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  • 1.
    Andrews, Paul
    University of Cambridge, UK.
    Comparative studies of mathematics teachers’ observable learning objectives: validating low inference codes2009Inngår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 71, nr 2, s. 97-122Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular.

  • 2.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    European mathematics curricula and classroom practices2014Inngår i: Masterclass in mathematics education: international perspectives on teaching and learning / [ed] Paul Andrews, Tim Rowland, London: Bloomsbury Academic, 2014, s. 179-190Kapittel i bok, del av antologi (Fagfellevurdert)
  • 3.
    Andrews, Paul
    University of Cambridge, UK.
    Finnish mathematics teaching: a case of uniquely implicit didactics2011Inngår i: Fourth Conference on Research in Mathematics Education: Mathematics Teaching Matters / [ed] Thérèse Dooley, Dolores Corcoran, Miriam Ryan, Drumcondra, Ireland: St. Patrick’s College , 2011, s. 3-18Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper reports on a qualitative analysis of video-taped mathematics lessons taught by four case study teachers, defined locally as effective, in a provincial university city in Finland. The aim was to examine how teachers conceptualise and present mathematics to their learners and, in so doing, understand the relationship between Finnish mathematics teaching practices, as reflected in case study lessons, and Finnish success on successive PISA assessments. Analysed by means of the process of constant comparison, the data yielded two key characteristics of case study classrooms. Firstly, irrespective of their intended learning outcome, teachers exploited a series of implicit didactic strategies focused on encouraging students to infer meaning. Secondly, three culturally located activities were identified that appeared complementary to this sense of the implicit. These were the systemic encouragement of students to make notes, teachers’ exploitation of the confident child and the assumed collaboration of parents.

  • 4.
    Andrews, Paul
    University of Cambridge, UK.
    Finnish mathematics teaching from a reform perspective: A video-based case study analysis2013Inngår i: Comparative Education Review, ISSN 0010-4086, E-ISSN 1545-701X, Vol. 57, nr 2, s. 189-211Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article offers a qualitative analysis of videotaped mathematics lessons taught by fourteachers in a provincial university city in Finland. My study is framed not only by Finnishsuccess on Programme for International Student Assessment (PISA) but also by theobjectives of current mathematics education reform, which are consistent with PISA’sgoals of measuring mathematical literacy. The analyses indicated that conceptual understandingand procedural fluency were addressed by all four teachers. However, adaptivereasoning, strategic competence, and the development of a productive dispositionappear rarely. I observed few occasions where students were invited to solve authenticproblems.

  • 5.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Flemish mathematics teaching: Bourbaki meets RME?2014Inngår i: Proceedings of the 8th British Congress of Mathematics Education 2014 / [ed] Sue Pope, 2014, s. 9-16Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The Programme of International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS) create much international interest in those countries perceived as high achieving. One such system, rarely acknowledged, is Flanders, the Dutch-speaking region of Belgium. In this paper I present the results of focused analyses of four sequences of video-taped mathematics lessons taught to students aged 10 to 14 years. These confirmed a mathematics education tradition drawing on two well-known curricular movements. The first presents mathematics as a Bourbakian set of interconnected concepts. The second exploits realistic problems in its presentation of mathematics.

  • 6.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Is the ‘telling case’ a methodological myth?2016Inngår i: International Journal of Social Research Methodology, ISSN 1364-5579, E-ISSN 1464-5300, Vol. 20, nr 5, s. 455-467Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper discusses the ‘telling case’ (Mitchell, 1984) and the manner and extent of its use in social research. The ‘telling case’, proposed by Mitchell as a counter to prevailing expectations of typicality, is an ethnographic case study, derived from analytic induction and focused on the exposure of new theoretical insights. By means of an evaluation of the available literature this paper summarises Mitchell’s construal of the ‘telling case’ before examining how it has been exploited by others. The evidence suggests that while authors acknowledge the source of the ‘telling case’ few offer any substantial acknowledgement of Mitchell’s conceptualisation, indicating that most ‘telling case’ research has employed Mitchell’s name somewhat disingenuously and contributed to the growth of a methodological myth. Moreover, despite its international spread, its origins seem located in the work of a small number of internationally recognised scholars and the mobility of their former graduate students.

  • 7.
    Andrews, Paul
    University of Cambridge, UK.
    Learning from others: Can PISA and TIMSS really inform curriculum development in mathematics?2012Inngår i: Mathematical Gazette, ISSN 0025-5572, Vol. 96, nr 537, s. 386-407Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    One of the problems that will vex any President of the Mathematical Association is the topic of the address with which he or she closes his or her year of office. This occupied me, on and off, for more than a year. In my case, in addition to my desire to acknowledge the honour of the invitation made to me, I was deeply conscious of the fact that I would be the 100th individual to serve as President. I dabbled with some pet themes, typically concerning the lack of genuine problem-solving or proof in English school mathematics, before concluding that the most sensible thing would be to talk on the topic about which I know most. My research interests are in comparative mathematics education. I have been fortunate, over the last twenty years or so, to have been able to visit and videotape mathematics classrooms in several European countries. In so doing I have had my understanding of mathematics teaching transformed in ways that led, almost inevitably, to the theme of both this talk and the conference which brought my Presidency to an end: Learning from Others.

  • 8.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Mathematics, PISA, and culture: An unpredictable relationship2015Inngår i: Journal of educational change, ISSN 1389-2843, E-ISSN 1573-1812, Vol. 16, nr 3, s. 251-280Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Recent studies have indicated, particularly in the European context, that students’ mathematical successes on international tests of student achievement may not be attributable to the quality of classroom instruction, although, as is shown, this is unlikely to be the case in Flanders, the autonomous Dutch-speaking region of Belgium. Flemish students’ mathematics performance on such tests have placed them at the head of the European rankings, warranting Flanders as a site of research interest that has been largely ignored by the international community. In this paper, drawing on analyses of four sequences of five lessons, taught by teachers construed locally as competent, I explore the nature of Flemish mathematics teaching. Framed by anecdotal reports that it reflects the structuralism of the now largely abandoned Bourbakian new mathematics movement humanised by the Dutch tradition of realistic mathematics education, the analyses focus on examining not only the extent to which these traditions are manifested in Flemish classrooms but the ways in which they interact. The dominant tradition seems to be that of mathematical structuralism mediated by teachers’ use of realistic problems; a tradition not unlikely to underpin Flemish students’ repeated successes. The results are discussed in relation to research highlighting the significance on students’ achievement of the broader cultural milieu in which they and their teachers operate.

  • 9.
    Andrews, Paul
    University of Cambridge, UK.
    Mathematics teacher typologies or nationally located patterns of behaviour?2007Inngår i: International Journal of Educational Research, ISSN 0883-0355, E-ISSN 1873-538X, Vol. 46, nr 5, s. 306-318Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper reports on a small-scale EU-funded study of the teaching of mathematics in the age range 10–14 in Flanders, England, Hungary, and Spain. Drawing on video recordings of sequences of lessons taught on standard topics, and exploiting a coding schedule developed from live observations in each country, the inferable learning objectives of, and the didactic strategies teachers employ during, each of a lesson's episodes are examined. Two analyses were undertaken. The first, despite some common ground, indicated that teachers in each country behave in ways similar to teachers from the same country that distinguishes them from teachers elsewhere. The second identified typologies of teacher behaviour that were international in their teacher composition and challenged the robustness of the national script.

  • 10.
    Andrews, Paul
    University of Cambridge, UK.
    Mathematics Teachers’ Didactic Strategies: Examining the Comparative Potential of Low Inference Generic Descriptors2009Inngår i: Comparative Education Review, ISSN 0010-4086, E-ISSN 1545-701X, Vol. 53, nr 4, s. 559-581Artikkel i tidsskrift (Fagfellevurdert)
  • 11.
    Andrews, Paul
    University of Cambridge, UK.
    Negotiating meaning in cross-national studies of mathematics teaching: kissing frogs to find princes2007Inngår i: Comparative Education, ISSN 0305-0068, E-ISSN 1360-0486, Vol. 43, nr 4, s. 489-509Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper outlines the iterative processes by which a multinational team of researchers developed a low‐inference framework for the analysis of video recordings of mathematics lessons drawn from Flemish Belgium, England, Finland, Hungary and Spain. Located within a theoretical framework concerning learning as the negotiation of meaning, we discuss problems of linguistic and conceptual equivalence and the manner by which they were resolved. Significantly, when compared with the time‐stamped codes of projects like the TIMSS video studies, we argue that the unit of analysis adopted, the episode, allowed for the distinctive patterns of a lesson to be retained for comparison with others. Also, we suggest that the framework’s generic, though subject‐focused, codes are amenable to adaptation to other curriculum areas, thus providing an opportunity for the comparative study of subjects not normally associated with work of this nature.

  • 12.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Practice to inspire: Mathematics teaching in one Hungarian grade one classroom2014Inngår i: "Do you think it's all the same?": Proceedings of the Julianna Szendrei Memorial Conference / [ed] Judit Szitanyi, 2014, s. 63-78Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    In this paper I introduce and categorise the concept of foundational number sense (FONS). Broadly described as the number related competences expected of grade one children, which research has shown to be necessary for the later study of mathematics, FONS is operationalised as an eight dimensional framework for analysing the number-related opportunities teachers present to their students. Drawing on data from a case study of exemplary teaching in grade one classrooms, I analyse one teacher’s, Klara’s, practice against the framework to show not only that she provides some profound opportunities for her students to learn but does so in ways that reflect the long-standing Hungarian tradition of mathematics as a problem solving discipline taught in collaborative and socially dynamic ways.

  • 13.
    Andrews, Paul
    University of Cambridge, UK.
    The Cultural Location of Teachers’ Mathematical Knowledge: Another Hidden Variable in Mathematics Education Research?2011Inngår i: Mathematical knowledge in teaching / [ed] Tim Rowland, Kenneth Ruthven, Springer Netherlands, 2011, 1, s. 99-118Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This chapter draws on an analysis of two sequences of five videotaped lessons taught by two case study teachers, one Flemish and one Hungarian, both of whom were defined locally as effective. The lesson sequences, both on linear equations, show how teachers’ didactic decision making is informed by three different curricula: an intended curriculum, an idealised curriculum and a received curriculum. An intended curriculum, as defined by the second international mathematics study (SIMS), draws on systemic expectations with regard to mathematics teaching and learning. The idealised curriculum reflects individual teachers’ personal but articulable beliefs about and goals for mathematics, its teaching and learning. The received curriculum reflects those beliefs and goals consequential of hidden and inarticulable cultural influences. The data indicate that where the three curricula converge, students are more likely to experience coherent learning experiences in relation to systemic goals than when they diverge.

  • 14.
    Andrews, Paul
    University of Cambridge, UK.
    The curricular importance of mathematics: a comparison of English and Hungarian teachers' espoused beliefs2007Inngår i: Journal of Curriculum Studies, ISSN 0022-0272, E-ISSN 1366-5839, Vol. 39, nr 3, s. 317-338Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper reports an interview study of 45 English and 10 Hungarian teachers of mathematics. The semi‐structured interviews focused on the teachers’ professional life‐histories and invited them to discuss their beliefs about the necessary subject content for the teaching and learning of mathematics. Substantial differences emerged between the two cohorts, which accord with well‐defined national perspectives on education in general and mathematics education in particular. They reflect, at national rather than individual levels, the expectations of the curricular frameworks within which teachers operate. English teachers tended to view mathematics as applicable number and the means by which learners are prepared for a world beyond school. Hungarian teachers privileged mathematics as problem‐solving and logical thinking.

  • 15.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    The Emperor’s new clothes: PISA, TIMSS and Finnish mathematics2014Inngår i: Spaces for learning: past, present and future: Proceedings of the FMSERA 30th annual symposium in Vaasa, November 6-8, 2013 / [ed] Ann-Sofi Röj-Lindberg, Lars Burman, Berit Kurtén-Finnäs, Karin Linnanmäki, Åbo Akademi University , 2014, s. 43-65Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    For nearly fifteen years, due to repeated successes on the Programme of International Student Assessment (PISA), Finnish education in general and mathematics education in particular have been construed internationally as benchmarks. In what is essentially a review paper I consider how the Finns explain their students’ repeated PISA successes before contrasting these explanations with observational evidence indicating that typical classroom practice is unlikely to account for such successes. In addition, I examine the relative failure of Finnish students on the Trends in International Mathematics and Science Study (TIMSS), particularly with respect to algebra and geometry, and highlight the extent to which Finnish students may be inadequately prepared for higher study of mathematics. I close by indicating that continued interest in Finland as a source of excellence in mathematics teaching may be misguided and that other European systems, like Flanders, may provide better warranted research locations for those interested in transferable insights.

  • 16.
    Andrews, Paul
    University of Cambridge, UK.
    The importance of acknowledging the cultural dimension in mathematics teaching and learning research2010Inngår i: Acta Didactica Napocensia, ISSN 2065-1430, Vol. 3, nr 2, s. 3-16Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, which is in four parts, I make a plea to those involved in research into mathematics teaching and learning of the need to acknowledge, however their work is framed, that it will be located in a culture, not always visible to a reader, that should be made explicit. In the first part I examine three key models of culture and their significance for education. In the second I further highlight the impact of culture on what children are expected by critiquing various models of curriculum. The third part examines how culture informs the particularities of four European mathematics curricula, while the fourth part explores culturally located differences in mathematics teaching. In so doing a plea to researchers is framed: Culture permeates all aspects of educational endeavour and should be acknowledged more explicitly than it is.

  • 17.
    Andrews, Paul
    University of Cambridge, UK.
    The teaching of linear equations: Comparing effective teachers from three high achieving European countries2011Inngår i: Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education / [ed] Marta Pytlak, Tim Rowland, Ewa Swoboda, Rzeszów: University of Rzeszów , 2011, , s. 1555-1564s. 1555-1564Konferansepaper (Fagfellevurdert)
    Abstract [en]

    On various international tests of achievement Finnish, Flemish and Hungarian students have been amongst the more successful in Europe. Linear equations, a topic students traditionally find difficult, is a key topic in the transition from mathematics as inductive and concrete to deductive and abstract. This paper, by means of an analysis of video-taped lessons taught by case study teachers, one from each of Finland, Flanders and Hungary, examines comparatively how teachers defined locally as effective construct opportunities for their students to learn the mathematics of linear equations. The findings show that all three teachers acted in ways contrary to received research wisdom, exploiting the balance scale as the key metaphor for inducting students into the solution processes of algebraic equations.

  • 18.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Understanding the Cultural Construction of School Mathematics2016Inngår i: Mathematical Cultures: The London Meetings 2012-2014 / [ed] Brendan Larvor, Springer, 2016, s. 9-23Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    In this chapter, I show how culture underpins all aspects of school mathematics, whether it be the curriculum specified by the system, the development of the textbooks that teachers may or may not be compelled to use, the ways teachers teach, the classroom interactions privileged by the system or the beliefs, attitudes and aspirations of teachers, students and parents. To do this, however, I will describe the nature of culture and its educational manifestation.

  • 19.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    What does PISA performance tell us about mathematics teaching quality? Case studies from Finland and Flanders2013Inngår i: Pisa, power and policy: the emergence of global educational governance / [ed] Heinz-Dieter Meyer, Aaron Benavot, Oxford: Symposium Books, 2013, s. 99-114Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Over the last decade Finnish students’ performance on the mathematical literacy components of PISA has created much international interest. However, with respect to the two times Finland has participated in the Trends in International Mathematics and Science Study (TIMSS), Finnish students’ mathematical performance has painted a very different picture, particularly at grade 8. What is less well known is that Flanders, whose Programme for International Student Assessment (PISA) achievements have been masked by those of Belgium as a whole, has performed as well as Finland with respect to mathematical literacy and, on the three TIMSS in which it has participated, it has been the most successful European system at grade 8. Thus, while Finnish performance on tests of technical competence, despite success on tests of mathematical applicability, has been moderate, Flemish students have led the Europeans on both. In this chapter, the author examines two sequences of videotaped lessons taught on percentages, a topic resonant with ambitions of both technical competence and mathematical applicability, by case-study teachers considered against local criteria to be effective. The evidence suggests that Finnish mathematics didactics are more likely to explain Finnish TIMSS failure than PISA success. Flemish didactics may have greater explanatory potential for both PISA and TIMSS success. Such findings suggest that performance on international tests of achievement may be unrelated to didactical quality as other, typically hidden, cultural factors intercede.

  • 20.
    Andrews, Paul
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Diego Mantecón, Jose
    Instrument adaptation in cross-cultural studies of students' mathematics-related beliefs: Learning from healthcare research2015Inngår i: Compare, ISSN 0305-7925, E-ISSN 1469-3623, Vol. 45, nr 4, s. 545-567Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Much comparative research into education-related beliefs has exploitedquestionnaires developed in one culture for use in another. This hasbeen particularly the case in mathematics education, the focus of thispaper. In so doing, researchers have tended to assume that translationalone is sufficient to warrant a reliable and valid instrument forcross-cultural research, prompting concerns that a number of necessaryequivalences are unlikely to have been addressed. In this paper, we considerthe nature of these equivalences before examining the literature ofa different field, healthcare research, to synthesise an approach to instrumentadaptation that is pragmatic but rigorous. Finally, we demonstratehow this pragmatic approach, incorporating extensive cognitive interviews,enabled us to adapt and refine a mathematics-related beliefsquestionnaire, developed in Flanders, for use with students aged 14–15in England and Spain. Analyses indicate that the instrument so developedis multidimensional, reliable and cross-culturally valid. Someimplications are discussed.

  • 21.
    Andrews, Paul
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Rowland, Tim
    Masterclass in mathematics education: international perspectives on teaching and learning2014Collection/Antologi (Fagfellevurdert)
  • 22.
    Andrews, Paul
    et al.
    Mälardalen University, Sweden.
    Ryve, Andreas
    Mälardalen University, Sweden.
    Hemmi, Kirsti
    Mälardalen University, Sweden.
    Sayers, Judy
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    PISA, TIMSS and Finnish mathematics teaching: an enigma in search of an explanation2014Inngår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 87, nr 1, s. 7-26Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Finnish students’ success on all three content domains of each of the four cycles ofthe OECD’s Programme for International Student Assessment (PISA) has created muchinternational interest. It has also prompted Finnish academics to offer systemic explanationstypically linked to the structural qualities of Finnish schooling and teacher education. Lesswell-known has been the modest mathematics performance of Finnish grade 8 students on thetwo Trends in International Mathematics and Science Study (TIMSS) in which Finland hasparticipated, which, when compared with its PISA successes, has created something of anenigma. In this paper, we attempt to shed light on this enigma through analyses of Finnishmathematics classroom practice that draw on two extant data sets—interviews with Finnishteacher educators and video-recordings of sequences of lessons taught on standard topics. Dueto the international interest in Finnish PISA success, the analyses focus primarily on theresonance between classroom practice and the mathematical literacy component of the PISAassessment framework. The analyses indicate that Finnish mathematics didactics are morelikely to explain the modest TIMSS achievements than PISA successes and allude to severalfactors thought to be unique to the Finns, which, unrelated to mathematics teaching practices,may be contributory to the repeated Finnish PISA successes. Some implications for policyborrowingare discussed.

  • 23.
    Andrews, Paul
    et al.
    University of Cambridge, UK.
    Sayers, Judy
    University of Northampton, UK.
    Comparative studies of mathematics teaching: does the means of analysis determine the outcome?2013Inngår i: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 45, nr 1, s. 133-144Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper addresses four questions concerning the influence of culture on mathematics teachers’ professional practice. Firstly, drawing on categorical data yielded by the application of low inference coding schedule to video recordings of sequences of lessons taught by case study teachers on four common topics in England, Flanders, Hungary and Spain, we undertook an exploratory factor analysis to examine the ways in which such coded variables interact. This process yielded five factors, each of which was interpretable against the literature and highlighted the extent to which dichotomisations of mathematics teaching as reform or traditional are not necessarily helpful, not least because all project teachers exhibited characteristics of both. Secondly, factors scores were analysed by nationality to reveal culturally located practices resonant with the available literature. Thirdly, cluster analyses yielded four well-defined cross-cultural clusters of episodes, each indicative of particular didactical perspectives that appeared to challenge the exclusivity of these culturally located practices. Finally, the key methodological finding was that the manner in which data are analysed influences greatly the outcomes of comparative mathematics research.

  • 24.
    Andrews, Paul
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Sayers, Judy
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Foundational number sense: A framework for analysing early number-related teaching2014Inngår i: Proceedings of MADIF 9, The Ninth mathematics Education Research Seminar, 2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, by means of an extensive review of the literature, we discuss the development of a framework for analysing the opportunities, both implicit and explicit, that grade one students receive for acquiring those number-related understandings necessary for later mathematical achievement but which do not occur without formal instruction. The framework, which we have called foundational number sense, currently comprises seven interrelated components, although additional components may exist. Each component, as warranted by earlier research, is known to underpin later mathematical understanding and, when viewed collectively, addresses a definitional gap in the literature.

  • 25.
    Andrews, Paul
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Sayers, Judy
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Identifying opportunities for grade one children to acquire foundational number sense: Developing a framework for cross cultural classroom analyses2015Inngår i: Early Childhood Education Journal, ISSN 1082-3301, E-ISSN 1573-1707, Vol. 43, nr 4, s. 257-267Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is known that an appropriately developedfoundational number sense (FONS), or the ability tooperate flexibly with number and quantity, is a powerfulpredictor of young children’s later mathematical achievement.However, until now not only has FONS been definitionallyelusive but instruments for identifyingopportunities for children to acquire its various componentshave been missing from the classroom observationtools available. In this paper, drawing on a constant comparisonanalysis of appropriate literature, we outline thedevelopment of an eight dimensional FONS framework.We then show, by applying this framework to three culturallydiverse European grade one lessons, one English,one Hungarian and one Swedish, that it is both straightforwardlyoperationalised and amenable to cross culturalanalyses of classroom practice. Some implications arediscussed.

  • 26.
    Andrews, Paul
    et al.
    University of Cambridge, UK.
    Sayers, Judy
    The University of Northampton, UK.
    Teaching linear equations: Case studies from Finland, Flanders and Hungary2012Inngår i: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 31, nr 4, s. 476-488Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we compare how three teachers, one from each of Finland, Flanders and Hungary, introduce linear equations to grade 8 students. Five successive lessons were videotaped and analysed qualitatively to determine how teachers, each of whom was defined against local criteria as effective, addressed various literature-derived equations-related problems. The analyses showed all four sequences passing through four phases that we have called definition, activation, exposition and consolidation. However, within each phase were similarities and differences. For example, all three constructed their exposition around algebraic equations and, in so doing, addressed concerns relating to students’ procedural perspectives on the equals sign. All three teachers invoked the balance as an embodiment for teaching solution strategies to algebraic equations, confident that the failure of intuitive strategies necessitated a didactical intervention. Major differences lay in the extent to which the balance was sustained and teachers’ variable use of realistic word problems.

  • 27.
    Andrews, Paul
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Sayers, Judy
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Marschall, Gosia
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Developing foundational number sense: Number line examples from Poland and Russia2015Inngår i: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer, Nad'a Vondrová, 2015, s. 1681-1687Konferansepaper (Fagfellevurdert)
    Abstract [en]

    For a variety of reasons children start school with differing number-related skills, leading to differences in later mathematics achievement. Such differences prompt the question, what number-related experiences are necessary if the first year of school is to prepare children appropriately for their learning of mathematics? In this paper we discuss the development of an eight dimensional framework, foundational number sense (FoNS), that characterises those learning experiences. We then demonstrate the framework's analytical efficacy by evaluating episodes from two sequences of lessons, one Polish and one Russian, focused on the use of the number line. The results show that the FoNS framework is cross-culturally sensitive, simply operationalised and analytically powerful.

  • 28.
    Andrews, Paul
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Xenofontos, Constantinos
    Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers2015Inngår i: Journal of Mathematics Teacher Education, ISSN 1386-4416, E-ISSN 1573-1820, Vol. 18, nr 4, s. 299-325Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this article, we analyse the problem-solving-related beliefs, competence and classroom practice of three Cypriot upper-primary teachers. Data derived from semi-structured interviews focused on teachers’ beliefs about the nature of mathematical problems, problem-solving, and their competence as both problem-solvers and teachers of problem-solving; clinical interviews during which teachers solved a context-free geometrical problem, and observations of a lesson during which teachers introduced that problem to students of grade six. Analyses, structured by a framework derived from key problem-solving literature, indicated firstly, that the framework was an effective tool, sensitive to variation within and across the data from teachers, and secondly, that all participants, in largely explicable ways, exhibited consistency and inconsistency in the ways in which their beliefs, competence and practice interacted. Some implications for further research are discussed.

  • 29.
    Back, Jenni
    et al.
    University of Cambridge, UK.
    Sayers, Judy
    University of Northampton, UK.
    Andrews, Paul
    National Centre for Excellence in the Teaching of Mathematics, UK.
    The development of foundational number sense in England and Hungary: A case study comparison2013Inngår i: Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education / [ed] Behiye Ubuz, Çiğdem Haser, Maria Alessandra Mariotti, 2013, s. 1835-1844Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Foundational number sense - being able to operate flexibly with number and quantity - is a predictor of later mathematical achievement. In this paper, drawing on lessons on number sequences to grade 1 children, we examine how two teachers, one English and one Hungarian, construed locally as effective, created opportunities for children to develop foundational number sense. The Hungarian teacher, in ways typical of that country’s mathematics teaching tradition, offered frequent and coherent opportunities for students to develop foundational number sense. The English teacher, working in a tradition whereby interactive technology increasingly mediates classroom discourse, offered few and less coherent opportunities, masked by the teacher’s frequent attention to display features of the technology.

  • 30.
    Larsson, Kerstin
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Ridderlind, Inger
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Mathematical games can make a difference: An intervention for children at risk2019Inngår i: / [ed] Jarmila Novotná, Hana Moraová, Prague: Charles University , 2019Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Children in public care are at risk not achieving academically to their potential. To support this group, Letterbox Club is an intervention program sending parcels with e.g. mathematical games to the children hoping this would increase their engagement to, and skills in, mathematics. We report of the effects of such an intervention where the LBC members were compared to their peers by pre- and post-test design. The over-all test results demonstrated promising effects, but no significant differences. However, certain tasks, especially subtraction tasks, stood out as LBC members had significant lower scores in the pre-test. There were also tasks where the LBC members improved significantly better than their peers. These promising results call for more studies of the effects of mathematical development by sending mathematical games to children in care.

  • 31.
    Larsson, Kerstin
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Pettersson, Kerstin
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Students’ conceptualisation of multiplication as repeated addition or equal groups in relation to multi-digit and decimal numbersManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Multiplicative understanding is essential for mathematics learning and is supported by models for multiplication, such as equal groups and rectangular area, different calculations and arithmetical properties, such as distributivity. We investigated two students’ multiplicative understanding through their connections between models for multiplication, calculations and arithmetical properties and how their connections changed during the school years when multiplication is extended to multi-digits and decimal numbers. The case studies were conducted by individual interviews over five semesters. The students did not connect calculations to models for multiplication, but showed a robust conceptualisation of multiplication as repeated addition or equal groups. This supported their utilisation of distributivity to multi-digits, but constrained their utilisation of commutativity and for one student to make sense of decimal multiplication.

  • 32.
    Larsson, Kerstin
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Pettersson, Kerstin
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Students' conceptualisations of multiplication as repeated addition or equal groups in relation to multi-digit and decimal numbers2017Inngår i: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 48, s. 1-13Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Multiplicative understanding is essential for mathematics learning and is supported by models for multiplication, such as equal groups and rectangular area, different calculations and arithmetical properties, such as distributivity. We investigated two students' multiplicative understanding through their connections between models for multiplication, calculations and arithmetical properties and how their connections changed during the school years when multiplication is extended to multi-digits and decimal numbers. The case studies were conducted by individual interviews over five semesters. The students did not connect calculations to models for multiplication, but showed a robust conceptualisation of multiplication as repeated addition or equal groups. This supported their utilisation of distributivity to multi-digits, but constrained their utilisation of commutativity and for one student to make sense of decimal multiplication.

  • 33.
    Larsson, Kerstin
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Pettersson, Kerstin
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    The ambiguous role of equal groups in students’ understanding of distributivityManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Distributivity is considered to be essential for multiplicative understanding but difficult to learn. The difficulties may arise as overgeneralisations of addition strategies. Rectangular models emphasise the two-dimensionality of multiplication, separating it from addition and are suggested to support understanding of distributivity better compared to equal groups. Coincidently, studies report of students’ understanding of distributivity based on equal groups, leaving no consensus on equal groups’ suitability for understanding distributivity. In this paper we investigate how students can exploit equal groups to understand distributivity, by analysis of two students’ reasoning when they successfully explain distributivity construing the multiplication as heaps of sticks and bags of coins. The role of equal groups with respect to multiplicative understanding of distributivity is discussed in relation to previous ambiguous findings and to the extension of multiplication beyond integers, in which the equal groups model may be inappropriate.

  • 34. Löwenhielm, Anna
    et al.
    Marschall, Gosia
    Sayers, Judy
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Opportunities to acquire foundational number sense: A quantitative comparison of popular English and Swedish textbooks2017Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper we present analyses of popular grade one textbooks, one from each of England and Sweden. Focused on Foundational Number Sense (FoNS), we examine how each book’s tasks facilitate children’s learning of those number-related competences that require instruction and which underpin later mathematical learning. Analyses identified both similarities and differences. Similarities lay in   books’ extensive opportunities for children to recognise and write numbers and undertake simple arithmetical operations. However, neither offered more than a few tasks related to estimation or simple number patterns. Differences lay in the Swedish book’s greater emphases on different representations of number, quantity discrimination and relating numbers to quantity, highlighting conceptual emphases on number. The English book offers substantially more opportunity for students to count systematically, highlighting procedural emphases.

  • 35.
    Marschall, Gosia
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Polish teachers’ conceptions of and approaches to the teaching of linear equations to grade six students: An exploratory case study2015Inngår i: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178, Vol. 17, nr 3, s. 220-238Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this article we present an exploratory case study of six Polish teachers’perspectives on the teaching of linear equations to grade six students. Data,which derived from semi-structured interviews, were analysed against an extantframework and yielded a number of commonly held beliefs about what teachersaimed to achieve and how they would achieve them. In general, teachers’ aimswere procedural fluency founded on students understanding the equals sign as arelational rather than an operational entity and the balance scale as arepresentation supportive of students’ understanding of an equation as theequivalence of two expressions. The analyses also indicated that the waysteachers proposed to conduct their lessons, whereby they pose single problemsfor individual work before inviting whole class sharing of solutions, resonateswith the didactical traditions found in other East and Central Europeancountries previously influenced by the Soviet Union.

  • 36.
    Pansell, Anna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    The teaching of mathematical problem-solving in Swedish classrooms: a case study of one grade five teachers practice2017Inngår i: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 22, nr 1, s. 65-84Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we examine the teaching of mathematical problem-solving to grade five students of one well-regarded and experienced Swedish teacher, whom we call Mary. Working within a decentralised curriculum in which problem-solving is centrally placed, Mary is offered little systemic support in her professional decision making with respect to problem-solving instruction. Drawing on Lester’s and Schroeder’s descriptions of teaching for, about and through problem-solving, we draw on multiple sources of data, derived from interviews and videotaped lessons, to examine how Mary’s problem-solving-related teaching is constituted in relation to the weaklyframed curriculum and the unregulated textbooks that on which she draws. The analyses indicate that Mary’s emphases are on teaching for and about problem-solving rather than through, although the ambiguities that can be identified throughout her practice with respect to goals, curricular aims and the means of their achievement can also be identified in the curricular documents from which she draws.

  • 37.
    Petersson, Jöran
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Marschall, Gosia
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Sayers, Judy
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Swedish year one teachers’ perspectives on homework in children’s learning of number: An ongoing controversy2018Inngår i: 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, s. 91-100Konferansepaper (Fagfellevurdert)
    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.

  • 38.
    Sayers, Judy
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Foundational Number Sense: Summarising the Development of an Analytical framework2015Inngår i: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer, Nad'a Vondrová, 2015, s. 361-367Konferansepaper (Fagfellevurdert)
    Abstract [en]

    What number-related competences do grade one students need to ensure later success and avoid later failure? We address this question by summarising recent work on the development of an eight component framework, which we call foundational number sense (FoNS), in which those necessary learning outcomes are categorised. We then present summaries of three case study evaluations of the FoNS framework. Each case study, which focused on the teaching of a different mathematical topic, was undertaken in two different European grade one classrooms. Analyses confirm the sensitivity of the FoNS framework to both cultural and mathematical context and indicate its potential as a powerful tool for both cross cultural research and teacher education practices.

  • 39.
    Sayers, Judy
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Foundational number sense: The basis for whole number arithmetic competence2015Inngår i: Conference proceedings of the ICMI Study 23: Primary mathematics study on whole numbers / [ed] Xuhua Sun, Berinderjeet Kaur, Jarmila Novotná, 2015, s. 124-131Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Children begin school with different number-related competences, typically due to variation in geographical location and familial circumstances. This variation, which necessarily creates inequity of opportunity, prompts the question, what number-related experiences are necessary if the first year of school is to prepare children equally and adequately for their learning of the mathematics? To address this question we summarise recent work on the development of an eight dimensional framework, which we have called foundational number sense (FoNS) that characterises those necessary learning experiences. We then show how FoNS can be simply operationalised for analysing the learning opportunities offered grade one students in five European contexts. The results indicate that FoNS, as an analytical tool, is not only cross-culturally sensitive but has the propensity to inform developments in curriculum, assessment and teacher education.

  • 40.
    Sayers, Judy
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Björklund Boistrup, Lisa
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    The role of conceptual subitising in the development of foundational number sense2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Evidence indicates that children with a well-developed number sense are more likely to experience long-term mathematical success than children without. However, number sense has remained an elusive concept. In this paper we summarise the development of an eight dimensional framework categorising what we have come to call foundational number sense, or those non-innate number-related competences typically taught during the first years of schooling. We also show, drawing on grade one lessons from Hungary and Sweden, how teaching focused on conceptual subitising, the teaching of children to identify and use easily recognisable groups of objects to structure children’s understanding of number, facilitates students’ acquisition of a range of foundational number sense-related competences.

  • 41.
    Sayers, Judy
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Björklund Boistrup, Lisa
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    The Role of Conceptual Subitising in the Development of Foundational Number Sense2016Inngår i: Mathematics Education in the Early Years: Results from the POEM2 Conference, 2014 / [ed] Tamsin Meaney, Ola Helenius, Maria L. Johansson, Troels Lange, Anna Wernberg, Cham: Springer, 2016, s. 371-394Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Evidence indicates that children with a well-developed number sense are more likely to experience long-term mathematical success than children without. However, number sense has remained an elusive construct. In this chapter, we summarise the development of an eight-dimensional framework categorising what we have come to call foundational number sense or those non-innate number-related competences typically taught during the first years of schooling. We also show, drawing on grade one lessons from Hungary and Sweden, how focused instruction on conceptual subitising, the teaching of children to identify and use easily recognisable groups of objects to structure children’s understanding of number, facilitates children’s acquisition of a range of foundational number sense-related competences.

  • 42.
    Sayers, Judy
    et al.
    University of Leeds, UK.
    Marschall, Gosia
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Petersson, Jöran
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    English and Swedish teachers’ perspectives on the role of parents in year one children’s learning of number: manifestations of culturally-conditioned norms2019Inngår i: Early Child Development and Care, ISSN 0300-4430, E-ISSN 1476-8275Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 43.
    Szabo, Attila
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Examining the interaction of mathematical abilities and mathematical memory: A study of problem-solving activity of high-achieving Swedish upper secondary students2017Inngår i: The Mathematics Enthusiast, ISSN 1551-3440, Vol. 14, nr 1-3, s. 141-159Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we investigate the abilities that six high-achieving Swedish upper secondary students demonstrate when solving challenging, non-routine mathematical problems. Data, which were derived from clinical interviews, were analysed against an adaptation of the framework developed by the Soviet psychologist Vadim Krutetskii (1976). Analyses showed that when solving problems students pass through three phases, here called orientation, processing and checking, during which students exhibited particular forms of ability. In particular, the mathematical memory was principally observed in the orientation phase, playing a crucial role in the ways in which students' selected their problem-solving methods; where these methods failed to lead to the desired outcome students were unable to modify them. Furthermore, the ability to generalise, a key component of Krutetskii's framework, was absent throughout students' attempts. These findings indicate a lack of flexibility likely to be a consequence of their experiences as learners of mathematics.

  • 44.
    Szabo, Attila
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik. Stockholm City Education Department, Sweden.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students2018Inngår i: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 62, nr 4, s. 555-569Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. Analyses indicated a repeating cycle in which students typically exploited abilities relating to the ways they orientated themselves with respect to a problem, recalled mathematical facts, executed mathematical procedures, and regulated their activity. Also, while the nature of this cyclic sequence varied little across problems and students, the proportions of time afforded the different components varied across both, indicating that problem solving approaches are informed by previous experiences of the mathematics underlying the problem. Finally, students’ whose initial problem formulations were numerical typically failed to complete the problem, while those whose initial formulations were algebraic always succeeded.

  • 45. Xenofontos, Constantinos
    et al.
    Andrews, Paul
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Defining mathematical problems and problem solving: prospective primary teachers' beliefs in Cyprus and England2014Inngår i: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 26, nr 2, s. 279-299Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Based on the idea that mathematics education is, in general, culturally located, this paper discusses the cultural dimensions of prospective elementary teachers’ beliefs in Cyprus and England, and how these relate to the general educational culture of the two countries. Two volunteer groups (twelve students from each country) from a notable university in each country accepted an open invitation for participation and were qualitatively interviewed. This paper discusses two common sub-themes that emerged under the general theme, Explicit Pedagogic Practice, and takes into close consideration students’ beliefs about the use of teaching resources and group work. The findings suggest that the beliefs held by each cohort are framed by the cultural educational rhetoric of its respective country. In the conclusion of the paper, some implications about teacher education are discussed.

  • 46.
    Xenofontos, Constantinos
    et al.
    University of Cambridge, UK.
    Andrews, Paul
    University of Cambridge, UK.
    Prospective teachers’ beliefs about problem-solving: Cypriot and English cultural constructions2012Inngår i: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178, Vol. 14, nr 1, s. 69-85Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we report on a small-scale comparative examination of prospective elementary teachers' beliefs about problem-solving in Cyprus and England. First year undergraduate students (13 from Cyprus and 14 from England) from a well-regarded university in each country were qualitatively interviewed at the commencement of their respective teacher education programmes. Data, which were analysed by means of a combination of theory- and data-driven coding, indicated that, in both countries, students entered university with beliefs about problems and problem-solving that were not only products of the cultures in which they were educated, but also frequently incommensurate with the problem-solving expectation of the curricular frameworks within which they would have to work as teachers. Also, the outcomes confirmed that, despite researchers’ assumptions of definitional convergence, the expressions ‘mathematical problem’ and ‘problem-solving’ continue to be used differently across cultures. Some implications for teacher education are discussed.

1 - 46 of 46
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