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  • 1.
    Andrews, Paul
    et al.
    Centre for Educational Research, VIA University College, Aarhus, Denmark;Department of Teaching and Learning, Stockholm University, Stockholm, Sweden.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL). Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Sayers, Judy
    School of Education, University of Leeds, Leeds, UK.
    Rosenqvist, Eva
    Department of Teaching and Learning, Stockholm University, Stockholm, Sweden.
    English and Swedish year-one teachers’ number-related learning goals: the influence of intended and received curricula2024Ingår i: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, s. 1-31Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, drawing on semi-structured interviews with generalist teachers of year-one children in England and Sweden, we examine comparatively the influence of the intended curriculum (teachers in both countries work within mandated national curricula) and the received curriculum (the collectively assumed efficacious practices and goals handed down from one generation of teachers to the next) on teachers’ expressed number-related learning goals. Analyses, framed by a literature-derived and curriculum-independent set of eight forms of number-related competence each implicated in later mathematical learning, identified both similarities and differences in the two groups’ expressed goals. Key similarities concerned expectations that all children should become additively competent, supported by supplementary goals concerning systematic counting, number bonds, the number line and an appropriate mathematical terminology. Key differences concerned English teachers’ strongly-expressed emphasis on place value and a desire for children to learn to multiply. Overall, the strongly-framed English curriculum appears to influence teachers’ goals more than the weakly-framed Swedish, while Swedish teachers seem to draw on a received curriculum more closely aligned with the literature-derived developmental goals than the English. Finally, when set against the literature-derived and curriculum-independent developmental goals, the English curriculum, unlike the Swedish, expects year-one children to learn much age-inappropriate material.

  • 2.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Students’ responses to the question: how does a computer do curve fitting?2024Ingår i: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 55, nr 5, s. 1226-1242Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Previous research has identified an unfilled gap between, on the one hand, mathematical prerequisites needed for a formal treatment of least squares and, on the other hand, only teaching procedural aspects of curve fitting. As a response to this, the present study explores students’ suggestions of how they think a computer or calculator does curve fitting. The data evolve through observations of mathematics classroom group work and interviews during a physics laboratory group work of year 10 secondary school students in Sweden. The results show that these students seemed well equipped to, on their own, suggest relevant and mathematically founded strategies for formal curve fitting though not least squares. Specifically, the students were inventive in their group work in the sense that several of their suggestions for how curve fitting could work are the same as those that appear in mathematics history from early 1700 until contemporary methods, covering both algebra and statistics. As such, the mathematical content in the results contrasts previous research on informal fit, which often results in the students counting the number of points over and under the fitted line but with less articulated justifications for their fit.

    Ladda ner fulltext (pdf)
    fulltext
  • 3.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS). Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    van Bommel, Jorryt
    Karlstad universitet.
    Teaching quality during mathematics lessons2024Ingår i: Skrifter från SMDF, Nr 18 : Mediating mathematics: Proceedings of MADIF 14, the fourteenth research conference of the Swedish Society for Research in Mathematics Education. Örebro, March 19–20, 2024 / [ed] Häggström, Johan; Kilhamn, Cecilia; Mattsson, Linda; Palmér, Hanna; Perez, Miguel; Pettersson, Kerstin; Röj-Lindberg, Ann-Sofi ; Teledahl, Anna, Göteborg, 2024, Vol. 18, s. 141-141Konferensbidrag (Refereegranskat)
    Abstract [en]

    This presentation focuses changes in elements of teaching quality during three parts of a mathematics lesson; start, middle and end. 64 grade 7 lessons were analysed using these partitions, forming a time series that shows decreasing quality for most elements (e.g., Modelling) from start to end of a lesson. Few elements showed an increase of quality (e.g., Intellectual Challenge). The structure of the lessons (whole class at start and individual work during middle and end) may partially account for a possible decrease. Even so, a decrease in quality is not desirable and implications on students’ learning are of concern.

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    Petersson_vanBommel_Madif2024
  • 4.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Sayers, Judy
    Faculty of Education Social Sciences and Law, University of Leeds, Leeds, UK.
    Rosenqvist, Eva
    Department of Teaching and Learning, Stockholm University, Stockholm, Sweden.
    Andrews, Paul
    Department of Teaching and Learning, Stockholm University, Stockholm, Sweden;Research Centre for Pedagogy and Education; Via University College, Aarhus, Denmark.
    Analysing English year-one mathematics textbooks through the lens of foundational number sense: A cautionary tale for importers of overseas-authored materials2023Ingår i: Oxford Review of Education, ISSN 0305-4985, E-ISSN 1465-3915, Vol. 49, nr 2, s. 262-280Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we present analyses of three textbooks currently used in the teaching of mathematics to year-one children in England. One is an established English-authored textbook, while the others are Singaporean-authored imports promoted by government as solutions to perceptions of systemic failure. Every task in each textbook was coded against a set of eight number-related competences known to support children’s learning in both short and long terms. Such a framework, which is literature-derived and curriculum-independent, enables meaningful comparison of materials deriving from different cultural contexts. Analyses of the proportions of all tasks coded for the different competences showed that none of the three books adequately addresses all eight competences, although the English-authored comes closest. Moving averages, undertaken to show the temporal location of the opportunities presented for children to acquire the eight competences, showed them distributed throughout the school year in the English-authored textbook but only during the first half of the school year in the two Singaporean-authored textbooks. Some implications for the importation of such materials are discussed.

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  • 5.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS). Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Larson, Niclas
    Universitetet i Agder, Norway.
    Palm Kaplan, Kristina
    Högskolan i Gävle, Sweden.
    Andrews, Paul
    Stockholms universitet, Sweden.
    Does solving arithmetic linear equations offer transferable algebraic competence?2023Ingår i: Proceedingsof the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) / [ed] Paul Drijvers; Csaba Csapodi; Hanna Palmér; Katalin Gosztonyi; Eszter Kónya, Budapest: Alfréd Rényi Institute of Mathematics and ERME , 2023, s. 642-649Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this study we have investigated the relation between grade 9 students’ responses to a simple linear equation and a visually similar but proportionally-based linear expression task. Analyses, based on data from the results of a test of 359 Swedish year Swedish students from six diverse schools, drew on written responses to the two tasks. Students giving algebra-based solutions to the linear equation are not only more likely to complete the proportional task but also offer better solutions than students giving arithmetic-based solutions. The results highlight the need for curricula, textbooks and teachers to revisit the place of algebraic equation-solving, whilst also encouraging students to verify their solutions.

    Ladda ner fulltext (pdf)
    CERME2023
  • 6.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Stokastikdidaktik del 1: Statistik, sannolikhetslära och kombinatorik för grund- och ämneslärare2023 (uppl. 1)Bok (Övrig (populärvetenskap, debatt, mm))
    Abstract [sv]

    Stokastik är ett samlingsnamn för statistik och sannolikhetslära och huvudinnehållet i denna bok är didaktik för stokastik och kombinatorik från tidiga skolår till gymnasiet. Vid sidan av huvudinnehållet visar boken med konkreta exempel hur didaktiska teorier såsom didaktisk transposition, praxeologi och teorier om representationsformer kan omsättas i lärares och elevers arbete med matematiska begrepp och modeller.

    Boken tar även upp didaktiska aspekter på digitala verktyg för att underlätta beräkningar, statistisk modellering och diagramkonstruktion. Andra områden är försöksplanering för skolmatematiken samt stokastikens idéhistoria och läroplanshistoria. Boken stödjer sig på en stor mängd forskningslitteratur med källor och tar även upp engelska termer i stokastik för att underlätta för läsaren att på egen hand kunna söka och läsa vidare inför skolutvecklingsarbete.

    Boken riktar sig till både grundlärarstudenter (del 1) och ämneslärarstudenter (del 1 + 2) då dessa utbildningar delvis överlappar varandra vad det gäller stokastikens didaktik. För grundlärarstudenter räcker bokens kapitel 1–9 och 11 i del 1 och de kan även hoppa över rubriker med ordet ”fördjupning” i sig. Kapitel 12–14 i del 2 ger en matematisk behandling av stokastik och modellering. Kapitel 10 (del 1) och 15 (del 2) ger en kort introduktion till vanliga kvantitativa forskningsmetoder inom skolutvecklingsarbete och utbildningsvetenskap såsom försöksplanering, enkäter, observationsprotokoll, enkäter, läromedelsanalys och statistisk analys.

  • 7.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Stokastikdidaktik del 2: Statistik, sannolikhetslära och kombinatorik för grund- och ämneslärare2023 (uppl. 1)Bok (Övrig (populärvetenskap, debatt, mm))
    Abstract [sv]

    Stokastik är ett samlingsnamn för statistik och sannolikhetslära och huvudinnehållet i denna bok är didaktik för stokastik och kombinatorik från tidiga skolår till gymnasiet. Vid sidan av huvudinnehållet visar boken med konkreta exempel hur didaktiska teorier såsom didaktisk transposition, praxeologi och teorier om representationsformer kan omsättas i lärares och elevers arbete med matematiska begrepp och modeller.

    Boken tar även upp didaktiska aspekter på digitala verktyg för att underlätta beräkningar, statistisk modellering och diagramkonstruktion. Andra områden är försöksplanering för skolmatematiken samt stokastikens idéhistoria och läroplanshistoria. Boken stödjer sig på en stor mängd forskningslitteratur med källor och tar även upp engelska termer i stokastik för att underlätta för läsaren att på egen hand kunna söka och läsa vidare inför skolutvecklingsarbete.

    Boken riktar sig till både grundlärarstudenter (del 1) och ämneslärarstudenter (del 1 + 2) då dessa utbildningar delvis överlappar varandra vad det gäller stokastikens didaktik. För grundlärarstudenter räcker bokens kapitel 1–9 och 11 i del 1 och de kan även hoppa över rubriker med ordet ”fördjupning” i sig. Kapitel 12–14 i del 2 ger en matematisk behandling av stokastik och modellering. Kapitel 10 (del 1) och 15 (del 2) ger en kort introduktion till vanliga kvantitativa forskningsmetoder inom skolutvecklingsarbete och utbildningsvetenskap såsom försöksplanering, enkäter, observationsprotokoll, enkäter, läromedelsanalys och statistisk analys.

  • 8.
    Sayers, Judy
    et al.
    University of Leeds.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Rosenqvist, Eva
    Stockholms universitet.
    Andrews, Paul
    Stockholms universitet.
    Swedish parents’ perspectives on homework: manifestations of principled pragmatism2023Ingår i: Education Inquiry, E-ISSN 2000-4508, Vol. 14, nr 1, s. 66-84Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Motivated by earlier research highlighting Swedish teachers’ beliefs that the setting of homework compromises deep-seated principles of educational equity, this paper presents an exploratory study of Swedish parents’ perspectives on homework in their year-one children’s learning. Twenty-five parents, drawn from three demographically different schools in the Stockholm region, participated in semi-structured interviews. The interviews, broadly focused on how parents support their children’s learning and including questions about homework in general and mathematics homework in particular, were transcribed and data subjected to a constant comparison analytical process. This yielded four broad themes, highlighting considerable variation in how parents perceive the relationship between homework and educational equity. First, all parents spoke appreciatively of their children receiving reading homework and, in so doing, indicated a collective construal that reading homework is neither homework nor a threat to equity. Second, four parents, despite their enthusiasm for reading homework, opposed the setting of any homework due to its potential compromise of family life. Third, seven parents indicated that they would appreciate mathematics homework where it were not a threat to equity. Finally, fourteen parents, despite acknowledging homework’s potential compromise to equity, were unequivocally in favour of mathematics homework being set to their children.

    Ladda ner fulltext (pdf)
    fulltext
  • 9.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Sayers, Judy
    School of Education, University of Leeds, Leeds, UK.
    Andrews, Paul
    VIA University College, Research Centre for Pedagogy and Education, Aarhus, Denmark;Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Two methods for quantifying similarity between textbooks with respect to content distribution2023Ingår i: International Journal of Research and Method in Education, ISSN 1743-727X, E-ISSN 1743-7288, Vol. 46, nr 2, s. 161-174Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Measures of association, which typically require pairwise data, are widespread in many aspects of educational research. However, due to the need to reduce their content to equal numbers of units of analysis, they are rarely found in the analysis of textbooks. In this paper, we present two methods for overcoming this limitation, one through the use of disjoint sections and the other through the use of overlapping moving averages. Both methods preserve the temporal structure of data and enable researchers to calculate a measure of association which, in this case, is the complementary Euclidean average distance, as an indicator of the books’ similarity. We illustrate these approaches by means of a comparative analysis of three commonly-used English and Swedish mathematics textbooks. Analyses were focused on individual tasks, which had all been coded according to the presence or absence of particular characteristics. Both methods produce nearly identical results and are robust with respect to both densely and sparsely occurring characteristics. For both methods, widening the aggregation window results in a slightly increased level of quantified similarity, which is the result of the ‘smoothing effect’. We discuss the relation between the window width and the choice of research question.

    Ladda ner fulltext (pdf)
    fulltext
  • 10.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Using the Gini coefficient for assessing heterogeneity within classes and schools2023Ingår i: SN Social Sciences, E-ISSN 2662-9283, Vol. 3, nr 11, artikel-id 186Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This study demonstrates that the Gini coefficient works as a dispersion measure for gauging educational heterogeneity in and between classrooms and schools. The method for this is to compare Gini coefficients for empirical data from various areas such as gender proportions in upper secondary school programmes and dispersion in achievement within classroom and between schools. The main results are that the Gini coefficient works for gauging heterogeneity on different statistical measurement scales and different sample sizes. An example of small sample is the nominal categories of upper secondary school study programmes, for which the Gini coefficient gauges differences in gender proportions while this sample size should be too small for several other measures of inequality and dispersion. An example of large sample of quotient scale data is two neighbour schools that mainly enrol different achievement strata from the same student cohort. Here the Gini coefficient displays the two schools’ student heterogeneity to be different. An example of moderate size sample is to explore how the teaching group heterogeneity, gauged as Gini coefficient on achievements, re-distributes from within to between classes as the same students proceed from cohesive compulsory school to the students’ individual choice of upper secondary school programmes. Since the Gini coefficient can gauge heterogeneity on small samples, a suggestion for further research is to use it for exploring the relation between strategies for classroom orchestration and levels of classroom heterogeneity, for example between teaching groups at different achievement strata. 

    Ladda ner fulltext (pdf)
    fulltext
  • 11.
    Andrews, Paul
    et al.
    Stockholms universitet.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Sayers, Judy
    University of Leeds.
    A methodological critique of research on parent-initiated mathematics activities and young children’s attainment2022Ingår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 109, s. 23-40Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, motivated by the desire to understand which forms of parent-initiated activity are productively implicated in young children’s mathematics learning, we present a methodological critique of recent research. Many such studies, based on assumptions that parent-initiated activities can be categorised as formal or informal, direct or indirect, or advanced or basic, exploit surveys to elicit how frequently parents engage their children in various predetermined activities. While such survey data have the potential to yield important insights, the analytical procedures typically employed prevent them. Studies involving factor analyses yield uninterpretable factors, which are then used to create summative variables based on the scores of individual activities. Other studies, drawing on untested preconceptions, simply create summative variables. In all cases, these summative variables are based on such a wide range of qualitatively different activities that labels like formal or informal become arbitrary and the potential of individual activities to support learning gets lost beneath colleagues’ desires for statistical significance. In closing, we ask colleagues, albeit somewhat rhetorically, what is the purpose of such research? Is it to identify those activities that support learning or to offer statistically robust factors, which, due to the diversity of activities embedded within them, offer few useful insights?

    Ladda ner fulltext (pdf)
    fulltext
  • 12.
    Bødtker Sunde, Pernille
    et al.
    Via University College.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL). Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Nosrati, Mona
    The Norwegian University of Science and Technology, Trondheim.
    Rosenqvist, Eva
    Stockholms universitet.
    Andrews, Paul
    Stockholms universitet.
    Estimation in the Mathematics Curricula of Denmark, Norway and Sweden: Inadequate Conceptualisations of an Essential Competence2022Ingår i: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 66, nr 4, s. 626-641Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Acknowledging evidence that the ability to estimate has major consequences for both later mathematics learning and real-world functionality, this paper examines the national mathematics curriculum for compulsory school for each of Denmark, Norway and Sweden for the estimation-related opportunities it offers children. Framed against four conceptually and procedurally different forms of estimation (computational, measurement, quantity and number line), each of which is implicated differently in the later learning of mathematics, analyses indicated that none of the four forms of estimation were addressed explicitly in the Norwegian curriculum. Expectations of computational and measurement estimation were present in both the Danish and the Swedish curricula, although neither referred to either quantity or number line estimation. Even when estimation-related learning outcomes were articulated, there was no evidence of the processes by which they might be realised. Finally, there were no acknowledgements that estimation may contribute to the learning of other mathematical topics.

    Ladda ner fulltext (pdf)
    fulltext
  • 13.
    Appelgren, Alva
    et al.
    Skolforskningsinstitutet.
    Wallin, Pontus
    Skolforskningsinstitutet.
    Jonsson, Lisa
    Skolforskningsinstitutet.
    Melin, Catarina
    Skolforskningsinstitutet.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Strandberg, Max
    Stockholms universitet.
    Läxor och likvärdiga förutsättningar för lärande: – lärares arbetssätt inför, under och efter läxan2022Rapport (Övrigt vetenskapligt)
    Abstract [sv]

    I denna systematiska översikt sammanställs forskning om hur lärares arbete med läxor kan bidra till likvärdiga förutsättningar för elevers lärande. Översikten utgår från följande frågeställning:

    Vad kännetecknar lärares arbete med läxor som kan bidra till likvärdiga förutsättningar för elevers lärande?

    Resultaten från de studier som ingår i översikten är sammanställda med fokus på lärares arbete med läxor inför, under och efter läxan. Sammantaget visar resultaten att lärare kan bidra till lik­värdiga förutsättningar för elevers lärande genom att planera utformningen av läxan, ta hänsyn till elevers situation i hemmet samt genom att följa upp läxarbetet i undervisningen.

    Översiktens resultat bygger på 15 forskningsstudier från olika länder som systematiskt har valts ut efter omfattande litteratursökningar i internationella referensdatabaser.

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    fulltext
  • 14.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Mathematical modelling in social sciences2022Ingår i: The relation between mathematics education research and teachers’ professional development / [ed] Mattsson, Linda; Häggström, Johan; Carlsen, Martin; Kilhamn, Cecilia; Palmér, Hanna; Perez, Miguel; Pettersson, Kerstin, Svensk förening för MatematikDidaktisk Forskning - SMDF, 2022, s. 141-141Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    This presentation outlines the mathematising of population pyramids in secondary education. The population pyramids are presented as reduced schemas, making them more accessible for use in both mathematics and social science classrooms. The outcome is that such schemes show useful for describing relations between the shape of a population pyramid and aspects of macroeconomic status of country; both when comparing countries with different shapes of the population pyramids at the same time period and when comparing one country over historical periods with different shapes of its population pyramids. Hence, this model opens for several societal applications, which in turn form bases for students’ discussion and interpretations of both simulation models and the principle of mathematical reductionism.

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    PeterssonJ_Madif2022presentation
  • 15.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Dahl, Jonas
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Jakobsson, Magnus
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Olofsson, Joakim
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Nya kursplanen: Enhetsanalys för attundervisa omhärledda enheter2022Konferensbidrag (Övrigt vetenskapligt)
    Abstract [sv]

    Härledda enheter ligger i området proportionalitet, vilket matematikdidaktisk forskning betraktar som både svårt att undervisa och svårt att lära sig. I ett regionalt skolutvecklingsprojekt omformade vi högskolematematikens enhetsanalys (dimensionsanalys) till att passa åk 7-gy då grundidén är att betrakta en storhets enhet, exempelvis kr/kg, och dra slutsatser om hur storheten (kvot eller produkt) ska beräknas. I projektet utvecklade vi både övningsproblem och undervisningsmetoder för detta.

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    Powerpoint presentation
  • 16.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Sayers, Judy
    Faculty of Education Social Sciences and Law, University of Leeds, Leeds, UK;Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Rosenqvist, Eva
    Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Andrews, Paul
    Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden;VIA University College, Aarhus, Denmark.
    Parent-initiated activities in support of Swedish year-one children’s learning of mathematics: age-appropriate complements to school?2022Ingår i: International Journal of Early Years Education, ISSN 0966-9760, E-ISSN 1469-8463, Vol. 30, nr 4, s. 831-846Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, motivated in part by evidence that Swedish teachers are sceptical of parents’ abilities to offer appropriate support, we present an exploratory investigation of the activities Swedish parents initiate to facilitate their year-one (first grade) children’s learning of mathematics. Data, derived from 25 semi-structured interviews conducted with parents from three demographically different schools, were subjected to constant comparison analyses and yielded three broad categories of activity. These concerned the use of games in the learning of mathematics, contextualised mathematics activities like cooking and shopping, and decontextualised mathematics activities like systematic counting. Collectively, the results indicate that while parents of year-one children are confident supporting their children’s learning of mathematics, they are also conscious of the need to avoid both undermining schools’ efforts and exacerbating educational inequity. With few exceptions, the activities parents described were age-appropriate and more likely to complement teachers’ actions than not.

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    fulltext
  • 17.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Weldemariam, Kassahun
    Göteborgs universitet.
    Prime Time in Preschool Through Teacher-Guided Play with Rectangular Numbers2022Ingår i: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 66, nr 4, s. 714-728Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In preschool, numbers and shapes typically appear as separate topics. This study explores how a game, designed as a guided play activity with figurate numbers, functions in a preschool context. The guided play involved parking Lego cars in a rectangular shape, and to find out for which number of Lego cars this is possible. Thirteen preschool children in three separate age groups, aged from four to six years, together with their teacher, participated in the study. Their communications through words and actions were recorded. The results exemplify how this guided play provides a rich context for engaging young children with mathematical activities such as counting, sorting, shaping, asking, justifying, and inferring, as well as emotional engagement with the activity.

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    fulltext
  • 18.
    Sayers, Judy
    et al.
    University of Leeds.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL). Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Marschall, Gosia
    Stockholms universitet.
    Andrews, Paul
    Stockholms universitet.
    Teachers’ perspectives on homework: manifestations of culturally situated common sense2022Ingår i: Educational review (Birmingham), ISSN 0013-1911, E-ISSN 1465-3397, Vol. 74, nr 5, s. 905-926Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper presents an exploratory study of English and Swedish teachers’ perspectives on the role of homework in year-one children’s learning of number. In order to ensure cultural integrity, data were analysed independently by two colleagues in each context. Analyses yielded three broad but cross-culturally common themes reflecting culturally situated notions of common sense. These concerned the existence of homework, the purpose of homework and the role of parents in homework’s completion. While homework was unproblematic for all English teachers, half the Swedish cohort spoke against it, arguing that variation in home background would compromise principles of equity. All teachers who set homework, whether English or Swedish, spoke of homework as a means of supporting children at risk of falling behind their peers, a process by which children practice routine skills. English teachers’ homework-related justifications were located in a discourse of target setting that was invisible in the Swedish.

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    fulltext
  • 19.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL). Institutionen för naturvetenskap, matematik och samhälle; Natural Science, Mathematics and Society.
    Timeseries analysis extends content analysis to exploring distribution of a topic among data2022Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    This poster shows that methods imported from timeseries analysis could benefit the use of content analysis through raising new research questions and allowing enhanced results by showing where, in a sequence of data, the studied phenomenon occurs. For methodological reasons, timeseries analysis in educational research has been effectively absent and, until recently, content analysis in educational research typically meant to look for the mere existence of some explored theme or for comparing their frequency in two data sets. A timeseries requires that the data are an ordered sequence of units of analysis. One example is the analysis of a classroom conversation where the data may follow clock-time. Another example is analysing exercises in a textbook, where the data may not follow clock-time since each exercise can require different amounts of time to solve. A first outcome of a timeseries analysis is a moving average diagram, which is a diagram of the same kind as temperature curves used in climate science for displaying temperature changes over time. For the case of analysing exercises in a mathematics textbook, this diagram shows the changes in the intensity of the explored learning object throughout the textbook. When analysing a classroom conversation, it allows the researcher to compare two moving average diagrams, each displaying where in the conversation two specified topics occur. Specifically, determining the correlation between two timeseries allows the researcher to explore how two learning objects or conversation topics interact with each other. Hence, timeseries analysis provides a new tool for the researcher.

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    QRM-poster
  • 20. Elvstam, Marie-Charlotte
    et al.
    Zaboli, Ghazal
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Rosenberg, Andreas
    Schoug, Annika
    Dima, Daniel
    Langeveld, Egbert
    Olofsson, Joakim
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Dahl, Jonas
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Lagnebo, Jörgen
    Beben, Magdalena
    Jakobsson, Magnus
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Delorme, Monica
    Lindén, Nicklas
    Munther, Olof
    Att organisera praktiknära skolforskning som ömsesidigt samarbetelärosäte-skolor2021Konferensbidrag (Övrigt vetenskapligt)
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    fulltext
  • 21.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Components of knowledge in solving linear equations2021Ingår i: Sustainable mathematics education in a digitalized world / [ed] Y. Liljekvist; L. Björklund Boistrup; J. Häggström; L. Mattsson, 2021, s. 41-50Konferensbidrag (Refereegranskat)
    Abstract [en]

    This article identifies knowledge components needed for successfully solving linear equations. Data for this purpose is 359 Swedish year 9 students’ written responses to the test task ”solve the equation 2x + 3 = 11”. The following set of knowledge components were identified; arithmetic knowledge, parsing knowledge, balancing equations, giving a value to the unknown, not omitting parts and the habit of verifying the solution. This paper discusses for which of these knowledge components, students could discover and correct their own errors if they would both solve an equation and verify its solution.

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    PeterssonJ_Madif2020_pdf
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    PeterssonJ_Madif2020_epub2
  • 22.
    Andrews, Paul
    et al.
    Stockholms universitet.
    Bødtker Sunde, Pernille
    VIA University College, Århus, Denmark.
    Nosrati, Mona
    NTNU: Norwegian University of Science and Technology.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Rosenqvist, Eva
    Stockholms universitet.
    Sayers, Judy
    University of Leeds.
    Xenofontos, Constantinos
    University of Stirling, Stirling, Scotland.
    Computational Estimation and Mathematics Education: A Narrative Literature Review2021Ingår i: Journal of Mathematics Education, ISSN 1945-7502, E-ISSN 1945-7448, Vol. 14, nr 1, s. 6-27Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Computational estimation, typically construed as an approximate mental calculation of an arithmetical problem, is an important skill in everyday life and a wide range of professional contexts. Despite its importance, textbooks and curricula address it inadequately, with the consequence that many teachers are uncertain as to why and how they should teach it. In this paper, we present a narrative literature review that brings together the extensive research of the cognitive psychologists and the limited research of the mathematics educators to clarify the nature of computational estimation and its development. Focused initially on the strategies used in computational estimation before turning to children’s and adults’ computational estimation competence, the review shows that computational estimation, which develops over time, draws on a wide range of strategies reciprocally dependent on a secure understanding of numbers and arithmetic. It shows that the poor estimation competence of children and adults’ is susceptible to interventions, particularly with respect to addressing a common misconception that the purpose of computational estimation is the mental calculation of exact solutions.

  • 23.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Sayers, Judy
    University of Leeds, UK.
    Andrews, Paul
    Stockholms universitet.
    Content Analysis of Mathematics Textbooks and Adapted Lorentz Curves2021Ingår i: Proceedings of the Eighth Conference on Research in Mathematics Education in Ireland / [ed] Kingston, M; Grimes, P, Dublin, 2021, s. 356-363Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we introduce an adaption of the Lorenz curve as a powerful tool for graphicallypresenting content analyses of mathematics textbooks. Three textbooks currently used withyear-one children in Sweden, one Swedish-, one Finnish and one Singaporean-authored, wereanalysed against the eight categories of Foundational Number Sense (FoNS), which is a set ofliterature-derived and instruction-dependent competences that all children need to acquire ifthey are to become successful learners of mathematics. The adapted Lorenz curvehighlighted, inter alia, major differences in the distribution of FoNS-related tasks across thethree textbooks. In general, the Swedish-authored textbook offers repeated cycles of FoNSrelated opportunities, the Finnish-authored textbook offers such opportunities continuously,and the Singaporean-authored textbook typically offers FoNS-related opportunities onlywithin its earlier pages. 

    Ladda ner fulltext (pdf)
    PeterssonSayersAndrews2021_MEI8paper
  • 24.
    Sayers, Judy
    et al.
    University of Leeds.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Rosenqvist, Eva
    Stockholms universitet.
    Andrews, Paul
    Stockholms universitet.
    Estimation: The missing competence in the mathematics experiences of year-one children2021Ingår i: / [ed] Judy Sayers, 2021Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    As part of our work on the Foundational Number Sense (FoNS) project, we undertook the development of a simple to operationalise framework for analysing the number-related learning opportunities received by year-one children (Andrews & Sayers, 2015). The eight categories of FoNS bridge the gap between those number-related understandings innate to all humans and forms of number sense typically associated with functional numeracy. Consequently, each FoNS competence is not only a prerequisite for later mathematical learning but dependent on instruction. One of these categories, estimation, has been identified as one of the three most important mathematical skills (Sriraman & Knott, 2009) and yet, as we discuss below, it is effectively absent from the curricula and textbooks that underpin the teaching and learning of year-one mathematics. Moreover, possibly a consequence of the above, during the early months of the project, a small set of serendipitously available year-one lessons from a number of European countries were analysed against the different FoNS categories and, across all systems, estimation was effectively invisible.

    The ability to estimate is widely recognised not only as a core skill of everyday life (White & Szűcs, 2012) but also a key determinant of later arithmetical competence, particularly in respect of novel situations (Booth & Siegler, 2008; Holloway & Ansari, 2009). However, the development of the ability to estimate is not a chance phenomenon but requires intervention (Joram et al., 2005; Peeters et al., 2016; White & Szűcs, 2012). Unfortunately, the teaching of estimation has been, historically, a neglected skill with textbooks colluding in this omission (Reys et al., 1982) by offering incomplete or inappropriate models (Joram et al., 1998).

    Broadly speaking, estimation takes four forms; computational estimation, number line estimation, quantity estimation and measurement estimation. Of these, number line estimation and quantity estimation are, we argue, lower level skills than computational estimation or measurement estimation and, as such, comprise the estimation elements of FoNS. That said, being able to undertake computational estimation is an essential life skill (Sekeris et al., 2019) and is, despite teacher scepticism (Alajmi, 2009), an important aid to children’s understanding of both place value and standard algorithms (Sowder, 1992). It is a skill that develops with age (Lemaire & Brun, 2014) but is an under-investigated area of arithmetic-related research (Lemaire & Lecacheur, 2011). Number line estimation, which draws on a child’s developing ability to exploit reference points (Sullivan & Barner, 2014), is a strong predictor of both mathematical learning difficulties (Siegler & Opfer, 2003) and mathematical achievement (Schneider et al., 2009). Instruction with respect to number line estimation is important if young children’s logarithmic estimations of quantity are to be replaced by linear (Siegler & Opfer, 2003), although others have argued that the logarithmic/linear distinction is less a developmental issue than one related to strategy choice (Ebersbach et al., 2008). Quantity (or numerosity) estimation is the ability to estimate the number of objects in a set. It is a skill that diminishes in accuracy as the numerosity of the set of objects grows (Smets et al., 2015). The ability to estimate quantities is closely tied to the ability to count (Barth et al., 2009) and has a developmental trajectory similar to number line estimation (Sella et al., 2015). Interestingly, the evidence indicates that young children tend exploit linear mappings in continuous conditions and logarithmic in discrete (Odic et al., 2013). While measurement estimation is an important life skill, with many users of mathematics using it as an everyday part of their professional decision making based on reference or anchor points (Jones & Taylor, 2009), it remains a neglected research field (Joram et al., 1998). It is known that children who employ references model to their estimates are more accurate than those who do not (Joram et al., 2005) and that context familiarity improves estimates (Jones et al., 2012).

    In this paper we will examine the materials available to support the teaching of estimation to year-one children. In particular, we will summarise how the curricula of ten European countries present estimation alongside analyses of six textbooks currently used in the year-one classrooms of England and Sweden. Two of these are authored by nationals of the two countries, while the remaining four are adaptations of textbooks drawn from countries typically seen as successful on international tests of achievement. The analyses indicate, confirming research undertaken nearly forty years ago, that across the board, estimation in any form is absent from year-one children’s opportunities to learn.

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    ERME9th_Sayers_et_al
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    Erme9th_Sayers_et_al
  • 25.
    Olande, Oduor
    et al.
    Linnéuniversitetet.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Horizontal and vertical mathematisation in inquiry based pedagogy2021Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    IBP (Inquiry Based Pedagogy) is a growing trend and is “…defined loosely as a way of teaching in which students are invited to work in ways similar to how mathematicians and scientists work.” (Artigue and Blomhøj, 2013, p.797), which means that the learner engages in a process of self-reflection and discovery. IBP open for a plethora of possible research issues and we illustrate this with our work with formulating and using the following task in IBP and analysing the outcome.

    The village association has decided to build a common well somewhere along the street in the village (see figure), where all households can go and fetch water. Your task is to suggest a rule for where to dig the well. It should be of mathematical nature and the villagers should find it fair. 

     

    When formulating a task for IBP, we first needed to consult cognitive research on concept formation in statistics education. We also considered the students’ prerequisites needed for IBP to work (Kirschner, Sweller, & Clark, 2006). In next phase, we used didactical engineering for refining the problem formulation and the lesson arrangement. While exploring the collected classroom data during one of the first iterations of refinement, we identified several aspects of research interest in students’ group work. We felt that besides describing this process in terms of Pólya’s cognitive phases of problem solving in Schoenfeld’s timeline protocol and the social co-operation following socio-mathematical norms, another unexplored option is to describe the students’ work process in terms Treffer’s horizontal and vertical mathematisation. Namely, that one student group seemed to work only mechanically while others also in a structural vein created what for them was new mathematics and regarded the realistic aspects of the problem. In particular, we saw that the working process in the latter groups shifted between realistic, structural and mechanical phases (and an intermittent idle phase) in a way that we think deserves a closer analysis on how these phases are distributed in time throughout the students’ group work. 

    References

    Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM Mathematics Education, 45(6), 797–810. doi:https://doi.org/10.1007/s11858-013-0506-6 

    Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86.

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    Olande_Petersson_Norma20
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    Olande_Petersson_Norma20
  • 26.
    Sayers, Judy
    et al.
    School of Education, Leeds University, Leeds, UK.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL). Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Rosenqvist, Eva
    Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Andrews, Paul
    Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Opportunities to learn foundational number sense in three Swedish year one textbooks: implications for the importation of overseas-authored materials2021Ingår i: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 52, nr 4, s. 506-526Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded against the eight categories of foundational number sense, which are the number-related competences literature has shown to be essential for the later mathematical success of year one learners. Two analyses were undertaken; the first was a frequency analysis of the tasks coded for a particular category, the second was a time-series analysis highlighting the temporal location of such opportunities. The frequency analyses identified statistically significant differences with respect to children's opportunities to acquire foundational number sense. Additionally, the time series showed substantial differences in the ways in which such tasks were located in the structure of the textbooks. Such differences, we argue, offer substantial didactical challenges to teachers trying to adapt their practices to the expectations of such imports.

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    fulltext
  • 27.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Westlund, Andreas
    Malmö kommun.
    Resolve possible confusion by distinguishing between reflexive and transitive formative assessment2021Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    AbstractThe review of assessment research by Black and Wiliam (1998) initiated a changed approach regarding teachers' classroom practice. They defined formative assessment as ”… encompassing all those activities undertaken by teachers, and/or by their students, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged” (Black & Wiliam, 1998, s. 7-8). This wide definition includes both teachers’ and their students’ activities, while as an example, the Swedish National Agency for Education instead confines formative assessment to the teachers’ work during the actual teaching process in order to find out where the student is in his learning, and to adapt the teaching accordingly (Skolverket, 2013). This pinpoints that we should distinguish between reflexive formative assessment, aiming to modify oneself, be it a student to himself or a teacher to herself and transitive formative assessment, aiming to modify someone else, be it from teacher to student or student to another student. Hirsh and Lindberg (2015) discussed this distinction though they did not coin a term for it as Westlund (2020) did. 

    ReferencesBlack, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: principles, policy & practice, 5(1), 7-74.

    Hirsh, Å., & Lindberg, V. (2015). Formativ bedömning på 2000-talet : En översikt av svensk och internationell forskning. In Forskning och skola i samverkan – Kartläggningar av forskningsresultat med relevans för praktiskt arbete i skolväsendet (pp. 105–109). Stockholm: Vetenskapsrådet.

    Skolverket. (2013). Forskning för klassrummet: vetenskaplig grund och beprövad erfarenhet i praktiken. Stockholm: Fritzes.

    Westlund, A. (2020). Formativ bedömning i ett lärarperspektiv – framträdande aspekter i undervisning och vad som behövs för implementering. (Master thesis of education). Malmö University.

    Ladda ner fulltext (epub)
    PeterssonWestlund_NoFa8
    Ladda ner fulltext (pdf)
    fulltext
  • 28.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Rosenqvist, Eva
    Stockholms universitet.
    Sayers, Judy
    University of Leeds.
    Andrews, Paul
    Stockholms universitet.
    Swedish parents’ perspectives on home-school communication and year-one pupils learning of mathematics2021Ingår i: Bringing Nordic mathematics education into the future / [ed] G. A. Nortvedt, N. F. Buchholtz, J. Fauskanger, F. Hreinsdóttir, M. Hähkiöniemi, B. E. Jessen, J. Kurvits, Y. Liljekvist, M. Misfeldt, M. Naalsund, H. K. Nilsen, G. Pálsdóttir, P. Portaankorva-Koivisto, J. Radišić, and A. Wernberg, Göteborg: Nationellt centrum för matematikutbildning (NCM), 2021, Vol. 14, s. 201-208Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper we explore parents’ perspectives on home-school communication with respect to year-one pupils’ learning of early numeracy. Constant comparison analyses of semi-structured interviews identified three forms of communication. The first, a weekly information letter, was appreciated and typically functioned as a starter for conversations with children about their learning of early numeracy. The second, the development talk, was appreciated as an indicator of a child’s progress, but proved controversial in the presentation of mixed messages to parents and limited with respect to helping parents support future mathematical learning. The third, parent-initiated contact, was discussed in ways that masked parents’ reasons for making contact and prevented, therefore, any insights into their contribution to mathematical learning. Some implications are discussed.

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    PeterssonRosenqvistSayersAndrews_Norma20
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    PeterssonRosenqvistSayersAndrews_Norma20
  • 29.
    Holmqvist, Mona
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Lelinge, Balli
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Svensson, Christina
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Öhrn, Johanna
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Teachers’ Academic literacy knowledge2021Ingår i: Abstract book nofa8, Western Norway University of Applied Sciences , 2021, 2021Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    In this study, a total of 18 in-service teachers participated in one cycle of a learning study (Marton, 2015; Holmqvist, 2011) aiming to study development of academic literacy. The study was guided by variation theory (Marton 2015; Holmqvist, Gustavsson & Wernberg, 2008). The object of learning is academic literacy, a subject of importance for all teachers, as their professional work is supposed to be conducted on scientific based knowledge. The capability to read and understand scientific publications, and to judge the scientific value of different sources used by teachers, are crucial for the quality of teachers’ professional work. The study was designed following the steps of a learning study. This means collaborative discussions among the teachers, in this case the researchers who are the authors of this abstract, testing the participants’ knowledge before the teaching activity, by designing and implementing instruction offer the participants to discern the critical aspects of academic literacy to gain deeper knowledge, analysis of post-tests to describe the learning outcome, and to present the results. The lesson was focusing on the structure of, and differences between, scientific and popular scientific texts. Two texts were used presenting the same study and by the same author. By that, the in-service teachers were offered to see the same topics differently described based on the two different genre’s requirements. The results show how the participants in the pre-test focuses on the texts’ similarities, with an unawareness of genre differences. In the post-test, the differences in genre is described. A limitation of the study is that the two texts used in pre and post-tests are focusing slightly different topics, which is discerned and focused by the participants – an aspect not critical for developing academic literacy at a general level.

    References

    Holmqvist, M. (2011). Teachers’ learning in a learning study. Instructional science, 39(4), 497-511.

    Holmqvist, M., Gustavsson, L. & Wernberg, A. (2008) Variation Theory – An Organizing Principle to 

    Guide Design Research in Education. In Kelly, A.E., Lesh, R., &. Baek J. (eds) Handbook of design research methods in education, p 111-130. New York: Routledge. 

    Marton, F. (2015). Necessary conditions of learning. London: Routledge.

  • 30.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Conde, Rosie
    Philippine Normal University.
    Dahl, Jonas
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Jakobsson, Magnus
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för naturvetenskap, matematik och samhälle (NMS).
    Andersson, Per
    Helsingborgs kommun.
    Beben, Magdalena
    Helsingborgs kommun.
    Beckman, Per
    Malmö kommun.
    Dahlbom, Staffan
    Helsinglands Utbildningsförbund.
    Delorme, Monica
    Helsingborgs kommun.
    Dima, Daniel
    Helsingborgs kommun.
    Elvstam, Marie-Charlotte
    Lomma kommun.
    Lagnebo, Jörgen
    Lomma kommun.
    Langeveld, Egbert
    Svedala kommun.
    Lindén, Nicklas
    Vellinge kommun.
    Munther, Olof
    Vellinge kommun.
    Rosenberg, Andreas
    Svedala kommun.
    Schoug, Annika
    Helsingborgs kommun.
    Zaboli, Ghazal
    Vellinge kommun.
    Teaching dimensional analysis in secondary school mathematics2021Ingår i: Abstract book nofa8, Western Norway University of Applied Sciences , 2021Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Abstract

    In its elementary form, the idea of dimensional analysis is to look at the unit of a magnitude, for example speed, and conclude that speed measured in m/s is a quotient having meters in the numerator and seconds in the denominator. However, despite dimensional analysis being a not un-common theme for research in mathematics education at tertiary level teaching, it seems in practice absent below that level. This is surprising since dimensional analysis is useful in mathematical problem solving involving proportionality. Even more so since, from halves and doubles in preschool to scalar multiplication in upper secondary school, proportionality permeates school mathematics and is well-researched (Lamon, 2007). Hence, the authors initiated a research project on how to teach dimensional analysis in school years 6-12. The novelty of this area made us choose didactical engineering (Artigue, 2015) as a theoretical framework suitable for developing the teaching of dimensional analysis. Accordingly, in a cycle of a priori and a posteriori analyses, the authors are developing an empirically based teaching model for dimensional analysis including the topic of constructing exercises for students. We present results from this on-going development project. 

    References

    Artigue, M. (2015). Perspectives on Design Research: The Case of Didactical Engineering. In A. Bikner-Ahsbahs, C. Knipping, N. Presmeg. (Eds.). Approaches to Qualitative Research in Mathematics Education. Dordrecht: Springer.

    Lamon, S. J. (2007). Rational numbers and proportional reasoning: Towards a theoretical framework. In F.K. Lester (red) Second handbook of research on mathematics teaching and learning, vol 2 (pp. 629–668). Charlotte, NC: NCTM.

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  • 31.
    Andrews, Paul
    et al.
    Stockholms universitet.
    Molina, Marta
    Universidad de Salamanca.
    Nosrati, Mona
    NTNU: Norwegian University of Science and Technology.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Rosenqvist, Eva
    Stockholms universitet.
    Sayers, Judy
    University of Leeds.
    Bødtker Sunde, Pernille
    VIA University College, Århus, Denmark.
    Xenofontos, Constantinos
    University of Stirling, Stirling, Scotland.
    The role of number line estimation in mathematics teaching and learning: A narrative literature review2021Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    While the importance of both computational estimation and measurement estimation in children’slearning of mathematics is well known and has been widely researched, little attention has been paidto number line estimation, a mathematical competence that has only in the last two decades gainedthe attention of researchers. In this paper, we present a narrative review of the literature relating tonumber line estimation in the teaching and learning of school mathematics. In so doing, we focus onthe development of number line estimation in children, the mathematics learning implications ofnumber line estimation competence and how different approaches to the investigation of number lineestimation have yielded different insights into children’s cognition. Finally, we consider thedidactical implications of the review and appeal to curriculum developers to integrate more widelythis important competence.

  • 32.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL). Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Sayers, Judy
    University of Leeds.
    Rosenqvist, Eva
    Stockholms universitet.
    Andrews, Paul
    Stockholms universitet.
    Two novel approaches to the content analysis of school mathematics textbooks2021Ingår i: International Journal of Research & Method in Education, ISSN 1743-7288, Vol. 44, nr 2, s. 208-222Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The analysis of the content of school textbooks, particularly in a time of cross-cultural borrowing, is a growing field restricted by the tools currently available. In this paper, drawing on the analyses of three English year-one mathematics textbooks, we show how two approaches to the analysis of sequential data not only supplement conventional frequency analyses but highlight trends in the content of such textbooks hidden from frequency analyses alone. The first, moving averages, is conventionally used in science to eliminate noise and demonstrate trends in data. The second, Lorenz curves, is typically found in the social sciences to compare different forms of social phenomena. Both, as we show, extend the range of questions that can be meaningfully asked of textbooks. Finally, we speculate as to how both approaches can be used with other forms of ordered classroom data.

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  • 33.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Debatt: Anpassa skolpengen – utifrån ansvaret att följa befolkningskurvan2020Ingår i: Jönköpingsposten, ISSN 1103-9469, nr 2020-12-23Artikel i tidskrift (Övrig (populärvetenskap, debatt, mm))
    Abstract [sv]

    Kommunala skolor har ett lagstadgat ansvar att ta höjd för variationer i befolkningskurvan. En friskola däremot kan välja att anpassa kostymen. Det är ett självklart och icke-ideologiskt argument för att betala ut en större skolpeng till kommunala skolor som är ålagda att ha en överkapacitet.

  • 34.
    Sayers, Judy
    et al.
    University of Leeds.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Rosenqvist, Eva
    Stockholms universitet.
    Andrews, Paul
    Stockholms universitet.
    Estimation: An inadequately operationalised national curriculum competence2020Ingår i: BSRLM Proceedings: Vol 40 No 1 at The University of Cambridge, Cambridge, on Saturday 7 th March 2020 / [ed] Marks, R., Cambridge: British Society for Research into Learning Mathematics , 2020, Vol. 40, s. 1-6Konferensbidrag (Refereegranskat)
    Abstract [en]

    Research has highlighted the importance of estimation, in various forms, as both an essential life-skill and a significant underpinning of other forms of mathematical learning. It has also highlighted a lack of opportunities for learners to acquire estimational competence. In this paper, we present a review of the literature that identified four forms of estimation. These are measurement, computational, quantity (or numerosity) and number line estimation. In addition to summarising the characteristics and significance of each form of estimation, we examine critically the estimation-related expectations of the English national curriculum for primary mathematics to highlight a problematic lack of opportunity.

  • 35.
    Petersson, Jöran
    et al.
    Stockholm University.
    Sayers, Judy
    Leeds University, England.
    Andrews, Paul
    Stockholm University.
    Time series analysis: Moving averages as an approach to analysing textbooks2020Ingår i: Proceedings of CERME11 / [ed] Jankvist, U. T., Van den Heuvel-Panhuizen, M., & Veldhuis, M., Freudenthal Group & Freudenthal Institute , 2020Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this study we introduce time series analysis, specifically moving averages, as a novel strategy for analysing mathematics textbooks. Such analyses show how different topics or mathematical processes are emphasised over different time periods, whether at the level of the lesson, the week, the month or year. In this paper, by way of example, we show how one of the eight categories of foundational number sense (Andrews & Sayers, 2015), namely simple addition and subtraction, is distributed and sequenced across three English, year one, textbooks. The analyses are compared empirically with four other methods found in the literature to show how time series analysis using moving averages helps address the shortcomings of these different approaches.

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  • 36.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Tänk om det som gäller friskolor även gällde i förlossningsvården2020Ingår i: Läraren : en tidning från Lärarförbundet, ISSN 2003-6035, nr 20-12-14Artikel i tidskrift (Övrig (populärvetenskap, debatt, mm))
    Abstract [sv]

    Från ett decennium till ett annat varierar elevkullarna stort och skolpengen kan baseras på skolformens ansvar att ta höjd för detta. Då en sådan skolpeng baserar sig på demografiska variationer och är lätt att beräkna, så undviker den många ideologiska och politiska låsningar.

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  • 37.
    Petersson, Jöran
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    A fit model for model fitting: an a-didactical situation for model building2019Ingår i: NOFA7 Abstracts, Stockholm University, 13 - 15 May 2019, 2019, s. 169-169Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Mathematical modelling in school mathematics encompasses a wide range of questions such as curricular aspects, mathematical concepts involved, orchestrating lesson activities, and many more. When building models, one approach is to use epistemological arguments and another approach is to base the model on empirical data. In the latter case, we can either focus on applying the resulting model to real life problems or we can focus on the mathematical methods needed to find the resulting model. 

    In this empirical study, students in school year 10 in Sweden were asked “How do you think a digital tool calculates the fitted curve?” Doing so, the students were given an open-response task where they themselves are expected to develop mathematical knowledge that is new to them. One outcome of the students’ work was the following: They suggested mathematical methods corresponding to those analytical and geometrical methods that have been developed and used through the history of mathematics. Moreover, they suggested both discrete and continuous metric spaces as a means for measuring the distance between data and model. They also suggested modern methods from exploratory data analysis such as trimming the empirical data before fitting the model to them. Another outcome was that the tasks for the students were formulated so that they promoted and enthused the students’ mathematical creativity and reasoning in a way that in this mathematical area reached far beyond the curriculum for secondary school mathematics.

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  • 38.
    Petersson, Jöran
    et al.
    Malmö universitet, Fakulteten för lärande och samhälle (LS), Institutionen för skolutveckling och ledarskap (SOL).
    Sayers, Judy
    University of Leeds.
    Andrews, Paul
    Stockholms universitet.
    Methods for visual and statistical comparison of the distribution of codes from content analyses2019Ingår i: NOFA7 Abstracts, Stockholm University, 13 - 15 May 2019, Stockholm: HSD, Stockholm University , 2019, s. 170-170Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    The FoNS-project (Foundational Number Sense) in Mathematics education at Stockholm University aims to compare different countries with respect to opportunities for acquiring FoNS in first school year. We do this by analysing textbooks, teachers’ classroom activities and parent engagement with respect to mathematics. This means that the FoNS-project focuses less on the pupils themselves, but more on the mathematical education environment the pupils meet. One part of the FoNS-project is to compare textbooks through content analysis. The generated data are a sequence of codes from each textbook. In the generated data, the authors found that besides comparing frequencies, there is also much to be found in comparing the distribution of the codes for different textbooks. For this purpose we developed a novel method that allows a visual comparison of how the content in each textbook is distributed and we present this method and compare it with other methods found in a literature review. Another challenge is to make statistical inference tests on the generated data.

    Typically, the generated data set is large and a drawback is that with large data sets even small differences can result in statistically significant but in practice irrelevant differences. The authors will also compare various statistical methods for dealing with this challenge for both the case of comparing frequency and for comparing distribution of the data.

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  • 39.
    Norén, Eva
    et al.
    Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Petersson, Jöran
    Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Sträng, Cecilia
    Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Svensson, Petra
    Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Newly arrived students in mathematics classrooms in Sweden2015Ingår i: Proceedings of the Ninth Congress of the European Society for Researchin Mathematics Education / [ed] Konrad Krainer, Nada Vondrová, 2015, s. 1630-1636Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper we discuss how newly arrived students experience, and perform in, school mathematics. There is little research on immigrant students' initial time in Swedish school, and it is methodologically underdeveloped. Our own research will be revisited, and we give an account of the methodologies we have developed. We look for analytical tools using both qualitatively as well as quantitatively, to interpret classroom interaction, social practises, individual performance and achievement. Our attention to diversity and equity issues includes avoiding deficit discourses explaining both success and failure in school mathematics, in relation to backgrounds, language and culture.

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