| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- Löwenhielm, Anna, et al.
(författare)
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Opportunities to acquire foundational number sense: A quantitative comparison of popular English and Swedish textbooks
- 2017
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 6. |
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| 7. |
- Sayers, Judy, 1960-, et al.
(författare)
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Foundational number sense : The basis for whole number arithmetic competence
- 2015
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Ingår i: Conference proceedings of the ICMI Study 23. - 9789996510663 ; , s. 124-131
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Konferensbidrag (refereegranskat)abstract
- 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.
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