| 1. |
- Petersson, Jöran
(författare)
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Components of knowledge in solving linear equations
- 2021
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Ingår i: Sustainable mathematics education in a digitalized world. - 9789198402445 ; , s. 41-50
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Konferensbidrag (refereegranskat)abstract
- This article identifies knowledge components needed for successfully solving linear equations. Data for this purpose is 359 Swedish year 9 students’ written responses to the test task ”solve the equation 2x + 3 = 11”. The following set of knowledge components were identified; arithmetic knowledge, parsing knowledge, balancing equations, giving a value to the unknown, not omitting parts and the habit of verifying the solution. This paper discusses for which of these knowledge components, students could discover and correct their own errors if they would both solve an equation and verify its solution.
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| 2. |
- Petersson, Jöran, et al.
(författare)
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Content Analysis of Mathematics Textbooks and Adapted Lorentz Curves
- 2021
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Ingår i: <em>Proceedings of the Eighth Conference on Research in Mathematics Education in Ireland</em>. - Dublin. ; , s. 356-363
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Konferensbidrag (refereegranskat)abstract
- In this paper, we introduce an adaption of the Lorenz curve as a powerful tool for graphicallypresenting content analyses of mathematics textbooks. Three textbooks currently used withyear-one children in Sweden, one Swedish-, one Finnish and one Singaporean-authored, wereanalysed against the eight categories of Foundational Number Sense (FoNS), which is a set ofliterature-derived and instruction-dependent competences that all children need to acquire ifthey are to become successful learners of mathematics. The adapted Lorenz curvehighlighted, inter alia, major differences in the distribution of FoNS-related tasks across thethree textbooks. In general, the Swedish-authored textbook offers repeated cycles of FoNSrelated opportunities, the Finnish-authored textbook offers such opportunities continuously,and the Singaporean-authored textbook typically offers FoNS-related opportunities onlywithin its earlier pages.
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| 3. |
- Petersson, Jöran
(författare)
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Debatt: Anpassa skolpengen – utifrån ansvaret att följa befolkningskurvan
- 2020
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Ingår i: Jönköpingsposten. - Jönköping. - 1103-9469. ; :2020-12-23
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Kommunala skolor har ett lagstadgat ansvar att ta höjd för variationer i befolkningskurvan. En friskola däremot kan välja att anpassa kostymen. Det är ett självklart och icke-ideologiskt argument för att betala ut en större skolpeng till kommunala skolor som är ålagda att ha en överkapacitet.
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| 4. |
- Petersson, Jöran
(författare)
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Mathematical modelling for futures of Anthropocene
- 2024
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Ingår i: Quaderni di Ricerca in Didattica" QRDM (Mathematics). - 1592-5137 .- 1592-4424. ; 13, s. 579-587
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Tidskriftsartikel (refereegranskat)abstract
- Applying mathematical modelling to the Anthropocene should give students tools to under-stand and reflect on their own role in causes and effects related to the Anthropocene. Three Anthropocene-related phenomena discussed in the media are, for example, transportation, food supply and mass extinction of species. This paper formulates mathematical modelling tasks for these three phenomena. It discusses them with respect to four key features of mathematical modelling, namely understanding, description, abstraction, and negotiation, and finds that each task includes several of these key features. An example of ‘describe’ is to translate extinction of species into a net change equation between formation and extinc-tion of species. An example of ‘abstraction’ is to calculate and find the maybe surprising re-sult that for producing the same amount of protein, cheese requires more land than tomato. The key feature of ‘negotiation’ is that when going by car, time for physical activity must be added corresponding to that of cycling the same distance. This promotes ‘understand’ in the sense of identifying factors that are crucial in explaining the dynamics of the phenome-non.
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| 5. |
- 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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| 6. |
- Petersson, Jöran, et al.
(författare)
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Prime Time in Preschool Through Teacher-Guided Play with Rectangular Numbers
- 2022
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Ingår i: Scandinavian Journal of Educational Research. - : Informa UK Limited. - 0031-3831 .- 1470-1170. ; 66:4, s. 714-728
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Tidskriftsartikel (refereegranskat)abstract
- In preschool, numbers and shapes typically appear as separate topics. This study explores how a game, designed as a guided play activity with figurate numbers, functions in a preschool context. The guided play involved parking Lego cars in a rectangular shape, and to find out for which number of Lego cars this is possible. Thirteen preschool children in three separate age groups, aged from four to six years, together with their teacher, participated in the study. Their communications through words and actions were recorded. The results exemplify how this guided play provides a rich context for engaging young children with mathematical activities such as counting, sorting, shaping, asking, justifying, and inferring, as well as emotional engagement with the activity.
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| 7. |
- Petersson, Jöran, et al.
(författare)
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Resolve possible confusion by distinguishing between reflexive and transitive formative assessment
- 2021
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- AbstractThe review of assessment research by Black and Wiliam (1998) initiated a changed approach regarding teachers' classroom practice. They defined formative assessment as ”… encompassing all those activities undertaken by teachers, and/or by their students, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged” (Black & Wiliam, 1998, s. 7-8). This wide definition includes both teachers’ and their students’ activities, while as an example, the Swedish National Agency for Education instead confines formative assessment to the teachers’ work during the actual teaching process in order to find out where the student is in his learning, and to adapt the teaching accordingly (Skolverket, 2013). This pinpoints that we should distinguish between reflexive formative assessment, aiming to modify oneself, be it a student to himself or a teacher to herself and transitive formative assessment, aiming to modify someone else, be it from teacher to student or student to another student. Hirsh and Lindberg (2015) discussed this distinction though they did not coin a term for it as Westlund (2020) did. ReferencesBlack, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: principles, policy & practice, 5(1), 7-74.Hirsh, Å., & Lindberg, V. (2015). Formativ bedömning på 2000-talet : En översikt av svensk och internationell forskning. In Forskning och skola i samverkan – Kartläggningar av forskningsresultat med relevans för praktiskt arbete i skolväsendet (pp. 105–109). Stockholm: Vetenskapsrådet.Skolverket. (2013). Forskning för klassrummet: vetenskaplig grund och beprövad erfarenhet i praktiken. Stockholm: Fritzes.Westlund, A. (2020). Formativ bedömning i ett lärarperspektiv – framträdande aspekter i undervisning och vad som behövs för implementering. (Master thesis of education). Malmö University.
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| 8. |
- 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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| 9. |
- Petersson, Jöran, et al.
(författare)
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Teaching dimensional analysis in secondary school mathematics
- 2021
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Ingår i: Abstract book nofa8. - : Western Norway University of Applied Sciences.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- AbstractIn its elementary form, the idea of dimensional analysis is to look at the unit of a magnitude, for example speed, and conclude that speed measured in m/s is a quotient having meters in the numerator and seconds in the denominator. However, despite dimensional analysis being a not un-common theme for research in mathematics education at tertiary level teaching, it seems in practice absent below that level. This is surprising since dimensional analysis is useful in mathematical problem solving involving proportionality. Even more so since, from halves and doubles in preschool to scalar multiplication in upper secondary school, proportionality permeates school mathematics and is well-researched (Lamon, 2007). Hence, the authors initiated a research project on how to teach dimensional analysis in school years 6-12. The novelty of this area made us choose didactical engineering (Artigue, 2015) as a theoretical framework suitable for developing the teaching of dimensional analysis. Accordingly, in a cycle of a priori and a posteriori analyses, the authors are developing an empirically based teaching model for dimensional analysis including the topic of constructing exercises for students. We present results from this on-going development project. ReferencesArtigue, M. (2015). Perspectives on Design Research: The Case of Didactical Engineering. In A. Bikner-Ahsbahs, C. Knipping, N. Presmeg. (Eds.). Approaches to Qualitative Research in Mathematics Education. Dordrecht: Springer.Lamon, S. J. (2007). Rational numbers and proportional reasoning: Towards a theoretical framework. In F.K. Lester (red) Second handbook of research on mathematics teaching and learning, vol 2 (pp. 629–668). Charlotte, NC: NCTM.
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| 10. |
- Petersson, Jöran, et al.
(författare)
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Time series analysis: Moving averages as an approach to analysing textbooks
- 2020
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Ingår i: Proceedings of CERME11. - : Freudenthal Group & Freudenthal Institute. - 9789073346758
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Konferensbidrag (refereegranskat)abstract
- In this study we introduce time series analysis, specifically moving averages, as a novel strategy for analysing mathematics textbooks. Such analyses show how different topics or mathematical processes are emphasised over different time periods, whether at the level of the lesson, the week, the month or year. In this paper, by way of example, we show how one of the eight categories of foundational number sense (Andrews & Sayers, 2015), namely simple addition and subtraction, is distributed and sequenced across three English, year one, textbooks. The analyses are compared empirically with four other methods found in the literature to show how time series analysis using moving averages helps address the shortcomings of these different approaches.
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