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  • 1. Holmström, Kenneth
    et al.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    A review of the parameter estimation problem of fitting positive exponential sums to empirical data2002In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 126, no 1, p. 31-61Article in journal (Refereed)
    Abstract [en]

    Exponential sum models are used frequently: in heat diffusion, diffusion of chemical compounds, time series in medicine, economics, physical sciences and technology. Thus it is important to find good methods for the estimation of parameters in exponential sums. In this paper we review and discuss results from the last forty years of research. There are many different ways of estimating parameters in exponential sums and model a fit criterion, which gives a valid result from the fit. We find that a good choice is a weighted two-norm objective function, with weights based on the maximum likelihood (ML) criterion. If the number of exponential terms is unknown, statistical methods based on an information criterion or cross-validation can be used to determine the optimal number. It is suitable to use hybrid Gauss–Newton (GN) and quasi-Newton algorithms to find the unknown parameters in the constrained weighted nonlinear least-squares (NLLS) problem formulated using an maximal likelihood (ML) objective function. The problem is highly ill conditioned and it is crucial to find good starting values for the parameters. To find the initial parameter values, a modified Prony method or a method based upon rewriting partial sums as geometrical sums is proposed.

  • 2.
    Norén, Eva
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Algebra tasks in a word problem and non-word problem context – a multilingual project2014In: Development of mathematics teaching: design, scale, effects: Proceedings of MADIF 9: the ninth Swedish mathematics education research seminar, Umeå, February 4-5, 2014 / [ed] Ola Helenius, Arne Engström, Tamsin Meaney, Per Nilsson, Eva Norén, Judy Sayers, Magnus Österholm, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2014Conference paper (Refereed)
    Abstract [en]

    Many students see algebra as a difficult topic. For second language speakers there might also be difficulties comprehending an algebra task linguistically correct. The authors suggest studying how knowledge in algebra and linguistic registers in mathematics interplay for both newly early arrived immigrants compared to first language speakers. We suggest the tools for such a study to be measuring achievement and solution strategy while varying the text intensity and mathematics register in algebra problems for students with different length of experience of Swedish language in school year 9. We want to discuss design of test instrument and methods for background data collection.

  • 3.
    Norén, Eva
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Sträng, Cecilia
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Svensson, Petra
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Newly arrived students in mathematics classrooms in Sweden2015In: Proceedings of the Ninth Congress of the European Society for Researchin Mathematics Education / [ed] Konrad Krainer, Nada Vondrová, 2015, p. 1630-1636Conference paper (Refereed)
    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.

  • 4.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    A PhD-project in multiculturalism: Ethnomathematics, language or educational systems2010In: Mathematics and mathematics education: Cultural and social dimensions: Proceedings of Madif7 / [ed] Christer Bergsten, Eva Jablonka, Tine Wedege, Linköping: Svensk förening för matematikdidaktisk forskning, Linköping universitet , 2010, p. 275-276Conference paper (Refereed)
    Abstract [en]

    What could a PhD-project within a multicultural perspective on mathematics education comprise? So far a literature survey suggests three possible aspects, namely ethno-mathematics, multilingualism or educational systems.

  • 5.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Begreppsrika matematiska experiment2007In: Matematikdidaktiska texter: beprövad erfarenhet och vetenskaplig grund / [ed] A. Pettersson, T. Englund & T. Tambour, Stockholm: Stockholm University, 2007, p. 56-70Chapter in book (Other academic)
    Abstract [sv]

    Matematiska experiment kan vara av högst skiftande utformning. En kategorisering är följande tre typer av matematiska experiment: Laborationer, simuleringar och tankeexperiment. Denna text definierar och exemplifierar dessa begrepp och belyser dem ur några didaktiska aspekter.

  • 6.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Den mystiska stjärnan – både science och fiction2013In: Tintinism: Årsbok 2013, Solna: Asterion media , 2013, p. 113-120Chapter in book (Other (popular science, discussion, etc.))
  • 7.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Det hemliga vapnet – i vätebombens skugga2015In: Tintinism 2015 / [ed] Björn Wahlgren, Solna: Asterion media , 2015Chapter in book (Other (popular science, discussion, etc.))
  • 8.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    First and second language students’ achievement in mathematical content areas2017In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 22, no 2, p. 33-50Article in journal (Refereed)
    Abstract [en]

    This study compares Swedish first (N=2 253) and second -language (N=248) students' achievement in mathematical content areas specified by the TIMSS-framework. Data on mathematics achievement from three national tests 2007-2009 in school year 9 are used. The present study found that the achievement difference between the mathematical content areas algebra and number was smaller for second language students than for first language students and this result holds with statistical significance (p=0.016). The same holds for algebra versus data and chance (p=0.00053). A hypothesis for further research is suggested; that students immigrating in late school years have contributed to the observed result by bringing experiences from other curricula into their new schooling.

  • 9.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Late-arrived immigrants in school and performance in algebra2013In: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education / [ed] Anke M. Lindmeier, Aiso Heinze, International Group for the Psychology of Mathematics Education , 2013, Vol. 5, p. 143-143Conference paper (Refereed)
    Abstract [en]

    This paper reports from a study on immigrant and native students tested in algebra asone of several topics in school mathematics. In general immigrant students performlower the later they have immigrated (Böhlmark, 2008). Students often find workingwith algebra difficult and Kieran (1992) noted that new-beginners in algebra oftenread algebraic expressions from left to right and might ignore the brackets.In this study 358 school year 9 students in six Swedish schools, with an over averagepercentage of immigrants, took a test. Several test problems were formulated so thatthey were likely to not cause too much of language obstacles for second languagelearners. In this report the test problem “a = 2, b = 4. What is a(b+2)+b?” is in focus.This problem was characterized in Duval’s (2006) semiotic registers as mainly“computations” and scarcely dependent on natural language.An important result is that the students who immigrated during school years 8 – 9performed better than the native students and much better than students whoimmigrated during school years 1 – 7. Most wrong solutions among all studentcategories were due to misuse of the distributive law in line with Kieran (1992).There were few arithmetic errors.In this on-going research project one conclusion is that there seems to be a need tosee early and late immigrants as having different challenges in being second languagelearners. The former have difficulties in following some advanced topics inmathematics teaching and the latter have difficulties in understanding some testquestions. A second conclusion is that there is a need in research to look at specifictopics in mathematics, especially advanced compulsory school mathematics such asnegative numbers and algebra, for these student categories.

  • 10.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Late-arrived immigrants in school and performance in arithmetic for negative numbers2013In: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education / [ed] Anke M. Lindmeier, Aiso Heinze, International Group for the Psychology of Mathematics Education , 2013, Vol. 5, p. 252-252Conference paper (Refereed)
    Abstract [en]

    This paper reports from a study on immigrant and native students tested in negative number arithmetic as one of several topics in school mathematics. In general immigrant students perform lower the later they have immigrated (Böhlmark, 2008). Students often find working with negative numbers difficult and Vlassis (2004) identified two kinds of conceptual changes needed for productive use of the minus and subtraction sign. First, the arithmetic rules are different for addition and subtraction. For example, subtraction is not commutative. Second, the minus sign has a flexible use exemplified by the expression (-23) + 9 = 9 – 23 = -(23 – 9). The expression uses the minus sign as a signed integer (non-operational), a subtraction (operational) and a reflection (operational) and a flexible change between these.

    In this study 356 school year 9 students in six Swedish schools, with an over average percentage of immigrants, took a test. Several test problems were formulated so that they were likely to not cause too much of language obstacles for second language learners. In this report the test problem “Calculate 12 – 23 + 9” is in focus. This problem was characterized in Duval’s (2006) semiotic registers as mainly “computations” and scarcely dependent on natural language. One result is that about half of the solutions contained sign errors. There were few arithmetic errors and few other unclassified errors. A second result is that the students who immigrated during school years 1 – 7 clearly underperformed compared to the other students while those who immigrated during school years 8 – 9 performed slightly better than the native students. In this on-going research project one conclusion is that there seems to be a need to see early and late immigrants as having different challenges in being second language learners. The former have difficulties in following some advanced topics in mathematics teaching and the latter have difficulties in understanding some test questions. A second conclusion is that there is a need in research to look at specific topics in mathematics, especially advanced compulsory school mathematics such as negative numbers and algebra, for these student categories.

  • 11.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Matematik: matematik för nyanlända2018Book (Other (popular science, discussion, etc.))
  • 12.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Matematik: matematik för nyanlända: Lärarguide2018Book (Other (popular science, discussion, etc.))
  • 13.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Mathematics achievement of early and newly immigrated students in different topics of mathematics2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis aims to explore the mathematics achievement of second language immigrants in compulsory school as they continue their schooling in Sweden. Specifically, the thesis aims to generate more knowledge about different sub-categories of second language students, namely newly arrived immigrants, early arrived immigrants and other second language students in compulsory school. The data in this thesis consists of students’ responses to test items and thus mainly contains mathematical symbols, essentially numbers in different representations, written by the students.

    Doing so, this thesis problematizes the concept of second language students in mathematics in two aspects. One aspect is to assess the first and second language students’ achievement in different mathematical content domains, instead of only assessing the total achievement. Another aspect is to see the second language students as different sub-categories of second language students.

    Papers I and II of this thesis found that the achievement difference between first and second language students is not homogeneous. Instead the achievement difference between first and second language students is larger for concepts that are rare in mathematics textbooks. Moreover, the achievement difference between first and second language students varies with the content domain. Another way to say this is that first and second language students have different achievement profiles.

    Papers III and IV of this thesis explored how sub-categories of second language students achieved on mathematics test items. Mathematics achievement studies on second language students often classify the second language students into a single category of students. Methodologically this imposes a concept of viewing second language students as homogeneous in proficiency in the language of instruction. This view is challenged in this thesis by dividing the second language students into newly arrived immigrants, early arrived immigrants and other second language students. These three sub-categories have different proficiency in Swedish language due to how long they have lived in Sweden. Papers III and IV found that these student categories both had different test achievement and, related to this, also used mathematical concept representations differently. In particular, the newly and early arrived immigrants seemed to experience on average different challenges during mathematics testing. The newly arrived students seemed more challenged with terminology but less with the mathematical content while the opposite seemed to hold for the early arrived students. An implication for teaching is that particularly early arrived second language children seem to be in urgent need of support in mathematical concept building from first day of schooling in the new country.

  • 14.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Newly and early arrived second language students’ achievement in data and chanceManuscript (preprint) (Other academic)
    Abstract [en]

    This study focuses second language students’ statistical literacy. Specifically it distinguishes between newly and early arrived second language students. This was done by exploring 259 Swedish grade 9 students’ responses to test items. The main result was that despite the newly arrived students’ lower proficiency in Swedish, they had larger proportions than early arrived students of responses with high mathematical quality while the newly arrived students had lower proportions than early arrived students of mathematically not appropriate responses. The newly arrived students on average were more familiar with the mathematical concepts but less familiar with the terminology, while the opposite holds for the early arrived. The results suggest that future research should pay attention to the alternative of seeing newly and early arrived second language students as meeting different challenges in their encounter with mathematical concepts and terminology respectively.

  • 15.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Newly- and early-immigrated second-language students’ knowledge of arithmetic syntax2018In: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 23, no 3-4, p. 105-122Article in journal (Refereed)
    Abstract [en]

    The present study investigated how 259 Swedish, grade 9 students, of whom 90 had an immigrant background, achieved on twelve written test items in the content area of number. Four of the twelve test items required good knowledge of arithmetic syntax, such as when it was appropriate to apply order-of-operation rules and the associative and distributive laws of arithmetic operations. On these four test items, the most-recently arrived students showed on average significantly more knowledge than the students who had immigrated when they were younger and had participated in Swedish schools for longer periods of time. The outcome suggests that these two groups of immigrant students in later school years should be considered as separate sub-categories of second-language students when it comes to teaching, assessment and research.

  • 16.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Rare mathematics – a needle eye for mathematics teachers of second language learners2012In: Proceedings of Norma 11: the 6th Nordic conference on mathematics education / [ed] G. H. Gunnarsdóttir, F. Greinsdóttir, G. Pálsdóttir, M. Hannula, M. Hannula-Sormunnen, E. Jablonka, U. T. Jankvist, A. Ryve, P. Valero, K. Waege, Reykjavik: University of Iceland Press, 2012, p. 483-492Conference paper (Refereed)
    Abstract [en]

    This paper compares performance in a Swedish national test in mathematics of second language learners and students without another mother tongue than Swedish. The result is that some test problems had statistically significant and large differences between the student groups. Using discourse as an analytical tool, the suggested explanation is that second language learners for different reasons have less frequent access to the teaching of mathematical concepts or activity fields that occur rarely in the mathematics teaching and textbooks.

  • 17.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Recent and early immigrants’ achievements in mathematics2015In: Nordic Conference on Subject Education: Book of Abstracts, University of Helsinki, 2015, p. 111-111Conference paper (Refereed)
    Abstract [en]

    Achievement in mathematics, science and language is often used as national indicators and a personal bridge for future opportunities to work and education. One Swedish school law defines a ‘recent immigrant’ as the first four semesters during school years 6-9 of immigrated students. In an ongoing research project, the distribution of students’ different solving strategies in a multilingual classroom is studied through a test. Preliminary results are that students who immigrated in school years 8-9 in many cases show higher mathematical quality than those who immigrated during school years 1-7. This can be interpreted as a partial exclusion from taking a productive part in the mathematics classroom due to being second language learner. This raises questions of extending the definition of recent immigrants to all newly immigrated students disregarding their age and thus allow all newcomers extra support needed to include them in the mathematics classroom.

  • 18.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Second language students’ achievement in linear expressions and time since immigration2018In: Nordic Research in Mathematics Education / [ed] Eva Norén, Hanna Palmér, Audrey Cooke, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018, p. 179-187Chapter in book (Refereed)
    Abstract [en]

    The present study investigated how 259 grade 9 students solved two test items in algebra involving linear expressions. Some students were early or newly immigrated second language students in Sweden, The findings are based on a categorization of the students’ written responses. The results show that for the more advanced test item on linear expressions and unknowns, early arrived second language students achieved worse than newly arrived and other second language students with statistical significance, while there was a minor achievement difference when solving an elementary linear equation. The interpretation of the results is that the early arrived immigrants suffer from having larger parts of their mathematics education as second language students and thus struggle with advanced mathematics.

  • 19.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Second language students’ mathematics education history and their knowledge in linear expressions2017Conference paper (Refereed)
    Abstract [en]

    The present study investigated how 259 grade 9 students solved two test items in algebra involving linear expressions. Some students were early and newly immigrated second language students in Sweden, The findings are based on a categorization of the students’ written responses. The results show that for the more advanced test item on linear expressions and unknowns, early arrived second language students achieved worse than newly arrived and other second language students with statistical significance, while there was a minor achievement difference when solving an elementary linear equation. This study suggests further research viewing newly and early arrived immigrants as possibly separate sub-categories of second language students and acknowledging especially newly arrived students’ mathematics educational history.

  • 20.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Students determining the median for different data sets: A spectrum of responses2017In: ICT in mathematics education: the future and the realities: Proceedings of MADIF 10 / [ed] J. Häggström, E. Norén, J. van Bommel, J. Sayers, O. Helenius, Y. Liljekvist, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2017, p. 145-145Conference paper (Refereed)
    Abstract [en]

    The present study reports on 359 students’ responses to two test items on the median. Among the responses were other measures of location such as the arithmetic mean and the midrange. Moreover, among those who used a median strategy there was a spectrum of sources of confusion in the data set. In one test item the data were given in a table of signed integers and some students ignored the negative signs in the data. In the other test item the data were given in a bivariate diagram. Instead of correctly using the horizontal coordinate of the data, several students used the axis grading or the vertical coordinates as data. A conclusion is that the representation format of the data had a large effect on the achievement on the two test items.

  • 21.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Tintin och matematiken2017In: Tintinism: Årsbok 2017, Solna: Asterion media , 2017, p. 65-70Chapter in book (Other (popular science, discussion, etc.))
    Abstract [sv]

    Kan man skämta om ämnet matematik på ett seriöst sätt? Kan man väva in seriös matematik i en tecknad serie? Faktum är att matematik i olika former förekommer i de flesta Tintinalbum. Det utgör ett utmärkt exempel på genren »edutainment«.

  • 22.
    Petersson, Jöran
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Marschall, Gosia
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Sayers, Judy
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Andrews, Paul
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Swedish year one teachers’ perspectives on homework in children’s learning of number: An ongoing controversy2018In: Perspectives on professional development of mathematics teachers: Proceedings of MADIF 11 / [ed] Johan Häggström, Yvonne Liljekvist, Jonas Bergman Ärlebäck, Maria Fahlgren, Oduor Olande, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018, p. 91-100Conference paper (Refereed)
    Abstract [en]

    This paper draws on semi-structured interviews undertaken with twenty teachers of year one children in Sweden. Interviews focused on teachers’ construal of their own and their pupils’ parents’ roles in supporting year one children’s learning of early number. Data, which were analysed by means of a constant comparison process, yielded homework as a theme that dichotomised teachers between those who set homework for learning number and those who do not. Of those who set homework, the majority construed it as a means of facilitating number-related fluency, particularly for children in danger of falling behind their peers. Of those who do not, the majority argued that differences in family backgrounds would compromise societal principles of equality of opportunity.

  • 23.
    Petersson, Jöran
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Norén, Eva
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    To halve a fraction: An issue for second language learners2017In: Education Inquiry, ISSN 2000-4508, E-ISSN 2000-4508, Vol. 8, no 3, p. 173-191Article in journal (Refereed)
    Abstract [en]

    The present study investigated test responses from 259 immigrant and non-immigrant school year 9 students in Sweden with the focus on how they solved two problems on fractions, one of them halving a fraction, in a test. The authors report three observations. Newly arrived second language immigrants seemed less likely to have the word ‘half’ in their Swedish mathematical vocabulary. Moreover, second language learners with longer experience of the new language connected the word ‘half’ with a division by two, but showed mathematical difficulties in correctly applying it to a fraction. A third finding was that the longer the experiences with Swedish school mathematics, the more likely both first and second language learners were to erroneously omit the percentage symbol, when choosing to use percentage representation of the fraction given in the test problem. The authors suggest seeing newly and early arrived second language immigrants as meeting different challenges. The newly arrived second language immigrants may know some mathematical concepts better and Swedish language less. In contrast the opposite seems to hold for second language learners with longer experience of the language of instruction.

  • 24.
    Petersson, Jöran
    et al.
    Malmö University, Faculty of Education and Society (LS), Department of School Development and Leadership (SOL).
    Sayers, Judy
    Andrews, Paul
    Time series analysis: Moving averages as an approach to analysing textbooks2020In: Eleventh Congress of the European Society for Research in Mathematics Education / [ed] Jankvist, U. T., Van den Heuvel-Panhuizen, M., & Veldhuis, M., 2020Conference paper (Refereed)
    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.

  • 25.
    Petersson, Jöran
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Sayers, Judy
    Rosenqvist, Eva
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Andrews, Paul
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Opportunities for year-one children to acquire foundational number sense: comparing English and Swedish adaptations of the same Singapore textbook2019In: Proceedings of the Seventh Conference on Research in Mathematics Education in Ireland (MEI 7) / [ed] Lorraine Harbison, Aisling Twohill, Dublin: Institute of Education, Dublin City University , 2019, p. 251-258Conference paper (Refereed)
    Abstract [en]

    In this paper we compare adaptations of a Singaporean year-one mathematics textbook for use in England and Sweden respectively. The texts were analysed in two different ways against the eight dimensions of Foundational Number Sense (FoNS), a set of core competences that the literature has shown to be necessary for year-one children’s later mathematical learning. The first analysis, based on frequencies, showed that neither adaptation incorporated any opportunities for children to acquire the two FoNS competence relating to estimation and number patterns respectively. They also showed that the English adaptation comprised significantly more tasks than the Swedish, particularly with respect to systematic counting, where the former comprises 26% more tasks than the latter. The second analysis, based on moving averages, showed that across five of the six FoNS categories for which there were data, the temporal location and emphases of FoNS-related learning were comparable, with, in particular, no such opportunities after the mid-point of the school year in either book. However, the English adaptation’s presentation of systematic counting, occurring at various points throughout the school year, was substantially different from the Swedish adaptation, highlighting differences due, we speculate, to interpretations of local didactical traditions.

  • 26.
    Sayers, Judy
    et al.
    University of Leeds, UK.
    Marschall, Gosia
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Andrews, Paul
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    English and Swedish teachers’ perspectives on the role of parents in year one children’s learning of number: manifestations of culturally-conditioned norms2019In: Early Child Development and Care, ISSN 0300-4430, E-ISSN 1476-8275Article in journal (Refereed)
    Abstract [en]

    This paper presents an exploratory study of English and Swedish teachers' perspectives on the role of parents in year one children's learning of number. Drawing on the results of semi-structured interviews, data from each cohort were analysed independently to ensure the cultural integrity of any response categories and the results of this process compared. Two broad themes were identified concerning implicit and explicit forms of parental involvement. The former, manifested similarly across the two cohorts, concerned the importance of parents presenting children with positive attitudes towards mathematics. The latter, incorporating three comparable subthemes, focused on the creation of number-rich home environments, home–school communication and parents' role in the completion of homework. All three subthemes differentiated the cohorts in ways that highlighted teachers' culturally situated perspective on teaching and learning. Some implications are discussed, particularly with respect to the challenge this study poses for developers of cross-cultural survey instruments.

  • 27.
    Sayers, Judy
    et al.
    Leeds University, UK.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Malmö University, Sweden.
    Rosenqvist, Eva
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Andrews, Paul
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Opportunities to learn foundational number sense in three Swedish year one textbooks: implications for the importation of overseas-authored materials2019In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed)
    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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