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Sökning: jöran petersson

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41.
  • Petersson, Jöran, 1967- (författare)
  • Students’ responses to the question: how does a computer do curve fitting?
  • 2022
  • Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; , s. 1-17
  • Tidskriftsartikel (refereegranskat)abstract
    • Previous research has identified an unfilled gap between, on the one hand, mathematical prerequisites needed for a formal treatment of least squares and, on the other hand, only teaching procedural aspects of curve fitting. As a response to this, the present study explores students’ suggestions of how they think a computer or calculator does curve fitting. The data evolve through observations of mathematics classroom group work and interviews during a physics laboratory group work of year 10 secondary school students in Sweden. The results show that these students seemed well equipped to, on their own, suggest relevant and mathematically founded strategies for formal curve fitting though not least squares. Specifically, the students were inventive in their group work in the sense that several of their suggestions for how curve fitting could work are the same as those that appear in mathematics history from early 1700 until contemporary methods, covering both algebra and statistics. As such, the mathematical content in the results contrasts previous research on informal fit, which often results in the students counting the number of points over and under the fitted line but with less articulated justifications for their fit.
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42.
  • Petersson, Jöran, Docent (författare)
  • Timeseries analysis extends content analysis to exploring distribution of a topic among data
  • 2022
  • Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
    • This poster shows that methods imported from timeseries analysis could benefit the use of content analysis through raising new research questions and allowing enhanced results by showing where, in a sequence of data, the studied phenomenon occurs. For methodological reasons, timeseries analysis in educational research has been effectively absent and, until recently, content analysis in educational research typically meant to look for the mere existence of some explored theme or for comparing their frequency in two data sets. A timeseries requires that the data are an ordered sequence of units of analysis. One example is the analysis of a classroom conversation where the data may follow clock-time. Another example is analysing exercises in a textbook, where the data may not follow clock-time since each exercise can require different amounts of time to solve. A first outcome of a timeseries analysis is a moving average diagram, which is a diagram of the same kind as temperature curves used in climate science for displaying temperature changes over time. For the case of analysing exercises in a mathematics textbook, this diagram shows the changes in the intensity of the explored learning object throughout the textbook. When analysing a classroom conversation, it allows the researcher to compare two moving average diagrams, each displaying where in the conversation two specified topics occur. Specifically, determining the correlation between two timeseries allows the researcher to explore how two learning objects or conversation topics interact with each other. Hence, timeseries analysis provides a new tool for the researcher.
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43.
  • Petersson, Jöran, Docent, et al. (författare)
  • Two methods for quantifying similarity between textbooks with respect to content distribution
  • 2023
  • Ingår i: International Journal of Research and Method in Education. - : Taylor & Francis. - 1743-727X .- 1743-7288. ; 46:2, s. 161-174
  • Tidskriftsartikel (refereegranskat)abstract
    • Measures of association, which typically require pairwise data, are widespread in many aspects of educational research. However, due to the need to reduce their content to equal numbers of units of analysis, they are rarely found in the analysis of textbooks. In this paper, we present two methods for overcoming this limitation, one through the use of disjoint sections and the other through the use of overlapping moving averages. Both methods preserve the temporal structure of data and enable researchers to calculate a measure of association which, in this case, is the complementary Euclidean average distance, as an indicator of the books’ similarity. We illustrate these approaches by means of a comparative analysis of three commonly-used English and Swedish mathematics textbooks. Analyses were focused on individual tasks, which had all been coded according to the presence or absence of particular characteristics. Both methods produce nearly identical results and are robust with respect to both densely and sparsely occurring characteristics. For both methods, widening the aggregation window results in a slightly increased level of quantified similarity, which is the result of the ‘smoothing effect’. We discuss the relation between the window width and the choice of research question.
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44.
  • Petersson, Jöran, Docent (författare)
  • Using the Gini coefficient for assessing heterogeneity within classes and schools
  • 2023
  • Ingår i: SN Social Sciences. - : Springer Nature. - 2662-9283. ; 3:11
  • Tidskriftsartikel (refereegranskat)abstract
    • This study demonstrates that the Gini coefficient works as a dispersion measure for gauging educational heterogeneity in and between classrooms and schools. The method for this is to compare Gini coefficients for empirical data from various areas such as gender proportions in upper secondary school programmes and dispersion in achievement within classroom and between schools. The main results are that the Gini coefficient works for gauging heterogeneity on different statistical measurement scales and different sample sizes. An example of small sample is the nominal categories of upper secondary school study programmes, for which the Gini coefficient gauges differences in gender proportions while this sample size should be too small for several other measures of inequality and dispersion. An example of large sample of quotient scale data is two neighbour schools that mainly enrol different achievement strata from the same student cohort. Here the Gini coefficient displays the two schools’ student heterogeneity to be different. An example of moderate size sample is to explore how the teaching group heterogeneity, gauged as Gini coefficient on achievements, re-distributes from within to between classes as the same students proceed from cohesive compulsory school to the students’ individual choice of upper secondary school programmes. Since the Gini coefficient can gauge heterogeneity on small samples, a suggestion for further research is to use it for exploring the relation between strategies for classroom orchestration and levels of classroom heterogeneity, for example between teaching groups at different achievement strata. 
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45.
  • Sayers, Judy, et al. (författare)
  • Estimation: The missing competence in the mathematics experiences of year-one children
  • 2021
  • Konferensbidrag (refereegranskat)abstract
    • As part of our work on the Foundational Number Sense (FoNS) project, we undertook the development of a simple to operationalise framework for analysing the number-related learning opportunities received by year-one children (Andrews & Sayers, 2015). The eight categories of FoNS bridge the gap between those number-related understandings innate to all humans and forms of number sense typically associated with functional numeracy. Consequently, each FoNS competence is not only a prerequisite for later mathematical learning but dependent on instruction. One of these categories, estimation, has been identified as one of the three most important mathematical skills (Sriraman & Knott, 2009) and yet, as we discuss below, it is effectively absent from the curricula and textbooks that underpin the teaching and learning of year-one mathematics. Moreover, possibly a consequence of the above, during the early months of the project, a small set of serendipitously available year-one lessons from a number of European countries were analysed against the different FoNS categories and, across all systems, estimation was effectively invisible.The ability to estimate is widely recognised not only as a core skill of everyday life (White & Szűcs, 2012) but also a key determinant of later arithmetical competence, particularly in respect of novel situations (Booth & Siegler, 2008; Holloway & Ansari, 2009). However, the development of the ability to estimate is not a chance phenomenon but requires intervention (Joram et al., 2005; Peeters et al., 2016; White & Szűcs, 2012). Unfortunately, the teaching of estimation has been, historically, a neglected skill with textbooks colluding in this omission (Reys et al., 1982) by offering incomplete or inappropriate models (Joram et al., 1998).Broadly speaking, estimation takes four forms; computational estimation, number line estimation, quantity estimation and measurement estimation. Of these, number line estimation and quantity estimation are, we argue, lower level skills than computational estimation or measurement estimation and, as such, comprise the estimation elements of FoNS. That said, being able to undertake computational estimation is an essential life skill (Sekeris et al., 2019) and is, despite teacher scepticism (Alajmi, 2009), an important aid to children’s understanding of both place value and standard algorithms (Sowder, 1992). It is a skill that develops with age (Lemaire & Brun, 2014) but is an under-investigated area of arithmetic-related research (Lemaire & Lecacheur, 2011). Number line estimation, which draws on a child’s developing ability to exploit reference points (Sullivan & Barner, 2014), is a strong predictor of both mathematical learning difficulties (Siegler & Opfer, 2003) and mathematical achievement (Schneider et al., 2009). Instruction with respect to number line estimation is important if young children’s logarithmic estimations of quantity are to be replaced by linear (Siegler & Opfer, 2003), although others have argued that the logarithmic/linear distinction is less a developmental issue than one related to strategy choice (Ebersbach et al., 2008). Quantity (or numerosity) estimation is the ability to estimate the number of objects in a set. It is a skill that diminishes in accuracy as the numerosity of the set of objects grows (Smets et al., 2015). The ability to estimate quantities is closely tied to the ability to count (Barth et al., 2009) and has a developmental trajectory similar to number line estimation (Sella et al., 2015). Interestingly, the evidence indicates that young children tend exploit linear mappings in continuous conditions and logarithmic in discrete (Odic et al., 2013). While measurement estimation is an important life skill, with many users of mathematics using it as an everyday part of their professional decision making based on reference or anchor points (Jones & Taylor, 2009), it remains a neglected research field (Joram et al., 1998). It is known that children who employ references model to their estimates are more accurate than those who do not (Joram et al., 2005) and that context familiarity improves estimates (Jones et al., 2012).In this paper we will examine the materials available to support the teaching of estimation to year-one children. In particular, we will summarise how the curricula of ten European countries present estimation alongside analyses of six textbooks currently used in the year-one classrooms of England and Sweden. Two of these are authored by nationals of the two countries, while the remaining four are adaptations of textbooks drawn from countries typically seen as successful on international tests of achievement. The analyses indicate, confirming research undertaken nearly forty years ago, that across the board, estimation in any form is absent from year-one children’s opportunities to learn.
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46.
  • Andrews, Paul, et al. (författare)
  • A methodological critique of research on parent-initiated mathematics activities and young children’s attainment
  • 2022
  • Ingår i: Educational Studies in Mathematics. - : Springer. - 0013-1954 .- 1573-0816. ; 109, s. 23-40
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, motivated by the desire to understand which forms of parent-initiated activity are productively implicated in young children’s mathematics learning, we present a methodological critique of recent research. Many such studies, based on assumptions that parent-initiated activities can be categorised as formal or informal, direct or indirect, or advanced or basic, exploit surveys to elicit how frequently parents engage their children in various predetermined activities. While such survey data have the potential to yield important insights, the analytical procedures typically employed prevent them. Studies involving factor analyses yield uninterpretable factors, which are then used to create summative variables based on the scores of individual activities. Other studies, drawing on untested preconceptions, simply create summative variables. In all cases, these summative variables are based on such a wide range of qualitatively different activities that labels like formal or informal become arbitrary and the potential of individual activities to support learning gets lost beneath colleagues’ desires for statistical significance. In closing, we ask colleagues, albeit somewhat rhetorically, what is the purpose of such research? Is it to identify those activities that support learning or to offer statistically robust factors, which, due to the diversity of activities embedded within them, offer few useful insights?
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47.
  • Andrews, Paul, 1954-, et al. (författare)
  • Computational Estimation and Mathematics Education : A Narrative Literature Review
  • 2021
  • Ingår i: Journal of Mathematics Education. - : Education for All. - 1945-7502 .- 1945-7448. ; 14:1, s. 6-27
  • Tidskriftsartikel (refereegranskat)abstract
    • Computational estimation, typically construed as an approximate mental calculation of an arithmetical problem, is an important skill in everyday life and a wide range of professional contexts. Despite its importance, textbooks and curricula address it inadequately, with the consequence that many teachers are uncertain as to why and how they should teach it. In this paper, we present a narrative literature review that brings together the extensive research of the cognitive psychologists and the limited research of the mathematics educators to clarify the nature of computational estimation and its development. Focused initially on the strategies used in computational estimation before turning to children’s and adults’ computational estimation competence, the review shows that computational estimation, which develops over time, draws on a wide range of strategies reciprocally dependent on a secure understanding of numbers and arithmetic. It shows that the poor estimation competence of children and adults’ is susceptible to interventions, particularly with respect to addressing a common misconception that the purpose of computational estimation is the mental calculation of exact solutions.
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48.
  • Andrews, Paul, et al. (författare)
  • The role of number line estimation in mathematics teaching and learning : A narrative literature review
  • 2021
  • Konferensbidrag (refereegranskat)abstract
    • While the importance of both computational estimation and measurement estimation in children’slearning of mathematics is well known and has been widely researched, little attention has been paidto number line estimation, a mathematical competence that has only in the last two decades gainedthe attention of researchers. In this paper, we present a narrative review of the literature relating tonumber line estimation in the teaching and learning of school mathematics. In so doing, we focus onthe development of number line estimation in children, the mathematics learning implications ofnumber line estimation competence and how different approaches to the investigation of number lineestimation have yielded different insights into children’s cognition. Finally, we consider thedidactical implications of the review and appeal to curriculum developers to integrate more widelythis important competence.
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49.
  • Appelgren, Alva, et al. (författare)
  • Läxor och likvärdiga förutsättningar för lärande : – lärares arbetssätt inför, under och efter läxan
  • 2022
  • Rapport (övrigt vetenskapligt/konstnärligt)abstract
    • I denna systematiska översikt sammanställs forskning om hur lärares arbete med läxor kan bidra till likvärdiga förutsättningar för elevers lärande. Översikten utgår från följande frågeställning:Vad kännetecknar lärares arbete med läxor som kan bidra till likvärdiga förutsättningar för elevers lärande?Resultaten från de studier som ingår i översikten är sammanställda med fokus på lärares arbete med läxor inför, under och efter läxan. Sammantaget visar resultaten att lärare kan bidra till lik­värdiga förutsättningar för elevers lärande genom att planera utformningen av läxan, ta hänsyn till elevers situation i hemmet samt genom att följa upp läxarbetet i undervisningen.Översiktens resultat bygger på 15 forskningsstudier från olika länder som systematiskt har valts ut efter omfattande litteratursökningar i internationella referensdatabaser.
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50.
  • Bødtker Sunde, Pernille, et al. (författare)
  • Estimation in the Mathematics Curricula of Denmark, Norway and Sweden : Inadequate Conceptualisations of an Essential Competence
  • 2022
  • Ingår i: Scandinavian Journal of Educational Research. - : Taylor & Francis. - 0031-3831 .- 1470-1170. ; 66:4, s. 626-641
  • Tidskriftsartikel (refereegranskat)abstract
    • Acknowledging evidence that the ability to estimate has major consequences for both later mathematics learning and real-world functionality, this paper examines the national mathematics curriculum for compulsory school for each of Denmark, Norway and Sweden for the estimation-related opportunities it offers children. Framed against four conceptually and procedurally different forms of estimation (computational, measurement, quantity and number line), each of which is implicated differently in the later learning of mathematics, analyses indicated that none of the four forms of estimation were addressed explicitly in the Norwegian curriculum. Expectations of computational and measurement estimation were present in both the Danish and the Swedish curricula, although neither referred to either quantity or number line estimation. Even when estimation-related learning outcomes were articulated, there was no evidence of the processes by which they might be realised. Finally, there were no acknowledgements that estimation may contribute to the learning of other mathematical topics.
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