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  • 1.
    Abdulrasul, Zahraa
    Södertörns högskola, Lärarutbildningen.
    Bråktal, decimaltal och procent: En kvalitativ studie om hur sambandet mellan bråktal, decimaltal och procent undervisas i årskurs 4-62017Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    The aim of this study is to investigate how the connection between fractions, decimals and percent are taught in grade 4-6 with more focuson the fractions. The empirical data was obtained by qualitative methods comprising interviews with four mathematic elementary school teachers, in addition to two observations with two classrooms in grade 6. The data presented is from one school. The theoretical framework is based on Liping Ma profound understanding of fundamental mathematics and theories of subject didactic concepts of Kilborn, Löwing, Karlsson & Kilborn and MacIntosh. The results of the interviews and observations show that the connection between fractions, decimals and percent is being taught without illuminating how the mentioned are connected. The aspect of fractions, which has been taught to show the relation between fractions and decimals, was division as metaphor. While there was no aspect of fractions has been taught to show the relation between it and percent except that a percent is a hundredth. Such as 40% is equal with 40/100. In addition, fractions has been taught by using visual aids, but never taught by using number line. In conclusion the connection between fractions, decimals and percent has not been related clearly with basic concept fractions.

    Fulltekst (pdf)
    fulltext
  • 2.
    Ablouh, Amin
    et al.
    Södertörns högskola, Lärarutbildningen.
    Sedraoui, Nasim
    Södertörns högskola, Lärarutbildningen.
    Traditionell undervisning gentemot det kooperativa lärandet: En interventionsstudie om användningen av det kooperativa lärandet i matematikundervisningen2023Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    This study aims to investigate the effects of cooperative learning on pupils’ knowledge and development with a particular focus on concepts and conceptual understanding in mathematics. By employing both qualitative and quantitative research methods, the study compared the effectiveness of cooperative learning to traditional teaching approaches in grade 4. The following question was formulated to research the aim of this study:

    • How does pupils’' understanding of concepts in mathematics differ after traditional teaching compared to teaching with cooperative learning in grade 4?

    Svanelid’s (2014) three aspects were used as an analysis model in this intervention study. With the analysis model, teachers can assess whether pupils have understood various mathematical concepts. The results of the aim showed that cooperative learning had a significant positive impact on pupils’ learning and their understanding of geometrical concepts. Through collaborative activities and interactive discussions, pupils actively participated in the learning process, leading to improved comprehension and retention of geometric concepts. However due to introduction of methodological weaknesses and potential biases the results can not be considered as statistically sound.

    The study indicated development in pupils’ learning and understanding of mathematics. In an attempt to pursue the main aim of this study, traditional teaching and cooperative learning were used as teaching techniques for pupils to study the development of their learning. After each teaching method, tests were used to identify the results of the analysis. The results indicated progression in the pupils’ learning by using cooperative teaching. Teachers are encouraged to further investigate cooperative learning techniques in their lessons as it potentially can increase pupils’ learning. More research is needed to establish a correlation between the use of cooperative learning in the teaching of mathematical concepts.

    Fulltekst (pdf)
    fulltext
  • 3.
    Acar, Nathalie
    Södertörns högskola, Lärarutbildningen.
    ”Rektangel – En avlång fyrkant, som formen av en fotbollsplan”: En kvalitativ studie om språket lärare använder i sin matematikundervisning i årskurs 4-62020Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    The purpose of this study is to investigate how teachers use everyday language in parallel with school language to support students to develop their language in mathematics in 4-6 th grade.

    To examine this, three research questions were formulated:

    • How do teachers use everyday language and school language in teaching mathematics?
    • In what way do teachers support students to develop their mathematical scientific language in teaching mathematics?
    • What type of interaction is given the opportunity in teaching mathematics for students to be able to develop their mathematical school language?

    To collect data for the study, four qualitative observations were performed of four different teachers av two different schools. Each observation was then followed by a qualitative interview.

    The result of the study indicates that teacher often use the everyday language to explain the school language for the students. Teachers also use different scaffolding methods as word explanations, asking questions or use student’s previous knowledge to support students to develop their mathematical scientific language. Finally, the result of the study shows that the students were given interaction with the teacher, interaction with each other but also individual learning to develop the mathematical school language.

    Fulltekst (pdf)
    fulltext
  • 4.
    Ahlgren, Anna
    Södertörns högskola, Lärarutbildningen.
    Har bilden en mening?: En studie om illustrerad multiplikation2018Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    Illustrated pictures play an important role as mediators of mathematical concepts and relations in mathematical textbooks used in Swedish primary school classrooms. Theories of the meaning of semiotics for teaching and learning, as well as the Variation theory of learning, are used as a framework to investigate the critical aspects for developing multiplicative reasoning through visual presentations. In this study143 students in 3rd grade (age 9-10) participated in a test where multiplication is represented with illustrations, using both additive and multiplicative groupings. The students were also instructed to draw multiplication expressions with various visual supports. Students’ responses were analyzed by quantifying groupings based on the multiplication expressions students identify, as well as the extend of which they use additive and multiplicative visual representations and support in their own drawings. Results show indications of different properties of multiplication that can be presented in illustrations. How teacher knowledge can be used to identify the critical aspects for learning multiplication is here discussed, leading to suggestions regarding ways is which textbook pictures can be useful tools in teaching and learning.

    Fulltekst (pdf)
    fulltext
  • 5.
    Ahlgren, Anna
    Södertörns högskola, Lärarutbildningen.
    Målande multiplikation: En undersökning av hur multiplikation illustreras i läroböcker för årskurs två2018Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    This study examines how illustrations are used to introduce the concept of multiplication in Swedish mathematics textbooks intended for use with 2nd grade students. The aim is to find out how instructions and tasks are supported by illustrations by using a sociocultural perspective on learning with focus of mediating artifacts. The findings are compared to research in the field of mathematics didactics, where the importance of teaching multiplicative structures to primary school students is emphasized. With a method that categorize illustrations, insight is gained into how well they connect to the subject content, and in addition if they show additive or multiplicative multiplication. This study also looks into the extent that students are being instructed and encouraged to illustrate their answers to the textbook assignments. Results from the analyses of four 2nd grade mathematics textbook series, show that illustrations are used to a large extent to support text and numbers in introducing multiplication, but that all books contain pictures that contradict the subject content. The results also show that the majority of the illustrations demonstrate multiplication as repeated addition. Furthermore, this study suggests that when students are encouraged to draw pictures themselves, they are in most cases not given support and instructions to draw multiplicative multiplication. Based on earlier research within this field, as well as the findings of this study, it is argued that the dominant focus on repeated addition in illustrations can trap students in patterns of additive reasoning. This can interfere with their perception and comprehension of multiplication structure, and lead to limitations of students’ further development and understanding of mathematic concepts.

    Fulltekst (pdf)
    fulltext
  • 6.
    Ahmed Omran, Zahraa
    Södertörns högskola, Lärarutbildningen.
    Språkutvecklande matematikundervisning inom problemlösning2019Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
  • 7.
    Altuntas, Ann-Sofie
    Södertörns högskola, Lärarutbildningen.
    ”Fröken, kan centikuber smälta i ett glas med saft?” – Undrande elev i klass 3: En studie kring vilka strategier/arbetssätt för formativ bedömning som fyra lärare i åk 3 använder sig av för flerspråkiga elever i matematikundervisningen.2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 8.
    Andersson, Jonas
    et al.
    Södertörns högskola, Institutionen för kultur och lärande, Medie- och kommunikationsvetenskap.
    Hammarlund, Johan
    M-Brain AB.
    Kontextförlust och kontextkollaps: Metodproblem vid innehållsanalys av sociala medier2016Inngår i: Nordicom Information, ISSN 0349-5949, Vol. 38, nr 3, s. 41-55Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The article proposes that social media platforms enable large volumes of user-driven circulation of media content, and argues for a combination of qualitative and quantitative considerations when analysing data from such platforms. Issues of context are vital; context must be understood both qualitatively (cultural setting) and quantitatively (statistical reference points for comparison). The authors emphasise that the possibilities of ‘big data’ should not tilt analyses so that sensitivities to subtler meanings are lost. By examining a recent research project of our own, examples are given of how topological network analysis can be successfully combined with close readings of strategically selected parts of the data and how, by doing so, context shifts can be identified that increase the reliability of the analysis. Consequently, it is recommended that mere number crunching is not enough, and that questions of ‘how,’ ‘why,’ and ‘whether’ are required in order to understand the phenomena in their societal settings. 

  • 9.
    Andersson, Julia
    Södertörns högskola, Lärarutbildningen.
    Att segla över ett okänt hav, till en okänd destination: En studie om att klargöra och delge lärandemål i matematik i en årskurs 22016Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    The aim of this study is to investigate how learning intentions are sheared and clarified during lessons, as a part of formative assessment. Studies have shown that the capability of formative assessment is an important part of teacher quality and that clarifying the intention with the lessons promotes the activity in the classroom. My study is going to focus on mathematic in a second grade class. The three questions that I am going to investigate are:

    • How learning intentions and criteria for success are sheared and clarified in the instruction in mathematic?
    • How do the pupils describe what the learning intentions in mathematic are?
    • How do the pupils describe how they get to know the learning intentions in mathematic?

     

    The method that I have used to investigate the first question is observation of eight lessons in mathematic, in two different mathematic groups. The second and third questions focus on the pupils and interviews with pupils are therefore used to investigate them.

     

    Formative assessment and strategy one, clarifying and shearing learning intentions and criteria for success are used as a theoretical framework in the analyze of the results. The conclusions I have reached are that the mathematic book is a big prat of the lessons and both the teacher and the pupils make it seem like the main intention of the lessons. A summative test was done during the study and it indicated that high scores seem to be more in focus than the knowledge and understanding. Almost all the pupil that I interviewed describe their IUP-intentions (plan for individually developing) that they have been given in the beginning of the year. The pupils were not sure what the intentions meant and told me that they never used them after they get them, which they do in the Swedish education.

    Fulltekst (pdf)
    fulltext
  • 10.
    Arslan, Hümeyra
    Södertörns högskola, Lärarutbildningen.
    Hur uppfattar du bråk?: En studie om elevers strategier vid problemlösning2020Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    The concept of fractions is necessary and vital knowledge in mathematics and has an essential role in perceptions of other mathematical areas. But many claims that this concept is both hard to teach and difficult to understand and thus avoids teaching and using fractions. To find out how the pupils perceive and reason about fractions, didactic theory, George Pólya's, and Frank Lester's problem-solving strategies and the subject theory has been used as a theoretical framework. In the study, which is a case study, participated 24 pupils the ages were between 9 and 10 and performed three diagnoses with a specific focus at part of a whole and part of a number. The diagnostic results were analyzed quantitatively, and then semi-structured interviews were conducted with six pupils according to the selection has obtained from the percentage of the solution frequencies. The results from the diagnoses show that the pupils' solution frequency on the diagnoses was between 14% and 90%. The analyzes from the semi-structured interviews show that the pupils with a lower solution frequency had inadequate knowledge of the concept of fractions and insufficient knowledge of the subject theory and used problem-solving strategies to a very meager extent. The pupils with a higher solution frequency had good perceptions of fractions and had good knowledge of the theory of the subject, and use problem-solving strategies to a much greater extent.

    Fulltekst (pdf)
    fulltext
  • 11.
    Berggren, My
    Södertörns högskola, Lärarutbildningen.
    Det kreativa matematiska resonemanget i dagens klassrum: Undersökning om möjligheter till att utveckla ett kreativt matematiskt resonemang i undervisning på mellanstadiet2019Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    The purpose of this study is to try to gain a deeper understanding of teachers' views on how teaching should be designed to promote creative mathematical reasoning in problem-solving. This will be examined on the basis of the following two questions: What opportunities in problem solving teaching can students use conceptual as well as procedural knowledge in order to develop a creative reasoning? And what opportunities for developing a creative reasoning are there in problem solving teaching? The teachers´ lessons were observed to answer the questions. Interviews of the teachers were conducted to supplement the observations and get a picture of their knowledge of the creative reasoning.

    Previous studies show that students rarely use a creative reasoning because teaching materials and examinations do not give students the opportunity to do so. Instead the students tend to use more imitative reasoning which is not built on deeper knowledge but is based on memorizing information. Therefore, it becomes relevant to investigate what opportunities classroom activities give students to make use of a creative mathematical reasoning. This study concludes that students are given a limited opportunity to use creative mathematical reasoning. Students can use both conceptual and procedural knowledge during the teacher-led teaching. The type of teaching that requires students to use creative reasoning is lacking. From interviews of the teachers, it emerges that the teachers do not know about the different types of mathematical reasoning. This may explain why students rarely need to use a creative reasoning that is based on a deeper understanding of the lessons learned on problem solving.

  • 12.
    Bisenius Sellgren, Kajsa
    Södertörns högskola, Lärarutbildningen.
    En studie om elevers val av metoder vid subtraktionsberäkningar2010Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this qualitative study of students’ methods of calculating subtractions, I have used interviews, subtraction exercises and analysis of teaching material. The purpose of my study was to explore which methods students in grade three uses when calculating subtractions. I also wanted to highlight which strategies the students use and their comprehension of the concept of subtraction. In the study, I also highlight the different pedagogical ideas on which the teaching material is based on and the students’ choice of methods.  The study shows that the students choose to use the methods”deduct” and “kind of number” independently. Further it also shows that the students choose to switch from the method “deduct” to “kind of number” when the numbers in the exercises are further up on the number axis. When asked, the students answered that subtraction means “minus” which they in turn explained as removing something, an explanation confirmed by the Swedish Academy dictionary. The students’ choice of methods and teaching material is based on different fundamental pedagogical view.

     

    Fulltekst (pdf)
    FULLTEXT02
  • 13.
    Blomskog, Stig
    Södertörns högskola, Institutionen för samhällsvetenskaper, Nationalekonomi.
    A formal analysis of a conventional job evaluation system2007Rapport (Annet vitenskapelig)
    Abstract [en]

    In this paper we analyze the use of numerical information in the context of job evaluation. The analysis is based on the job evaluation system Steps to Pay Equity, which is recommended by the European Project on Equal Pay supported by the European commission. The main findings can be summarized as follows. Firstly, in Steps to Pay Equity no method is suggested that can be used in order to construct stronger scales than ordinal scales. This implies that rankings of jobs are based on the addition of ordinal scales, which means that the rankings are very unstable for admissible transformations. Secondly, there is no explicit definition or explanation how the weights should be interpreted, something that hampers an assessment about the reasonability of the assigned weights. Thirdly, the convention to classify jobs on predefined levels can give rise to heavy deformations of relevant differences between jobs, which means that received rankings of jobs are unjustified guidance for impartial pay setting. We suggest a possible remedy by illustrating the use of a specific multi-attribute evaluation model.

    Fulltekst (pdf)
    A formal analysis of a conventional job evaluation system
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  • 14.
    Blomskog, Stig
    Södertörns högskola, Institutionen för samhällsvetenskaper, Nationalekonomi.
    An analysis of the principle ”Equal Pay for Jobs of Equal Value”2007Rapport (Annet vitenskapelig)
    Abstract [en]

    In this paper we analyze a number of assumptions and conceptual issues that arise in applications of conventional job evaluations, which are used in order to implement the principle “Equal Pay for Jobs of Equal Value” according to the Equal Pay Acts.

    The main findings of the analysis can be summarized as follows: 1) A lack of a distinction between subjective and objective criteria as well as between descriptive and evaluative criteria, 2) A defective interpretation of independency conditions that are necessary in order to represent evaluation of jobs by weighted sums of scores, 3) An incorrect diagnosis and subsequently incorrect remedies of defects in job evaluation methods, 4) An incorrect interpretation of the meaning of key concepts such as “Jobs of Equal Value”, 5) Unwarranted assumptions about formal features of relations defined by the concept “Jobs of Equal Value”.

    Fulltekst (pdf)
    An analysis of the principle ”Equal Pay for Jobs of Equal Value”
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  • 15.
    Blomskog, Stig
    Södertörns högskola, Institutionen för samhällsvetenskaper, Nationalekonomi.
    An Evaluation of Employee Performance Based on Imprecise Value Judgments: Two Experiments2007Rapport (Annet vitenskapelig)
    Abstract [en]

    In this paper we test the usefulness of imprecise value judgments in evaluating employee performance. The test is based on two experiments which evaluate the performance of college lecturers. The experiments are carried out by applying the PRIME model (Preference Ratios in Multi-attribute Evaluation), a specific multi-attribute value model that supports the use of imprecise value judgments. The test shows that the use of imprecise value judgments, as synthesized by the PRIME model, can remedy a number of defects that are identified in conventional evaluation models in regard to job requirements and employee performance.

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    An Evaluation of Employee Performance Based on Imprecise Value Judgments
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  • 16.
    Blomskog, Stig
    Södertörns högskola, Institutionen för samhällsvetenskaper, Nationalekonomi.
    Analys av ett individuellt lönesystem baserad på mångdimensionell beslutsteori2003Rapport (Annet vitenskapelig)
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    Analys av ett individuellt lönesystem baserad på mångdimensionell beslutsteori
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  • 17.
    Bryngelsson, Erik
    Södertörns högskola, Lärarutbildningen.
    Mathematical Knowledge for Teaching (MKT) i praktiken: Vilka kunskaper krävs för att undervisa matematik?2020Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    The following study aims to examine the special mathematical knowledge needed in order to teach mathematics. Furthermore, the study attempts to explore how teachers’ views on the knowledge needed in order to teach mathematics affects their student’s opportunities to develop their conceptual understanding.

    Qualitative and quantitative empirical data was attained by observations and complementary interviews. A total of three teachers, all working at the same school, was observed and interviewed. The study used Ball, Thames & Phelps (2008) practice-based theory of mathematical knowledge for teaching, MKT, as its theoretical framework when analyzing the empirical data.

    The result of the observations displays that math teachers tend to use common content knowledge far more than specialized content knowledge during their lessons. The outcome of this also study reveals that there is a tendency among teachers to interfuse mathematical concepts with terminology. Conceptual understanding is equated with the use of correct terminology. The students are not exposed to the underlying ideas of the mathematical concepts. The study also concludes that there seems to be a sectioning between the mathematical content taught in grade 4-6 from the rest of the content being taught in elementary school, with a low number of connections being made between mathematical topics and concepts included in the curriculum.

    Fulltekst (pdf)
    fulltext
  • 18. Burenin, Anatoliy A.
    et al.
    Zinovyev, Pavel V.
    Lebedeva, Natalia F.
    Construction of approximate solutions of the non-stationary one-dimensional axially symmetric tasks of dynamics of an incompressible elastic medium2002Inngår i: Advanced Problems in Mechanics  2002.: Proceeding, St.Peterburg: Russian Academy of Sciences, 2002, s. 134-138Konferansepaper (Fagfellevurdert)
  • 19. Burenin, Anatoly A.
    et al.
    Lebedeva, Natalia F.
    On constructing approximate solutions för problems in dynamics of incompressible elastic medium with axial symmetry2002Konferansepaper (Fagfellevurdert)
  • 20.
    Do-Quang, Minh
    et al.
    KTH.
    Amberg, Gustav
    KTH.
    Numerical simulation of the coupling problems of a solid sphere impacting on a liquid free surface2010Inngår i: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 80, nr 8, s. 1664-1673Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper presents a model, using a phase-field method, that is able to simulate the motion of a solid sphere impacting on a liquid surface, including the effects of capillary and hydrodynamic forces. The basic phenomena that were the subject of our research effort are the small scale mechanism such as the wetting property of the solid surface which control the large scale phenomena of the interaction. The coupled problem during the impact will be formulated by the inclusion of the surface energies of the solid surface in the formulation, which gives a reliable prediction of the motion of solid objects in/on/out of a liquid surface and the hydrodynamic behaviours at small scales when the inertia of fluid is less important than its surface tension. Numerical results at different surface wettabilities and impact conditions will be presented and compared with the experiments of Duez el al. [C. Duez, C. Ybert, C. Clanet, L. Bocquet, Nat. Phys. 3 (2007) 180-183] and Lee and Kim [D. Lee. H. Kim, Langmuir 24 (1) (2008) 142]. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.

  • 21.
    Engblom, S.
    et al.
    Uppsala University.
    Do-Quang, Minh
    KTH.
    Amberg, Gustav
    KTH.
    Tornberg, Anna-Karin
    KTH.
    On diffuse interface modeling and simulation of surfactants in two-phase fluid flow2013Inngår i: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 14, nr 4, s. 879-915Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An existing phase-fieldmodel of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.

  • 22.
    Gunnarsson, Hugo
    Södertörns högskola, Lärarutbildningen.
    En bekant kontext: En kartläggning och jämförelse av ämnesspråk i Sveriges mest använda matematikbok samt i de nationella proven för elever i årskurs 6.2017Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    A Familiar Context - a survey and comparison of mathematical language in the most widely-used mathematics textbook and in the standardized national tests for grade 6 students in Sweden.

    Studies have shown that language has a crucial role when students learn mathematics but there is a lack of empirical surveys mapping how mathematical language is used in different practices. One aspect of mathematical language called personification, which is associated with something that generates personal interest or contributes with a familiar context, seems to affect low-performing students in a negative way in their problem solving in the subjects of algebra and geometry.

    The overall aim of this study is to perform an empirical survey and analysis over how the personification of the mathematical language is used in the most commonly used mathematics textbook and the standardized national tests for students in grade 6 in Sweden. To answer this purpose, two research questions have been formulated:

    To what extent are natural language, mathematical imagery and mathematical symbols personalized in the field of algebra and geometry?

    How do typical mathematical tasks differ in the subjects of algebra and geometry?

    Method: Selected mathematical tasks from the most commonly used mathematics textbook and the national tests were analyzed in regards to personification. These selected tasks were also analyzed in regards to the concepts, metonymy and metaphor which can be used to distinguish the core of natural language in mathematical tasks.

    Results: There are differences between the uses of personification in the subjects of algebra and geometry. Personification was also found to be more common in the national tests than in the mathematics textbook. A comparison between the typical tasks from each subject area in the mathematics textbook and the national tests also showed that metaphorical form, a concept like personification associated with familiar context, is used more in the national tests than in the mathematics book.

    Conclusions: A clear difference in the use of personification and metaphorical form between textbooks and standardized national tests in mathematics for year 6 students was identified. Such differences in language usage may impair mathematics knowledge assessment. It is therefore important to make authors aware of how language use can affect a student's problem solving ability and raises the question as to whether personification and metaphorical form should be included in testing mathematical knowledge?

    Fulltekst (pdf)
    fulltext
  • 23.
    Ivarsson, Mabel Rocio
    Södertörns högskola, Lärarutbildningen.
    Matematik i förskolan: Barns antalsuppfattning i de tidiga åren2011Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    Purpose: The current thesis assignment aims to explain, understand and follow the strategies the young children employ into a conception of numbers. This thesis is based on a study performed by Doverborg and Pramling Samuelson.

    The following research questions serve to refine the stated goal:

    • How mathematical thinking regarding conception of numbers occurs within younger children and which strategies they use?
    • How is the interaction between the teacher and the younger children?

    Method: The study is organized as a qualitative study and was conducted in a pre-school with a group of four children. The children that have participated within my study are between two and three years old. They were filmed in four exercises. Then the films were transcribed. The method used is an analytic approach intentional analysis which allows studying the children´s strategies according to the established questions and also it makes it possible to follow how they think regarding mathematics.

    Conclusion: My study group shows in the final results that they in their strategies made use of one or more principles in their conception of numbers.

    Fulltekst (pdf)
    fulltext
  • 24.
    Jaddo, Tara
    Södertörns högskola, Lärarutbildningen.
    Elevers strategianvändning vid arbete med problemlösning: En studie om elevers individuella utveckling av strategierna de använder vid samtal i heterogena grupper med fokus på cirkelns area2021Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    This study aims to investigate students’ strategy use in performing problem-solving tasks about the measurement of a circle's area, and whether the students' individual strategy thinking develops during discussions about strategic choices in heterogeneous groups.

    The theories that are linked to this study are Strategy use, Heterogeneity, and Classroom norms. The theories about strategy use are about the student’s choice of strategies and about the students' understanding of the strategy they choose to use. The theory about Classroom norms indicates that teachers and other students influence students' mathematical reasoning and calculation. Finally, the theory about Heterogeneity, tells us how students' different knowledge levels, backgrounds and experiences influence the development of mathematics.

    The study was implemented in two classes from year six in primary school, where a total of four heterogeneous groups from these classes were created. The students had to individually perform three problem-solving tasks which involved calculating the area of ​​the circle. The students were taught different strategies for making these calculations and they could use any strategy. Students then discussed their solution strategies in groups before they had to solve the next task. 

    The results of the research show that the only relevant strategy used in the four groups was the multiplication strategy. The reason why the students used the multiplication strategy was directly connected to the classroom norms the teacher had presented. Therefore, students learned the multiplication strategy and they implemented it immediately without understanding why they calculated it in that way. Because the students only used one relevant strategy to calculate the area of ​​the circle in all groups, there was no exchange of strategies. There was, however, an exchange of experience. Since the students who used irrelevant strategies understood how other students solved the problem-solving tasks about the area of ​​the circle with the multiplication strategy. As a result of the discussions in heterogeneous groups, the students who used irrelevant strategies started using the multiplications strategy eventually. 

    Fulltekst (pdf)
    Elevers strategianvändning vid arbete med problemlösning
  • 25.
    Johansson, Jeanette
    Södertörns högskola, Lärarutbildningen.
    Att bråkas med bråk!: En kvalitativ studie i årskurs 3, som med hjälp av Diamantdiagnosens formativa bedömning ger inblick i elevers svårigheter med bråk.2017Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    The purpose of this study is to understand the difficulties third grade students have with fractions. Previous research indicates that students have difficulties understanding fractions, and fractions as a number seem to be the most difficult, while fractions as part of whole seem less difficult. Further, research also shows that fractions as numbers are the most important for student understanding of advanced levels of mathematics, such as algebra.

    This study is based on diagnostic tests using the diagnostic tool “Diamantdiagnosen” and follow-up interviews of 6 students. The diagnostic tool is available on the Skolverkets website and serves as a support for teachers to do a formative assessment of students. The diagnostic test was followed by interviews where the students could elaborate on the difficulties they encountered and how they felt when solving the assignments. In order to categorize the difficulties the students encountered during the diagnostic part, theory of formative assessment, variation and perception of number skills was used.

    The result of the diagnostic test showed that the students made the most errors with fractions as part of a whole, contrary to previous research.  However, the interviews showed a different result where the students felt that the part of diagnosis with fractions as a number was the most difficult. Comparing the result of the diagnostic test in this study with previous research, the results do not come to the same conclusion. If we look at the views expressed in the interviews, and the assistance strategies (drawing), the students needed help with fractions as numbers in the diagnostic test, and the result pointing in the same direction as previous research. Research conducted in a different setting with older students and slightly more advanced tasks.

    Fulltekst (pdf)
    fulltext
  • 26.
    Jägerfeld, Caroline
    Södertörns högskola, Institutionen för kultur och lärande, Litteraturvetenskap.
    En aning om ett sällsamt universum: En undersökning av C.J.L. Almqvists ”poetiska fuga”2020Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    ABSTRACT And concrete diction

    Carl Jonas Love Almqvist’s Drottningens juvelsmycke (The Queen's Tiara; 1834) is, along with Amorina, the work primarily associated with the ”poetic fugue” – a concept the author develops in ”Om enheten av epism och dramatism; en aning om den poetiska fugan” (”On the unity of epism and dramatism; a notion of the poetic fugue”; 1821); an essay often considered vague and theoretical by researchers in the field. The meaning of the poetic fugue has been regarded unclear, but mainly considered as some kind of synthesis of epic and dramatic writing. This essay argues that that is not the case, and that this one-dimensional approach both limits the interpretations of the essay and the poetic fugue as a whole. From a multidisciplinary perspective, with myself and my own reader as a part of the fugue itself, the aim of this essay is to highlight a very important overseen aspect of the poetic fugue, and Almqvist’s writing in general – the connections to mathematics, the analogies between abstract and concrete levels, and how these are deeply intertwined. The results in this essay are derived from a close reading technique based on mathematical problem solving called the ideotic method (den ideotiska metoden), and analyzed with Douglas Hofstadter's theory of Strange loops in Gödel, Escher, Bach – an eternal golden braid (1979). This analysis shows that this analogy is not just about the composition of a poetic piece of art, a synthesis of epic and dramatic writing, or the relation between music and text. Instead the results do point to an alternative interdisciplinary interpretation, where the relations between parts and units, realities and fictions, readers and texts, make the poetic fugue more of an analogy for the universe as a whole – a living and breathing ”animal coeleste” in contrast to the Newtonian ”mechanical coeleste”. An analogy which, thanks to its mathematical construction and way of looking at time as non-linear, is connected to both Einstein’s theory of relativity and quantum theory – the science of the very big and the very small, parts and units, of everything, including ourselves. 

    Fulltekst (pdf)
    C.Jägerfeld En Aning Om Ett Sällsamt Universum
  • 27. Jää-Aro, Kai-Mikael
    Implementing a CFD steering system for immersive environments2003Inngår i: CAVE Programming Workshop 2003, 2003Konferansepaper (Annet vitenskapelig)
  • 28.
    Jää-Aro, Kai-Mikael
    et al.
    KTH.
    Engquist, Erik
    Visualization2005Inngår i: Introduction to High-Performance Computing—material for the PDC summerschool 2005 / [ed] Andersson, Ulf, Stockholm: Kungliga Tekniska högskolan, 2005Kapittel i bok, del av antologi (Annet vitenskapelig)
  • 29.
    Jää-Aro, Kai-Mikael
    et al.
    KTH.
    Weber, Tomas
    Specification of methods of displaying CFD data, Specification of immersive user interface: VIRTUALFIRES : Deliverables 4.1 & 4.22002Rapport (Annet vitenskapelig)
  • 30.
    Kaipainen, Mauri
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Medieteknik.
    Hautamäki, A.
    University of Helsinki, Helsinki, Finland.
    Analysis and synthesis with a three component inferential system: Augmenting the explanatory scope of conceptual spaces2017Inngår i: Artificial Intelligence and Cognition 2016: Proceedings of the 4th International Workshop on Artificial Intelligence and Cognitionco-located with the Joint Multi-Conference on Human-Level Artificial Intelligence (HLAI 2016) / [ed] Antonio Liet; Mehul Bhatt; Alessandro Oltramari; David Vernon, 2017, s. 124-137Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The study introduces a model of analysis and synthesis, respective abductive and deductive reasoning, using the three-component inferential system, which is constituted by a perspective-relative augmentation of Gärdenfors's theory of Conceptual Spaces (CS). A general formulation of Perspective, based on our earlier work, corresponds to prioritization among property dimensions. Instead of assuming one conceptual space as in the CS, a distinction is made between the high-dimensional description of the discourse/domain termed Ontospace, and the two-dimensional perspectival space onto which a Perspectiverelative hierarchical conceptualization is projected, referred to as the Perspectival Space. In this setting, deduction is the inference of Perspective-relative conceptualization of the ontospace, while abduction is the reasoning of the Perspective that accounts for a given conceptualization of the ontospace, given in a form of a target cluster This model is articulated on an abstraction level beyond algorithmic implementation.

  • 31.
    Karlsson, Natalia
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Forskningsanktnytning i lärarutbildningen2019Konferansepaper (Annet (populærvitenskap, debatt, mm))
    Abstract [sv]

    Presentation bygger på forskning som ligger till grund för kvalitets-och utvecklingsarbete i matematikämnets didaktik i lärarutbildningen på Södertörns högskola. Syftet är att koppla samman lärarstudenters behållning av högskolestudier med lärares praktik i syfte att samordna vetenskaplig grund och beprövad erfarenhet.

  • 32.
    Karlsson, Natalia
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Lärarstuderandes förmågor och attityder2016Konferansepaper (Fagfellevurdert)
  • 33.
    Karlsson, Natalia
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Matematik i lärarutbildningen: Studenters kunskaper i och uppfattningar om matematik: En forskningsrapport från MIL- och SKUM-projekten2015Rapport (Annet vitenskapelig)
    Abstract [sv]

    Under de senaste decennierna har såväl svenska som internationella undersökningar visat på svenska elevers bristande kunskaper i matematik. En konsekvens av detta är att de studenter som nu kommer till högskolan tillhör en generation som enligt TIMSS (2011) och PISA (2015) lyckats mindre bra med den matematik de läst i skolan.

    I undervisningen på lärar­utbildningen på Södertörns högskola har vi konstaterat att många av dagens studenter har en proce­durell och ytinriktad uppfattning om matematik och att de bygger sina kunskaper på formler som de inte alltid kan hantera. Denna upp­fattning om ämnet gör det svårt för dem att utgående från dagens utbild­ningsramar uppnå rimliga mål i lärarutbildningen. Detta är bak­grunden till projekten SKUM (Studenters kunskaper i och uppfattning om matematik) och MIL (Matematik i lärarutbildningen) för vilka det övergripande syftet varit att bygga upp kunskaper som kan ligga till grund för en funktionell lärar­utbildning. En sådan utbildning bör vila på veten­skap­lig grund och vara väl anpassad till dagens studenter och deras möjlig­heter att till­godo­göra sig undervisningen på högskolan.

    I den här rapporten presenteras resultaten från en diagnos om grund­läg­gande aritmetik (taluppfattning) och algebra. Lärarstuderande med inrikt­ning mot årskurs 4 till 6 fick diagnosen vid starten av sin första kurs i mate­matikämnets didaktik. Avsikten var att kartlägga studenternas styrkor och svagheter med avsikten att därefter planera en utbildning som var anpassad till deras förmågor och attityder till ämnet. Resultaten visar att de flesta av studenterna hade mer eller mindre allvarliga brister när det gällde att lösa enkla uppgifter. Det innebar i sin tur att de fick svårt att följa under­vis­ningen på högskolan.

    Fulltekst (pdf)
    Matematik i lärarutbildningen: Studenters kunskaper i och uppfattningar om matematik: En forskningsrapport från MIL- och SKUM-projekten
    Download (jpg)
    presentationsbild
  • 34.
    Karlsson, Natalia
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Matematiken i skola och högre utbildning2020Konferansepaper (Annet vitenskapelig)
    Abstract [sv]

    Vår senaste forskning, som är kopplad till projekt Content knowledge in a Pedagogical kontext: Bråk, Förhållande och Proportionalitet, visar på bristande kontinuitet i undervisningen från lågstadium till högstadium. Konsekvenser av detta blir uppenbara när vi möter våra lärarstudenter. Genom att följa undervisningen från årskurs 2 till årskurs 8 blir det tydligt hur missuppfattningar uppstår och utvecklas med tiden. Vi har speciellt studerat kontinuiteten i undervisningen från multiplikation och bråk till proportionalitet. Det bir då uppenbart att de flesta av de lärare vis studerat har missuppfattat viktiga aspekter av dess begrepp något som i sin tur leder missuppfattningar redan under tidigare skolor och som är svåra att korrigera under senare skolår och inom högre utbildning. Under presentationen tar jag upp ett teoretiskt ramverk om hur matematiska begrepp kan transformeras i matematikundervisningen med fokus på kontinuitet. Vad jag efterlyser i presentationen är också en saklig diskussion om hur vi kan säkerställa en undervisning som från skola till högskola/universitet vilar på korrekta och utvecklingsbara matematiska begrepp och metoder.

  • 35.
    Karlsson, Natalia
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Vet inte, har inte en aning, kommer inte ihåg2015Inngår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, nr 3, s. 49-52Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [sv]

    De studerande som antagits till svenska lärarutbildningar har var och en uppsättning förmågor i matematik. Hur ser denna ut i relation till vad eleverna i nionde klass kan förväntas uppvisa? Vi tar här del av ett projekt där just dessa lärarstuderandes förmågor undersökts.

    Fulltekst (pdf)
    fulltext
  • 36.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilbon, Wiggo
    Konkretisering och förmågorna2016Inngår i: Konkretisering och förmågorna, 2016Konferansepaper (Annet vitenskapelig)
    Abstract [sv]

    Med konkretisering menar vi all didaktisk verksamhet som leder till abstraktion, alltså förståelse av, och förmåga att, använda begrepp, strukturer och metoder. Under föreläsningen diskuterar vi, med belysande exempel för-och nackdelar med olika sätt att konkretisera. Vi behandlar såväl induktiva metoder som bygger på åskådlighet eller erfarenhet som deduktiva metoder som bygger på att undersöka och analysera innebörden av begrepp.

  • 37.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Lärarutbildningen, Matematikämnets didaktik.
    Kilborn, Wiggo
    University of Gothenburg, Sweden.
    Arithmetic and algebraic knowledge in student learning of concepts2023Inngår i: 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, s. 3-7Konferansepaper (Fagfellevurdert)
    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.  

  • 38.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Att konkretisera och förstå multiplikationstabellen2016Inngår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 198, nr 2, s. 20-24Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [sv]

    Vari ligger skillnaden i att kunna använda sig av multiplikationstabellen och att förstå multiplikation? Behöver det ena utesluta det andra? Vilka möjligheter och hinder finns med de konkretiserande bilder som används i undervisningen? Dessa är några av de frågeställningar som diskuterar mönster och multiplikation i artikeln.

    Fulltekst (pdf)
    fulltext
  • 39.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Det räcker om de förstår den: En studie av lärares och elevers uppfattningar om multiplikation och multiplikationstabellen2018 (oppl. 1)Bok (Fagfellevurdert)
    Abstract [sv]

    För att bygga upp en matematikundervisning som utgår från aktuell forskning och skolans behov, krävs en hållbar lärarutbildning. Eftersom lärarutbildningen måste utgå från studenternas aktuella kunskaper i matematik, blir en central fråga hur de tillägnat sig sina kunskaper och uppfattningar. Mot denna bakgrund har vi genomfört en studie med fokus på multiplikation och dess invers division. Studien har i huvudsak genomförts i årskurserna 3 och 5.

    Studien visar att undervisningen om multiplikation i årskurs 3 enbart handlar om upprepad addition. Undervisningen om multiplikationstabellen handlar inte om mönster i multiplikationstabellen utan enbart om att göra så kallade ”hopp” i tabellen. Detta gör det svårt för eleverna att senare förstå begrepp och mönster som är grundläggande för att kunna generalisera sina kunskaper till nya talområden och för att förstå den grundläggande algebran. Vi menar, att detta leder till problem som vi under senare år kunnat iaktta bland våra lärarstudenter.

    Fulltekst (pdf)
    Det räcker om de förstår den: En studie av lärares och elevers uppfattningar om multiplikation och multiplikationstabellen
    Download (jpg)
    presentationsbild
  • 40.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Gothenburg University, Sweden.
    Development and progression in students' experience of fractions and proportion2021Inngår i: Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1) / [ed] Maitree Inprasitha; Narumon Changsri; Nisakorn Boonsena, Khon Kaen, Thailand: PME , 2021, Vol. 1, s. 150-Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In a recent study we followed the teaching and learning of fractions and proportion with focus on how students develops their knowledge from grade 4 to grade 8. Another focus was on teachers’ ability to identify the object of learning and its crucial aspects.

    A qualitative analysis of the date shows that the students often failed in understanding crucial aspects of fractions and proportion and for that reason they made systematic mistakes later on. One reason for this appeared to be teachers’ lack of subject matter knowledge and an insufficient focus on the object of teaching. This became most evident in grade 8, where students’ misconceptions of fractions and extending of fractions, forced the teachers to introduce procedural methods like cross-multiplication. However, such teaching methods caused still more confusion and new misconceptions.

  • 41.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Göteborgs universitet.
    En hållbar matematikundervisning: Från addition till bråk2020Konferansepaper (Fagfellevurdert)
    Abstract [sv]

    Vi har i flera år studerat hur undervisningen av multiplikation och tal i bråkform går till. Genom att analysera ett stort antal lektioner, från årskurs 2 till årskurs 8, har vi kunnat kartlägga orsaker till hur vanliga missuppfattningar om bråk, och operationer med tal i bråkform, har uppstått. Under vår föreläsning kommer vi inte bara att presentera detta utan även ge exempel på hur dessa missuppfattningar kan undvikas.

    Download (pdf)
    Presentation
  • 42.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Formativ bedömning och didaktiskt stöd i matematik för lärarstudenter: Diagnoser med didaktisk uppföljning2017Bok (Annet vitenskapelig)
    Abstract [sv]

    Boken omfattar diagnoser som är ett utprövat material för att stärka det grundläggande matematikkunnande, främst riktat till blivande lärare inom lärarutbildning med inriktning på förskola och grundskolans tidiga år.

  • 43.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik. Södertörns högskola, Lärarutbildningen.
    Kilborn, Wiggo
    Matematik och språk: Kommunikation och resonemangsförmåga2018Konferansepaper (Fagfellevurdert)
  • 44.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Lärarutbildningen, Matematikämnets didaktik.
    Kilborn, Wiggo
    Matematikens didaktik och undervisningens innehåll i årskurs 1-6: guidat lärande med praktiska exempel2023 (oppl. 1)Bok (Annet vitenskapelig)
    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. 

  • 45.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Om proportionalitet2016Inngår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, nr 3, s. 25-28Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [sv]

    En typ av problem i skolans matematikundervisning som vållar svårigheter för elever och därmed också för deras lärare är de som bygger på proportionalitet. Artikelförfattarna följer här upp en artikel från Nämnaren 2015:3 och diskuterar hur en laboration kan leda eleverna in i proportionalitetstänkande.

    Fulltekst (pdf)
    fulltext
  • 46.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Lärarutbildningen, Matematikämnets didaktik.
    Kilborn, Wiggo
    University of Gothenburg, Sweden.
    Pre-service teacher' knowledge of mathematics: A framework for sustainable development of student knowledge2023Inngår i: Education and New Developments 2023: Volume 1 / [ed] Mafalda Carmo, Lisboa, Portugal: inSciencePress , 2023, Vol. 1, s. 196-200Konferansepaper (Fagfellevurdert)
    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. 

  • 47.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Problemlösning och matematisk modellering2015Bok (Annet vitenskapelig)
    Abstract [sv]

    I nationalencyklopedin beskrivs matematik som en "abstrakt och generell vetenskap för problemlösning, metodutveckling..". För en elev handlar detta om att lära sig använda matematiska modeller som inte bara löser enstaka problem utan modeller som kan modifieras och generaliseras till att lösa olika problem och nya typer av problem. Det som idag kallas problemlösning borde därför snarare heta matematisk modellering.

    Målen för skolans problemlösning bör vara klara. Dels handlar det om att förbereda eleverna för vanligt förkommande rutinproblem i vardagen, dels om att resonera sig fram till lösningar på nya typer av problem. Detta gäller också att bygga upp ett positivt förhållningssätt till problemlösning.

    Boken vänder sig till blivande och verksamma lärare på grundskola och gymnasieskola.

  • 48.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    WK Utbildningskonsult AB.
    Problemlösningsförmåga och matematiska modeller2016Inngår i: Problemlösningsförmåga och matematiska modeller, 2016Konferansepaper (Annet vitenskapelig)
  • 49.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Teacher's and student's perception of rational numbers2020Inngår i: Interim Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education: Mathematics Education in the 4th Industrial Revolution: Thinking skills for the Future / [ed] Inprasitha, M., Changsri, N. & Boonsena, N., Khon Kaen, Tailand: PME , 2020, , s. 291 - 297s. 291-297Konferansepaper (Fagfellevurdert)
    Abstract [en]

    It is known from several studies, that students have problems when treating rational numbers. In this paper, there is a focus on rational numbers as equivalent classes, in teaching expressed as extending of fractions. The current research shows how three teachers mediate extending of fractions and how their students understood this concept. The main outcome of the research is that most of the misconceptions were caused by shortcomings in teachers’ subject matter knowledge. For that reason, they were not able to find crucial aspects of the object of learning. Consequently, their students tried to find other, however irrelevant, patterns.

  • 50.
    Karlsson, Natalia
    et al.
    Södertörns högskola, Institutionen för naturvetenskap, miljö och teknik, Matematikens didaktik.
    Kilborn, Wiggo
    Gothenburg University, Sweden.
    Teachers' and students' perception of rational numbers2021Inngår i: Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3) / [ed] Maitree Inprasitha; Narumon Changsri; Nisakorn Boonsena, Khon Kaen, Thailand: PME , 2021, Vol. 3, s. 120-127Konferansepaper (Fagfellevurdert)
    Abstract [en]

    It is known from several studies, that students have problems when treating rational numbers. In this paper, there is a focus on rational numbers as equivalent classes, in teaching and learning. 

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