests. Findings from this study show that the impact of teachers’ subjectmatter knowledge and ability to identify the objects of learning, and apply this inteaching, strongly influenced the development of students’ conceptual learning aboutfractions and proportion.

  • 8.
    Karlsson, Natalia
    et al.
    Södertörn University, Teacher Education, Mathematics Education.
    Kilborn, Wiggo
    University of Gothenburg, Sweden.
    Towards a generalization: what students learn about multiplication2023In: Education Applications & Developments VIII: Advances in Education and Educational Trends / [ed] Mafalda Carmo, Lisboa, Portugal: inSciencePress , 2023, p. 51-62Chapter in book (Refereed)
    Abstract [en]

    This chapter examines and analyzes students’ learning about aspects of the concept of multiplication with a focus on perceptions and representations, and how they apply this to handling multiplicative situations and patterns in the multiplication tables. The analysis has been performed in the context of the generalization process related to teaching activities, with a focus on students’ perception of multiplication. The theoretical approach is based on Davydov’s (1990) view of theoretical generalization as a perception-conception-elementary concept (PCE model). The current mathematical content was classified according to: (1) multiplicative structures (Vergnaud, 1983);and (2) basic laws of algebra (van der Waerden, 1971). The relationship between students’ learning and the teaching process was studied in order to identify students’ learning in action. The study comprises two teachers and 40 students in two classes in grade 3 and was followed up two years later in grade 5 with one teacher and 25 students. The findings of this study can provide knowledge about students’ learning about multiplication using structures and multiplication tables in a conceptual context.

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