| 1. |
- Helenius, Ola, 1970, et al.
(författare)
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Measuring temperature within the didactic space of preschool
- 2016
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Ingår i: Nordisk matematikkdidaktikk, NOMAD. - : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 21:4, s. 155-176
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Tidskriftsartikel (refereegranskat)abstract
- The informal character of preschool mathematics, engaged in during children’s play, places complex requirements on preschool teachers. It also leads to challenges in developing appropriate analytical tools for researching teacher work. In this paper a framework, the ”didaktic space”, is described and used to analyse interactions between preschool teachers and children in relationship to mathematical learning situations. An interaction between a preschool teacher and a group of children about how to compare their temperatures is analysed, using this framework. The analysis focuses on how the teacher’s contributions as well as those of the children changed as the role of the mathematics changed. The paper discusses how the didaktic space offers a nuanced understanding of preschool mathematical situations, both to researchers and to teachers.
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| 2. |
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| 3. |
- Barza, Sorina, et al.
(författare)
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A Sawyer duality principle for radially monotone functions in Rn
- 2005
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Ingår i: Journal of Inequalities in Pure and Applied Mathematics. - 1443-5756. ; 6:2
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Tidskriftsartikel (refereegranskat)abstract
- Let f be a non-negative function on ℝn, which is radially monotone (0 < f↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup ∫ℝ fg/f↓r(∫ℝn fp v)1/p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given. © 2005 Victoria University
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| 4. |
- Gogatishvili, Amiran, et al.
(författare)
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Characterisation of embeddings in Lorentz spaces
- 2007
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Ingår i: Bulletin of the Australian Mathematical Society. - 0004-9727 .- 1755-1633. ; 76:1, s. 69-92
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Tidskriftsartikel (refereegranskat)abstract
- Some new integral conditions characterising the embedding Λp(v) → Γq(w), 0 < p, q ≤ co are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) 1 = ∞, 1 < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space Γuq(w). In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embeddingSome new integral conditions characterising the embedding Λp(v) → Γq(w), 0 < p, q ≤ co are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) 1 = ∞, 1 < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space Γuq(w). In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embedding
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| 5. |
- Helenius, Ola, et al.
(författare)
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Analysing Instrumental and Pedagogic Situations in Preschools using the Didaktic Space
- 2014
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Ingår i: Development of mathematics teaching: Design, Scale, Effects. - : Svensk förening för matematikdidaktisk forskning (SMDF). - 9789197393492
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Konferensbidrag (refereegranskat)abstract
- Researchers rarely discuss methodological issues in regard to preschoolmathematics education and if they do, they do not take their starting point fromreconceptualisations of what mathematics might be for preschool children. Thispaper presents as an analytical tool the “didaktic space” that arose whenresponding to issues related to the analysis of data collected in a Swedishpreschool. The issues that arose from categorising situations using Bishop’s sixactivities required some reconsiderations of the methodology in relationship tothe research questions. The paper discusses how methodological decisions canaffect the analysis and the future possibilities that the didaktic space offers.
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| 6. |
- Helenius, Ola, et al.
(författare)
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Beginning early : mathematical exclusion
- 2015
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Ingår i: Proceedings of the Eight International Mathematics Education and Society Conference. - Portland : Portland State University. ; , s. 596-609
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Konferensbidrag (refereegranskat)
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| 7. |
- Helenius, Ola, et al.
(författare)
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Intruction
- 2016
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Ingår i: Mathematics Education in the Early Years. - Cham : Encyclopedia of Global Archaeology/Springer Verlag. - 9783319239330 - 9783319239354 ; , s. 3-17
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- One of Bishop’s six mathematical activities is playing which includes modelling, hypothetical thinking and abstraction. These can be in young children’s play, but do they by their presence make this play mathematical? In this chapter, we explore this question by first defining play and then comparing its features with what is known about mathematicians’ academic play and how mathematics education researchers have described young children’s play. From this theoretical discussion, we discuss the features of play, which can enable it to be described as mathematical. We use these features to analyse a small episode of children playing to discuss if and how their play could be considered to be mathematical
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| 8. |
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| 9. |
- Helenius, Ola, et al.
(författare)
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Mathematical exclusion with the every day
- 2015
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Ingår i: Proceedings of the Ninth Conference of the European Society for Research in Mathematics Education (CERME9). - : Charles University, Faculty of Education. ; , s. 1584-1590
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Konferensbidrag (refereegranskat)abstract
- Problem solving can involve using mathematics to solve everyday problems. In this study, we examine an interaction between a teacher and a class of six-year olds in Sweden around an open-ended problem, from an everyday context. Using Bernstein's ideas about vertical and horizontal discourse, a mixture of everyday and mathematics understandings is identified in the interaction. This mixture seems to result in confusion for both the teacher and the children over what should be the focus. This paper raises issues about how the connection to the everyday in problem solving could reduce children's opportunities to learn mathematics.
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| 10. |
- Helenius, Ola, et al.
(författare)
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Preschool Teachers' Awareness of Mathematics
- 2014
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Ingår i: Development of mathematics teaching: Design, Scale, Effects. - Göteborg : Svensk förening för matematikdidaktisk forskning (SMDF). - 9789197393492
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Konferensbidrag (refereegranskat)abstract
- Preschool teachers’ expectations about what mathematics they should engagechildren in are generally centred about numbers and counting. However, theSwedish preschool curriculum and research into young children’s developmentof mathematical understanding suggest that children can be offered a muchricher set of ideas. In this paper, we examine material from a professionaldevelopment course which indicates that discussing Bishop’s six universalmathematical activities provided preschool teachers with a wider perspective fordiscussing the mathematics, which children in their preschools engaged with.
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