| 1. |
- Andrews, Paul, et al.
(författare)
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A methodological critique of research on parent-initiated mathematics activities and young children’s attainment
- 2022
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Ingår i: Educational Studies in Mathematics. - : Springer. - 0013-1954 .- 1573-0816. ; 109, s. 23-40
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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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| 2. |
- 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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| 3. |
- Andrews, Paul, 1954-, et al.
(författare)
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Developing foundational number sense : Number line examples from Poland and Russia
- 2015
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Ingår i: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. - 9788072908448 ; , s. 1681-1687
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 4. |
- 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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| 5. |
- Andrews, Paul, Professor, 1954-, 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
-
Ingår i: International Journal of Mathematical Education in Science and Technology. - 0020-739X .- 1464-5211.
-
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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| 6. |
- Andrews, Paul, 1954-, et al.
(författare)
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Estimation in the primary mathematics curricula of the United Kingdom : Ambivalent expectations of an essential competence
- 2022
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Ingår i: International Journal of Mathematical Education in Science and Technology. - 0020-739X .- 1464-5211. ; 53:8, s. 2199-2225
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we examine the national curricula for primary mathematics for each of the four constituent nations of the United Kingdom (England, Northern Ireland, Scotland and Wales) for the estimation-related opportunities they offer children. Framed against four conceptually and procedurally different forms of estimation (computational, measurement, quantity and number line), the analyses indicate that computational estimation and measurement estimation were addressed in all four curricula, albeit from a skills-acquisition perspective, with only the Scottish offering any meaningful justification for their inclusion. The process of rounding, absent in the Northern Ireland curriculum, was presented as an explicit learning objective in the English, Scottish and Welsh curricula, although it was only the Scottish that made explicit the connections between rounding and computational estimation. In all curricula, both quantity estimation and number line estimation were effectively absent, as was any explicit acknowledgement that learning to estimate, irrespective of its form, has a developmental role in the learning of other mathematical topics.
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| 7. |
- Andrews, Paul, 1954-, et al.
(författare)
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Foundational number sense : A framework for analysing early number-related teaching
- 2014
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Ingår i: Proceedings of MADIF 9, The Ninth mathematics Education Research Seminar.
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 8. |
- Andrews, Paul, 1954-, et al.
(författare)
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Identifying opportunities for grade one children to acquire foundational number sense : Developing a framework for cross cultural classroom analyses
- 2015
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Ingår i: Early Childhood Education Journal. - : Springer Science and Business Media LLC. - 1082-3301 .- 1573-1707. ; 43:4, s. 257-267
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 9. |
- Andrews, Paul, 1954-, et al.
(författare)
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PISA, TIMSS and Finnish mathematics teaching : an enigma in search of an explanation
- 2014
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Ingår i: Educational Studies in Mathematics. - : Springer Science and Business Media LLC. - 0013-1954 .- 1573-0816. ; 87:1, s. 7-26
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 10. |
- 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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