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  • 1.
    Abdulrasul, Zahraa
    Södertörn University, Teacher Education.
    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 credits / 15 HE creditsStudent thesis
    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.

  • 2.
    Ahlgren, Anna
    Södertörn University, Teacher Education.
    Har bilden en mening?: En studie om illustrerad multiplikation2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    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.

  • 3.
    Ahlgren, Anna
    Södertörn University, Teacher Education.
    Målande multiplikation: En undersökning av hur multiplikation illustreras i läroböcker för årskurs två2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    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.

  • 4.
    Altuntas, Ann-Sofie
    Södertörn University, Teacher Education.
    ”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 credits / 15 HE creditsStudent thesis
  • 5.
    Andersson, Jonas
    et al.
    Södertörn University, School of Culture and Education, Media and Communication Studies.
    Hammarlund, Johan
    M-Brain AB.
    Kontextförlust och kontextkollaps: Metodproblem vid innehållsanalys av sociala medier2016In: Nordicom Information, ISSN 0349-5949, Vol. 38, no 3, p. 41-55Article in journal (Refereed)
    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. 

  • 6.
    Andersson, Julia
    Södertörn University, Teacher Education.
    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 credits / 15 HE creditsStudent thesis
    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.

  • 7.
    Bisenius Sellgren, Kajsa
    Södertörn University College, Lärarutbildningen.
    En studie om elevers val av metoder vid subtraktionsberäkningar2010Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    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.

     

  • 8.
    Blomskog, Stig
    Södertörn University, School of Social Sciences, Economics.
    A formal analysis of a conventional job evaluation system2007Report (Other academic)
    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.

  • 9.
    Blomskog, Stig
    Södertörn University College, School of Social Sciences, Economics.
    An analysis of the principle ”Equal Pay for Jobs of Equal Value”2007Report (Other academic)
    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”.

  • 10.
    Blomskog, Stig
    Södertörn University College, School of Social Sciences, Economics.
    An Evaluation of Employee Performance Based on Imprecise Value Judgments: Two Experiments2007Report (Other academic)
    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.

  • 11.
    Blomskog, Stig
    Södertörn University College, School of Social Sciences, Economics.
    Analys av ett individuellt lönesystem baserad på mångdimensionell beslutsteori2003Report (Other academic)
  • 12. 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 medium2002In: Advanced Problems in Mechanics  2002.: Proceeding, St.Peterburg: Russian Academy of Sciences, 2002, p. 134-138Conference paper (Refereed)
  • 13. Burenin, Anatoly A.
    et al.
    Lebedeva, Natalia F.
    On constructing approximate solutions för problems in dynamics of incompressible elastic medium with axial symmetry2002Conference paper (Refereed)
  • 14.
    Do-Quang, Minh
    et al.
    KTH.
    Amberg, Gustav
    KTH.
    Numerical simulation of the coupling problems of a solid sphere impacting on a liquid free surface2010In: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 80, no 8, p. 1664-1673Article in journal (Refereed)
    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.

  • 15.
    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 flow2013In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 14, no 4, p. 879-915Article in journal (Refereed)
    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.

  • 16.
    Gunnarsson, Hugo
    Södertörn University, Teacher Education.
    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 credits / 15 HE creditsStudent thesis
    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?

  • 17.
    Ivarsson, Mabel Rocio
    Södertörn University College, Lärarutbildningen.
    Matematik i förskolan: Barns antalsuppfattning i de tidiga åren2011Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    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.

  • 18.
    Johansson, Jeanette
    Södertörn University, Teacher Education.
    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 credits / 15 HE creditsStudent thesis
    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.

  • 19. Jää-Aro, Kai-Mikael
    Implementing a CFD steering system for immersive environments2003In: CAVE Programming Workshop 2003, 2003Conference paper (Other academic)
  • 20.
    Jää-Aro, Kai-Mikael
    et al.
    KTH.
    Engquist, Erik
    Visualization2005In: Introduction to High-Performance Computing—material for the PDC summerschool 2005 / [ed] Andersson, Ulf, Stockholm: Kungliga Tekniska högskolan, 2005Chapter in book (Other academic)
  • 21.
    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 & 4.22002Report (Other academic)
  • 22.
    Kaipainen, Mauri
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Media Technology.
    Hautamäki, A.
    University of Helsinki, Helsinki, Finland.
    Analysis and synthesis with a three component inferential system: Augmenting the explanatory scope of conceptual spaces2017In: 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, p. 124-137Conference paper (Refereed)
    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.

  • 23.
    Karlsson, Natalia
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Forskningsanktnytning i lärarutbildningen2019Conference paper (Other (popular science, discussion, etc.))
    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.

  • 24.
    Karlsson, Natalia
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Lärarstuderandes förmågor och attityder2016Conference paper (Refereed)
  • 25.
    Karlsson, Natalia
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Matematik i lärarutbildningen: Studenters kunskaper i och uppfattningar om matematik: En forskningsrapport från MIL- och SKUM-projekten2015Report (Other academic)
    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.

  • 26.
    Karlsson, Natalia
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Vet inte, har inte en aning, kommer inte ihåg2015In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 3, p. 49-52Article in journal (Other academic)
    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.

  • 27.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Kilbon, Wiggo
    Konkretisering och förmågorna2016In: Konkretisering och förmågorna, 2016Conference paper (Other academic)
    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.

  • 28.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Kilborn, Wiggo
    Att konkretisera och förstå multiplikationstabellen2016In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 198, no 2, p. 20-24Article in journal (Other academic)
    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.

  • 29.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Kilborn, Wiggo
    Det räcker om de förstår den: En studie av lärares och elevers uppfattningar om multiplikation och multiplikationstabellen2018 (ed. 1)Book (Refereed)
    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.

  • 30.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Kilborn, Wiggo
    Formativ bedömning och didaktiskt stöd i matematik för lärarstudenter: Diagnoser med didaktisk uppföljning2017Book (Other academic)
    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.

  • 31.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching. Södertörn University, Teacher Education.
    Kilborn, Wiggo
    Matematik och språk: Kommunikation och resonemangsförmåga2018Conference paper (Refereed)
  • 32.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Kilborn, Wiggo
    Om proportionalitet2016In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 3, p. 25-28Article in journal (Other academic)
    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.

  • 33.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Kilborn, Wiggo
    Problemlösning och matematisk modellering2015Book (Other academic)
    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.

  • 34.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Kilborn, Wiggo
    WK Utbildningskonsult AB.
    Problemlösningsförmåga och matematiska modeller2016In: Problemlösningsförmåga och matematiska modeller, 2016Conference paper (Other academic)
  • 35.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching. Södertörn University, Teacher Education.
    Kilborn, Wiggo
    Teori, praktik och kontinuitet: Multiplikativa strukturer och lärares matematikdidaktiska kompetenser2018Conference paper (Refereed)
  • 36.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Kilborn, Wiggo
    University of Gothenburg.
    Olteanu, Constanta
    Linnaeus University.
    Teachers and student - teacher's challenges with addition and multiplication strategy problems2019In: Proceedings 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education / [ed] Mellony Graven, Hamsa Venkat, Anthony A Essien and Pamela Vale, Pretoria, South Africa: PME , 2019, Vol. 4, p. 53-Conference paper (Refereed)
  • 37.
    Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Ljubimova, Olga
    Pestov, Konstantin
    Mathematical modeling of heat transfer processes with phase transitions in layered materials2016Report (Other academic)
    Abstract [en]

    In this paper we propose a model and numerical scheme for quantifying the motion of the phase transition front and the temperature fields in layered materials using boundary conditions of the third kind at the surface.

  • 38.
    Koc, Bobil
    Södertörn University, Teacher Education.
    Induktiv och deduktiv konkretisering i praktiken: En studie i årskurs 1-3 om hur induktiv och deduktiv konkretisering som didaktisk metod i matematikundervisning kan främja ett utvecklande av kunskap och lärande2017Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The aim of this study is to examine how inductive and deductive concreteization as a didactic method in mathematics teaching can promote the development of knowledge and learning among students. It is also of interest to hear a number of interviewed teachers perceptions about inductive and deductive concretization as a method in mathematics teaching. The examination is for grades 1-3. Theories dealt with in the study are learning promoting theories such as concretization, proximal development zone, conceptualization and creative reasoning.The study's questions will therefore examine:· How can inductive and deductive concretization as a didactic method in mathematics teaching promote the development of knowledge and learning to students?· What perceptions do teachers in grades 1-3 have regarding inductive and deductive concretization as a method of mathematics teaching? In order to answer the study's questions, qualitative methods have been used through interviews with teachers and observations in classrooms. The conclusions of the analysis of material shows that concretization through inductive and deductive methods helps students to participate in situations where different mathematical didactic consequences arise in the teaching based on the theories.

  • 39.
    Krikourian, Narine
    Södertörn University, Teacher Education.
    Vart har alla riktiga problem tagit vägen?: Analys av läromedel i matematik med fokus på problemlösning2017Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Research has shown that the mathematics textbooks are the most widely used in Swedish schools, compared to textbooks in other subjects. At the same time, studies have shown that the content of the textbooks do not fulfil the goals presented in the national education steering documents regarding problem solving in math.

    The purpose of this study is to analyze textbooks and corresponding teacher’s guide in mathematics for the second grade. Starting from a didactic perspective as an approach to problem solving in order to analyze the teaching material, I decided to use the analytical model constructed by Ann Kristin Larsen.

    In order to conduct the study, the following questions have been used in this study:

    • In what way the problem solving has been presented in the textbooks? Which problem solving strategies are presented in respective teaching material based on didactic perspective?
    • What types of problem solving tasks are presented in respective teaching material?
    •  In what way the concept problem solving is presented in the teacher’s guide?

    In conclusion, the result of the study shows that there are both similarities and differences between the two instructional materials that have been studied in the way they presented problem solving. The study shows that the teaching material is not compatible with Charles and Lester’s (1982) criteria. As for the teacher's guide and the support it provides, the investigation shows that different textbooks give different support and guidance to teachers.

  • 40.
    Laayab, Chayma
    Södertörn University College, Lärarutbildningen.
    En givande undervisning i problemlösning för andraspråkselever: En studie i årskurs 3 vid en mångkulturell skola i södra Stockholm2010Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Thanks to I have got to explore different teaching ways around the problem solving in a year 3, in a multicultural school which is located south of Stockholm, I have been able to answer my question at issue in my degree work. My question at issue on this investigation and the purpose with my degree work was to explore different teaching ways that promotes pupils with another mother tongue than Swedish, to develop reading comprehension and to get a better understanding of mathematical concepts in problem solving tasks. On this investigation have I chosen to teach these pupils to explore, reach and gain a deeper understanding of what teaching about problem solving promotes these pupils. I have when it concerns choice of method and material collections assumed from a qualitative investigation and gathered the material with help from participation notices and interviews. 

    I have in my investigation reached the conclusion that those pupils with another mother tongue than Swedish developed reading comprehension and got a better understanding of mathematical concepts in problem solving tasks by being taught in a creative and varied teaching. A creative and varied teaching as I taught those pupils in contained:

    • the pupils had to work with living-related problem tasks
    • the pupils had to work in pairs to resolve problem solving
    • the pupils had to work in larger groups to resolve problem solving
    • the pupils had to work in a creative way, by writing and drawing pictures and do their own mathematical fairy tale in problem solving
    • the pupils had to work with manipulatives to resolve problem solving in half classes.
  • 41.
    Lebedeva Karlsson, Natalia
    et al.
    Södertörn University, School of Natural Sciences, Technology and Environmental Studies, Mathematics Teaching.
    Morozov, Vitaly
    Vladivostok State University of Economics and Service, Valdivostok, Russia.
    Solodukhin, Konstantin
    Vladivostok State University of Economics and Service, Valdivostok, Russia.
    Нечёткие методы формализации стратегических карт Стейкхолдер организаций [Fuzzy methods of formalizing strategy maps of Steakholder organizations]2017In: Azimuth of Scientific Research: Economics and Management [Азимут научных исследований: Экономика и управление], ISSN 2309-1762, Vol. 6, no 4(21), p. 216-220Article in journal (Refereed)
  • 42. Lebedeva, Natalia F.
    Analytical modeling of shock waves in curved coordinates2005In: Book of Abstracts: Advanced Problems in Mechanics 2005, St.Petersburg: Russian Academy of Sciences, 2005, p. 1 s. (62)-Conference paper (Refereed)
  • 43. Lebedeva, Natalia F.
    Radial front exapansions in finite-difference approximation of equations for dynamics of deformable medium2001In: Advanced Problems in Mechanics 2001.: Proceedings, St. Petersburg: Rossijskaja akademija nauk / Russian Academy of Sciences, 2001, , p. 416 - 421p. 416-421Conference paper (Refereed)
  • 44. Lebedeva, Natalia F.
    Одномерная задача об ударном нагружении деформированного несжимаемого упругого слоя  [One-dimensional problem of shock loading of the deformed incompressible elastic layer]2000In: Reports of the Far Eastern State Technical University, p. 154-Article in journal (Refereed)
  • 45. Lebedeva, Natalia F.
    Одномерные нестационарные задачи об ударном нагружении несжимаемых упругих сред[One-dimensional non-stationary problems of shock loading uncompressible elastic solids]1997Doctoral thesis, monograph (Other academic)
  • 46. Lebedeva, Natalia F.
    et al.
    Chuyko, Vikorya M.
    The ray method of aproximation solutions construction of dynamic nonstationary problem of incompressed solid medium1997Conference paper (Refereed)
  • 47. Lebedeva, Natalia F.
    et al.
    Yarushina, Viktorya M.
    Лабораторные работы и методические указания по курсу " Математическая статистика"[Laboratory activities and methodical guidance for course "Mathematical Statistics"]2001Other (Other academic)
  • 48. Lebedeva, Natalia F.
    et al.
    Yarushina, Viktorya M.
    Элементы математического анализа в задачах [ Elements of mathematical analysis in tasks]2002Report (Other academic)
  • 49.
    Milanda, Ibrahim
    Södertörn University College, Lärarutbildningen.
    Matematikundervisning för andraspråkselever: En kvalitativ studie om lärares arbetssätt i matematik2010Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
  • 50.
    Mohammed, Shamim
    Södertörn University, Lärarutbildningen.
    ”Men snöbollarna är ju mer än tio!”: en vetenskaplig essä om matematik, lek och lärande i förskolan2012Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    My aim with the experience-based essay is that I want to explore the implications of mathematics on children's development. I also want to examine my approach in relation to the various mathematical tasks. Why do we think that mathematics is important for pre-school children? What does the research say about how the teacher is thinking about mathematics? Can the teacher combine playing and learning and create meaningful moments and activities related to mathematics? I also want to explore our policies and the objectives that the teacher should relate to. What is required of me as a teacher in order to meet those goals?

    My essay is about mine and my boss’s view of the mathematical tasks that I usually perform in the preschool. She thinks that they might create a pressure on the children. My reflection on this will help me to understand my mathematical activities in a deeper way. During my research trip I will examine how the teacher can combine mathematics, playing and learning to form pleasurable moments of them. I want to show how the interaction and storytelling can create a link between the teacher and child. My role as an educator is an important part of children’s development, because it is me who opens or restricts the child's ability to grow and learn.

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