| 1. |
- Björklund Boistrup, Lisa, 1960-
(author)
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Assessment Discourses in Mathematics Classrooms : A Multimodal Social Semiotic Study
- 2010
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Doctoral thesis (other academic/artistic)abstract
- This is a study of assessment in mathematics classrooms and assessment is here regarded as a concept with broad boundaries including e.g. diagnostic tests, portfolios, and acts in teacher-student communication. The study’s purpose is to analyse and understand assessment acts in discursive practices in mathematics classroom communication in terms of affordances for students’ active agency and learning. Five mathematics classrooms are visited and the main data consists of video-recordings and written classroom material. In the study, I examine assessment acts, focuses of assessment acts, and roles of semiotic resources (symbols, gestures, speech etc.). With these findings as a basis, four discourses of assessment in mathematics classrooms are construed. A main conclusion is how the construed discourses hold different affordances for students’ active agency and learning. One discourse, “Do it quick and do it right” has similarities to a traditional discourse of assessment described in previous research. In a second discourse, “Anything goes”, students’ performances that can be regarded as mathematically inappropriate are left unchallenged. In both these discourses the affordances for students’ active agency and learning of mathematics are considered low. In a third discourse, “Anything can be up for a discussion”, the focuses of assessment acts are mainly on mathematics processes and available semiotic resources are connected to these focuses. The fourth discourse, “Reasoning takes time”, takes it one step further with a lower pace and an emphasis on mathematics processes such as reasoning and problem-solving. In these two latter discourses the affordances for students’ active agency and learning of mathematics are high. I contend that there is positive power in an increased awareness of discourses like these. The four discourses of this study can be powerful in discussions about, understandings of, and positive changes in assessment practices in mathematics classrooms.
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| 2. |
- Mårtensson, Pernilla
(author)
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Att få syn på avgörande skillnader : Lärares kunskap om lärandeobjektet
- 2015
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Doctoral thesis (other academic/artistic)abstract
- Lärare som undervisar i matematik förväntas kunna mer avancerad matematik än vad de undervisar om. Men formell matematikkunskap anses inte vara tillräckligt för att lärare ska kunna undervisa så att ämnesinnehållet blir begripligt för eleverna, de behöver även pedagogical content knowledge (PCK). Begreppet belyser en speciell form av ämneskunskap för undervisning och skiljer sig från den matematikkunskap som används av andra välutbildade vuxna. Det har föreslagits att olika arrangemang av kollegialt och praktikbaserat lärande kan utveckla lärares PCK. Ett exempel på ett sådant arrangemang är learning study. Den här avhandlingen handlar om den kunskap om lärande och undervisning i matematik som studiens lärare utvecklar då de deltar i learning studies och utforskar sin praktik utifrån ett variationsteoretiskt perspektiv. Det yttersta syftet med en learning study är att utveckla elevernas lärande om specifika lärandeobjekt, genom att undersöka vad som kan vara kritiskt för elevernas lärande. I ett samarbetsprojekt med fyra högstadielärare genomfördes två learning studies i matematik, under ett år. Lärargruppen undersökte vad eleverna behöver lära för att de ska förstå i) varför en kvot kan vara större än talet i täljaren och ii) olika representationer av konstanterna k och m i räta linjens ekvation. Under learning study-arrangemangets olika steg samlades studiens empiri in och denna består av filmade lektioner, inspelade möten där lärargruppen planerade och analyserade undervisning och elevers lärande, skriftliga elevtest samt elevintervjuer. Studien har en variationsteoretisk utgångspunkt, vilket innebär att lärande förklaras ske när en person ser något på ett nytt och mer kvalitativt sätt, genom att personen urskiljer aspekter som han/hon inte tidigare har urskilt. Studien visar de två lärandeobjektens kritiska aspekter samt hur de kritiska aspekterna gradvis förändrades och specificerades. Förändringen var ett resultat av att lärargruppen fick syn på avgörande detaljer om på vilket sätt eleverna förstod ämnesinnehållet samt hur skilda sätt att förstå kunde användas i undervisningen för att utveckla elevernas lärande. Där av titeln att få syn på avgörande skillnader. Denna form av utvecklad kunskap om lärandeobjektet kan ses som ett bidrag om PCK och vad det kan vara.
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| 3. |
- Olande, Oduor
(author)
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Students' narratives from graphical artefacts : Exploring the use of mathematics tools and forms of expression in students' graphicacy
- 2013
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Doctoral thesis (other academic/artistic)abstract
- The research concerns presented in this dissertation addresses aspects of students’ interaction with commonly occurring graphical artefacts in teaching and learning environments. In particular, focus is on how the students make sense of these artefacts in relation to subject specific tools and forms of expression.The dissertation comprises of four studies guided by a semiotics cultural- historical perspective to cognition. The first study which is largely quantitative, analyses the percentage scores from students’ responses to selected items from OECD PISA surveys for items containing graphical elements. The second and the third studies in keeping with a more sociocultural perspective to learning as point of departure, examine the students’ collaborative interaction around tasks containing graphical elements. The fourth study explores the nature of students’ solutions from the Swedish national test in mathematics based on a tools and forms of expression sensitive empirically derived construct of Identification contra Critical-analytical approach to graphicacy.The main outcomes of these studies can be summarised as follows: first there is justification for re-examining the predominant characterisation of students’ interaction with graphical artefacts. Secondly, while it is not uncommon for students to take a more visual-perceptive and intuitive approach to graphicacy, results from task items interactions indicate that a Critical-analytical approach seems to be more reliable and capable of yielding desirable outcomes. The outcomes of these studies call for vigilance on the type of tasks used in relation to graphicacy and how these can be used to foster students’ Critical-analytical disposition.
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| 4. |
- Bergvall, Ida, 1975-
(author)
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Bokstavligt, bildligt och symboliskt i skolans matematik : – en studie om ämnesspråk i TIMSS
- 2016
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Doctoral thesis (other academic/artistic)abstract
- The overall aim of this thesis is to deepen the understanding of mathematical subject language regarding three semiotic resources, written language, images and mathematical symbols. The theses also investigates high- and low-performingstudents encounter with mathematical subject language.Based on previous research on language and from a theoretical foundation based on systemic functional linguistics (SFL) and social semiotics, four meaning dimensions – packing, precision, personification and presentation – were identified as central in academic language in general and in mathematical subject language. A didactically based reception theoretical perspective has been used for an analysis of high and low achieving students' encounter with the mathematical subject language.The thesis comprises three studies each examining the mathematical subject language in TIMSS 2011 from various angles. The analyzes were conducted on four content areas algebra, statistics, geometry and arithmetic in the Swedish version of the international study Trends in International Mathematics and Science Study 2011 (TIMSS).In a summary, the results showed that the mathematical subject language was used in different ways in the four content areas in TIMSS where colloquial and subject-specific forms of languages had different roles and were expressed in varying degrees by the written language, images and mathematical symbols. Thus each content area was expressed by its own register which means that is not sufficient to talk about mathematical subject language as one single language.The result shows that two forms of language, subject specific and everyday language were used parallel in the TIMSS material. The subject specific forms were most salient in algebra and geometry and the more everyday forms of language were more common in statistics and arithmetic.The results from the correlation analyses indicated that fewer students managed the encounter with tasks in algebra and geometry when they were expressed by subject specific language. In contrast, the results indicated that students were able handle the encounter with the more colloquial expressions of the content areas statistics and arithmetic.
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| 5. |
- Dahl, Thomas
(author)
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Problem-solving can reveal mathematical abilities : How to detect students' abilities in mathematical activities
- 2012
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Licentiate thesis (other academic/artistic)abstract
- Dahl, Thomas (2012). Problemlösning kan avslöja matematiska förmågor. Att upptäcka matematiska förmågor i en matematisk aktivitet (Problem-solving can reveal mathematical abilities: How to detect students‟ abilities in mathematical activities). Linnéuniversitetet 2012; ISBN:978-91-86983-28-4. Written in Swedish.The thesis deals with the problem of identifying and classifying components of mathematical ability in students‟ problem-solving activities. The main theoretical framework is Krutetskii‟s theory of mathematical abilities in schoolchildren. After a short historical background focusing on the question of differentiation or integration among students on the basis of their various aptitudes for studies, the theory of mathematical ability and especially the Krutetskiian theory are described. According to Krutetskii mathematical ability should be looked upon as a structure of seven or eight different components called abilities which may appear and be subject to analysis during a mathematical activity.Krutetskii used school pupils and experimental problems to establish the relevance of his structure of abilities. However, in this work the theme is approached from the opposite perspective: If a problem and an experimental person are given, which mathematical abilities will appear and in what ways do they appear in the mathematical activity? The empirical study uses three so called “rich mathematics problems” and 98 students of which 37 study at the lower secondary school, 39 at the upper secondary school and 22 at the teacher education programme. The output data is either the written outcomes of the students‟ individual work on a problem or the recordings from small groups of students solving a problem in cooperation with their peers.In order to identify and classify abilities, the separate components of mathematical ability must be interpreted and adapted to the specific problem on which the students are working. I call this process of conformation of the abilities operationalization and the question in focus is if such an operationalization can be done successfully. The results indicate that it could be done and several examples are given which show how one or several mathematical abilities may come out more or less strongly in the mathematical activity of problem solving. The results also indicate that even low or average achieving students may show significant creative abilities. Another observation from the empirical study is that creative abilities do not seem to be more abundant among upper than lower secondary students. These two observations point out possible pathways to proceed further in the study of mathematical abilities.
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| 6. |
- Eriksson, Helena
(author)
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Rationella tal som tal : Algebraiska symboler och generella modeller som medierande redskap
- 2015
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Licentiate thesis (other academic/artistic)abstract
- In this study the teaching of mathematics has been developed in relation to rational numbers and towards a learning activity. At the same time topic-specific mediated tools have been studied. The iterative model for learning study has been used as research approach.The purpose of the study was to explore what in an algebraic learning activity enables knowledge of rational numbers to develop. The specific questions answered by the study are how an algebraic learning activity can be formed in an otherwise arithmetic teaching tradition, what knowledge is mediated in relation to different mediated tools and what in these tools that enable this knowledge.The result of the study shows how an algebraic learning activity can be developed to support the students to understand rational numbers even in an arithmetic teaching tradition. The important details that developed the algebraic learning activity were to identify the problem to create learning tasks and the opportunity for the students to reflect that are characteristic of a learning activity. The result also shows that the mediating tools, the algebraic symbols and the general model for fractional numbers, have had significant importance for the students' possibilities to explore rational numbers. The conditions for the algebraic symbols seem to be the possibilities for these symbols to include clues to the meaning of the symbol and that the same symbol can be used in relation to several of other mediated tools. The conditions in the general model consisted of that the integer numbers and the rational numbers in the model could be distinguished and that the students could reflect on the meaning of the different parts. The general model consists of the algebraic symbols, developed in the learning activity. The algebraic symbols make the structure of the numbers visible and the general model mediates the structure of additive and multiplicative conditions that are contained in a rational number.The result of the study contributes in part to the field of mathematics education research by examining Elkonin's and Davydov's Mathematical Curriculum in a western teaching practice and in part to a development of the model of Learning study as a didactical research approach by using an activity-theoretical perspective on design and analysis.
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| 7. |
- Lundberg, Anna, L., V.
(author)
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Proportionalitetsbegreppet i den svenska gymnasiematematiken : en studie om läromedel och nationella prov
- 2011
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Licentiate thesis (other academic/artistic)abstract
- Proportionalitet är ett centralt begrepp i skolmatematiken. Begreppet introduceras i de lägre stadierna och återkommer i så gott som samtliga kurser från årskurs 9 tillsista kursen på gymnasiet. Det övergripande syftet med denna studie är att undersöka hur det matematiska begreppet proportionalitet hanteras i den svenska gymnasieskolan. En generell problematik kopplad till detta syfte är hur skolans styrdokument realiseras i läromedel och nationella prov. Fokus för denna avhandling har varit hur proportionalitet hanteras i det svenska gymnasiet i kursen Matematik A i några läromedel och nationella prov. För att undersöka detta utvecklades ett analysverktyg utifrån det teoretiska ramverket i ATD (Anthropological Theory of the Didactic). Av intresse är här relationer mellan de olika nivåerna i den didaktiska transpositionen, som berör just hur skolans styrdokument realiseras i läromedel och nationella prov. För det empiriska studiet av materialet användes från ATD begreppet matematisk organisation, genom att använda ett analysverktyg för att granska typer av uppgifter om proportionalitet, lösningstekniker och teoretiska modeller för proportionalitetsbegreppet.De data som presenterats i denna studie ger en ganska ostrukturerad bild av de matematiska organisationer av begreppsområdet proportionalitet som presenteras i läromedel och i nationella prov och de ser även olika ut när det gäller hur proportionalitet hanteras i läromedlen respektive det nationella provet för Matematik A. Resultatet visar att ungefär var fjärde uppgift i de studerade kapitlen och de nationella proven berör proportionalitet men att begreppet hanteras ensidigt vad avser uppgiftstyp. Skillnader observerades mellan läromedel och nationella prov när det gäller hur lösningstekniker rekommenderas för olika typer av proportionalitetsuppgifter. De två teoretiska modeller för proportionalitet som har undersökts, dvs. statisk och dynamisk proportionalitet, finns representerade i ungefär lika omfattning i både läromedel och nationella prov. Vid uppgifter inom geometri handlar det dock ofta om statisk proportionalitet medan det inomområdet funktioner är vanligare att använda dynamisk proportionalitet.Lärare bör få kunskap om skillnader mellan läromedel och läroplaner, och hur dessa tolkas i nationella prov, så att de i sin verksamhet kan välja det undervisningsinnehåll, inklusive övningsuppgifter, som ger en god variation för eleven kopplat till kursplanernas mål
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| 8. |
- Mellroth, Elisabet, 1971-
(author)
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High achiever! Always a high achiever? : A comparison of student achievements on mathematical tests with different aims and goals
- 2014
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Licentiate thesis (other academic/artistic)abstract
- This study explored changes in relative achievement over time. It also investigated differences in how two groups of students activate mathematical competencies. The aim of the study was to investigate students’ relative achievement in mathematics over time, and how mathematical competencies can be used to explore differences between groups of students on a non-curriculum based test in mathematics. The study was divided in two parts. Study 1 compared students’ (n=568) relative achievement in two national tests in mathematics (years 3 and 6). Study 1 explored changes in relative achievement between the two national tests as well as differences in relative achievement between the national test in year 6 and the mathematical kangaroo in year 7 (age 13). The study identified, from a sample (n=264) of study 1, two groups of students with high achievements in only one of the tests, the national test in year 6 or the mathematical kangaroo. Study 2 explored how differences between those students relative achievement on the mathematical kangaroo could be explained through activation of mathematical competencies. The results in study 1 show that students undergo large changes, both increases and decreases, in relative achievement between the national tests in years 3 and 6. Study 2 shows how the two identified groups activate the mathematical competencies differently on the mathematical kangaroo. 9% of the students achieve highly in the mathematical kangaroo although they do not in the national test. The study implicates the importance of using non-curriculum bounded tests to identify strength in mathematical competencies among students that not are able to show them through the national test.
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| 9. |
- Nagy, Caroline, 1971-
(author)
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Fler bråk i matematikundervisningen : En aktionsforskningsstudie där lärare lär om progression
- 2017
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Licentiate thesis (other academic/artistic)abstract
- Few studies have a focus on progression in teaching and learning mathematics. An assumption for this study was that progression in teaching between school stages was important. The approach of the study was based on action research. Four teachers from preschool to 9th grade (age 1-16) were invited to a temporary team, a community of practice. The overall aim of the study was to develop knowledge about teaching fractions when teachers used students’ understandings as a point of departure for their action plans. A second aim was to illuminate what influences progression in their teaching.The team of teachers used the four phases of action research: plan, act, observe and reflect, during their learning processes. The teachers’ learning sessions were videotaped and transcribed and this provided the main data that formed the basis of the results. Wenger’s dimensions of social learning were used as an analytical tool: joint enterprise, mutual engagement and shared repertoire.Four themes that described teachers’ negotiation of qualities in mathematics instruction were identified: interpreting students’ understandings, basing instruction on students’ understandings, visualizing fractions and ensuring students’ understanding. When teachers, regardless of what stage was involved, reified similar instructions, it did not benefit students’ learning opportunities. In order to improve progression in teaching fractions, it was important that teachers succeeded in identifying students’ understandings and that the team negotiated different qualities in their community of practice. The shared repertoire (the pre-tests and the video recordings) formed the core of negotiating progression based on students’ understandings. The team showed a mutual engagement, with students’ learning as their joint enterprise. An implication of the study is that teachers from different educational stages can negotiate progression and improve it.
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| 10. |
- Norén, Eva, 1957-
(author)
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Flerspråkiga matematikklassrum : Diskurser i grundskolans matematikundervisning
- 2010
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Doctoral thesis (other academic/artistic)abstract
- The aim of this thesis is to investigate and analyze practices in multilingual mathematics classrooms in compulsory school in Sweden. By using ethnographic methods, mainly participant observation, data were collected in a number of multilingual mathematics classrooms in suburban areas of a major city. The data include field notes, interviews and informal conversations with students, teachers and school administrators. The analysis is based on a coordination of Foucault’s discourse theory and Skovsmose’s critical mathematics education. The socio-political viewpoint defines power as relational and as having an effect on school mathematics practices. Discourse, agency, foreground and identity are used as analytic tools. In five articles, the thesis investigates how the various discourses affect multilingual students’ agency, foreground and identity formation as engaged mathematics learners. The effects of students’ and teachers’ agency on discourse switching in multilingual mathematics classrooms are also investigated. The findings indicate that bilingual communication in the mathematics classroom enhances students’ identity formation as engaged mathematics learners. Language- and content-based instruction seems to do the same, though monolingual instruction may jeopardize students’ identities as bilinguals while the discourse may normalize Swedish and Swedishness exclusively. Focus on linguistic dimensions in mathematics build up a communicative reform-oriented school mathematics discourse. The competing and intersecting discourses available in the multilingual mathematics classroom affect students’ agency, foreground and identity formation as engaged mathematics learners. For example, a reform-oriented school mathematics discourse intersecting with a social-relational discourse affects students’ active agency allowing power relations to be negotiated. A principal conclusion is that the success or failure of multilingual students in multilingual mathematics classrooms cannot be explained in terms of language and cultural factors alone, but only in relation discourse, and to social and political conditions in society at large.
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