| 1. |
- Petersson, Jöran, et al.
(författare)
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Opportunities for year-one children to acquire foundational number sense : comparing English and Swedish adaptations of the same Singapore textbook
- 2019
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Ingår i: Proceedings of the Seventh Conference on Research in Mathematics Education in Ireland (MEI7). - Dublin : Institute of Education, Dublin City University. - 9781873769959 ; , s. 251-258
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 2. |
- Petersson, Jöran, et al.
(författare)
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Parent-initiated activities in support of Swedish year-one children’s learning of mathematics : age-appropriate complements to school?
- 2022
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Ingår i: International Journal of Early Years Education. - : Taylor & Francis. - 0966-9760 .- 1469-8463. ; 30:4, s. 831-846
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, motivated in part by evidence that Swedish teachers are sceptical of parents’ abilities to offer appropriate support, we present an exploratory investigation of the activities Swedish parents initiate to facilitate their year-one (first grade) children’s learning of mathematics. Data, derived from 25 semi-structured interviews conducted with parents from three demographically different schools, were subjected to constant comparison analyses and yielded three broad categories of activity. These concerned the use of games in the learning of mathematics, contextualised mathematics activities like cooking and shopping, and decontextualised mathematics activities like systematic counting. Collectively, the results indicate that while parents of year-one children are confident supporting their children’s learning of mathematics, they are also conscious of the need to avoid both undermining schools’ efforts and exacerbating educational inequity. With few exceptions, the activities parents described were age-appropriate and more likely to complement teachers’ actions than not.
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| 3. |
- Petersson, Jöran, et al.
(författare)
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Swedish parents’ perspectives on home-school communication and year-one pupils learning of mathematics
- 2021
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Ingår i: Bringing Nordic mathematics education into the future. - Göteborg : Nationellt centrum för matematikutbildning (NCM). ; , s. 201-208
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Konferensbidrag (refereegranskat)abstract
- In this paper we explore parents’ perspectives on home-school communication with respect to year-one pupils’ learning of early numeracy. Constant comparison analyses of semi-structured interviews identified three forms of communication. The first, a weekly information letter, was appreciated and typically functioned as a starter for conversations with children about their learning of early numeracy. The second, the development talk, was appreciated as an indicator of a child’s progress, but proved controversial in the presentation of mixed messages to parents and limited with respect to helping parents support future mathematical learning. The third, parent-initiated contact, was discussed in ways that masked parents’ reasons for making contact and prevented, therefore, any insights into their contribution to mathematical learning. Some implications are discussed.
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| 4. |
- Petersson, Jöran, et al.
(författare)
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Two novel approaches to the content analysis of school mathematics textbooks
- 2021
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Ingår i: International Journal of Research & Method in Education. - : Taylor & Francis. - 1743-7288 .- 1743-727X. ; 44:2, s. 208-222
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Tidskriftsartikel (refereegranskat)abstract
- The analysis of the content of school textbooks, particularly in a time of cross-cultural borrowing, is a growing field restricted by the tools currently available. In this paper, drawing on the analyses of three English year-one mathematics textbooks, we show how two approaches to the analysis of sequential data not only supplement conventional frequency analyses but highlight trends in the content of such textbooks hidden from frequency analyses alone. The first, moving averages, is conventionally used in science to eliminate noise and demonstrate trends in data. The second, Lorenz curves, is typically found in the social sciences to compare different forms of social phenomena. Both, as we show, extend the range of questions that can be meaningfully asked of textbooks. Finally, we speculate as to how both approaches can be used with other forms of ordered classroom data.
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| 5. |
- Petersson, Jöran, 1967-, et al.
(författare)
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Analysing English year-one mathematics textbooks through the lens of foundational number sense : A cautionary tale for importers of overseas-authored materials
- 2023
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Ingår i: Oxford Review of Education. - : Taylor & Francis Group. - 0305-4985 .- 1465-3915. ; 49:2, s. 262-280
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present analyses of three textbooks currently used in the teaching of mathematics to year-one children in England. One is an established English-authored textbook, while the others are Singaporean-authored imports promoted by government as solutions to perceptions of systemic failure. Every task in each textbook was coded against a set of eight number-related competences known to support children’s learning in both short and long terms. Such a framework, which is literature-derived and curriculum-independent, enables meaningful comparison of materials deriving from different cultural contexts. Analyses of the proportions of all tasks coded for the different competences showed that none of the three books adequately addresses all eight competences, although the English-authored comes closest. Moving averages, undertaken to show the temporal location of the opportunities presented for children to acquire the eight competences, showed them distributed throughout the school year in the English-authored textbook but only during the first half of the school year in the two Singaporean-authored textbooks. Some implications for the importation of such materials are discussed.
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| 6. |
- Sayers, Judy, et al.
(författare)
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Estimation: The missing competence in the mathematics experiences of year-one children
- 2021
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)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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| 7. |
- Andrews, Paul, 1954-, et al.
(författare)
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Computational Estimation and Mathematics Education : A Narrative Literature Review
- 2021
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Ingår i: Journal of Mathematics Education. - : Education for All. - 1945-7502 .- 1945-7448. ; 14:1, s. 6-27
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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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| 8. |
- Andrews, Paul, et al.
(författare)
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English and Swedish year-one teachers’ number-related learning goals : the influence of intended and received curricula
- 2024
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; , s. 1-31
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, drawing on semi-structured interviews with generalist teachers of year-one children in England and Sweden, we examine comparatively the influence of the intended curriculum (teachers in both countries work within mandated national curricula) and the received curriculum (the collectively assumed efficacious practices and goals handed down from one generation of teachers to the next) on teachers’ expressed number-related learning goals. Analyses, framed by a literature-derived and curriculum-independent set of eight forms of number-related competence each implicated in later mathematical learning, identified both similarities and differences in the two groups’ expressed goals. Key similarities concerned expectations that all children should become additively competent, supported by supplementary goals concerning systematic counting, number bonds, the number line and an appropriate mathematical terminology. Key differences concerned English teachers’ strongly-expressed emphasis on place value and a desire for children to learn to multiply. Overall, the strongly-framed English curriculum appears to influence teachers’ goals more than the weakly-framed Swedish, while Swedish teachers seem to draw on a received curriculum more closely aligned with the literature-derived developmental goals than the English. Finally, when set against the literature-derived and curriculum-independent developmental goals, the English curriculum, unlike the Swedish, expects year-one children to learn much age-inappropriate material.
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| 9. |
- Andrews, Paul, et al.
(författare)
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The role of number line estimation in mathematics teaching and learning : A narrative literature review
- 2021
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)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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| 10. |
- Bødtker Sunde, Pernille, et al.
(författare)
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Estimation in the Mathematics Curricula of Denmark, Norway and Sweden : Inadequate Conceptualisations of an Essential Competence
- 2022
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Ingår i: Scandinavian Journal of Educational Research. - : Taylor & Francis. - 0031-3831 .- 1470-1170. ; 66:4, s. 626-641
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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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