| 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, 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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| 4. |
- 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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| 5. |
- Appelgren, Alva, et al.
(författare)
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Läxor och likvärdiga förutsättningar för lärande : – lärares arbetssätt inför, under och efter läxan
- 2022
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- I denna systematiska översikt sammanställs forskning om hur lärares arbete med läxor kan bidra till likvärdiga förutsättningar för elevers lärande. Översikten utgår från följande frågeställning:Vad kännetecknar lärares arbete med läxor som kan bidra till likvärdiga förutsättningar för elevers lärande?Resultaten från de studier som ingår i översikten är sammanställda med fokus på lärares arbete med läxor inför, under och efter läxan. Sammantaget visar resultaten att lärare kan bidra till likvärdiga förutsättningar för elevers lärande genom att planera utformningen av läxan, ta hänsyn till elevers situation i hemmet samt genom att följa upp läxarbetet i undervisningen.Översiktens resultat bygger på 15 forskningsstudier från olika länder som systematiskt har valts ut efter omfattande litteratursökningar i internationella referensdatabaser.
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| 6. |
- 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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| 7. |
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| 8. |
- Holmqvist, Mona, et al.
(författare)
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Teachers’ Academic literacy knowledge
- 2021
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Ingår i: Abstract book nofa8, Western Norway University of Applied Sciences , 2021.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In this study, a total of 18 in-service teachers participated in one cycle of a learning study (Marton, 2015; Holmqvist, 2011) aiming to study development of academic literacy. The study was guided by variation theory (Marton 2015; Holmqvist, Gustavsson & Wernberg, 2008). The object of learning is academic literacy, a subject of importance for all teachers, as their professional work is supposed to be conducted on scientific based knowledge. The capability to read and understand scientific publications, and to judge the scientific value of different sources used by teachers, are crucial for the quality of teachers’ professional work. The study was designed following the steps of a learning study. This means collaborative discussions among the teachers, in this case the researchers who are the authors of this abstract, testing the participants’ knowledge before the teaching activity, by designing and implementing instruction offer the participants to discern the critical aspects of academic literacy to gain deeper knowledge, analysis of post-tests to describe the learning outcome, and to present the results. The lesson was focusing on the structure of, and differences between, scientific and popular scientific texts. Two texts were used presenting the same study and by the same author. By that, the in-service teachers were offered to see the same topics differently described based on the two different genre’s requirements. The results show how the participants in the pre-test focuses on the texts’ similarities, with an unawareness of genre differences. In the post-test, the differences in genre is described. A limitation of the study is that the two texts used in pre and post-tests are focusing slightly different topics, which is discerned and focused by the participants – an aspect not critical for developing academic literacy at a general level.ReferencesHolmqvist, M. (2011). Teachers’ learning in a learning study. Instructional science, 39(4), 497-511.Holmqvist, M., Gustavsson, L. & Wernberg, A. (2008) Variation Theory – An Organizing Principle to Guide Design Research in Education. In Kelly, A.E., Lesh, R., &. Baek J. (eds) Handbook of design research methods in education, p 111-130. New York: Routledge. Marton, F. (2015). Necessary conditions of learning. London: Routledge.
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| 9. |
- Holmström, Kenneth, et al.
(författare)
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A review of the parameter estimation problem of fitting positive exponential sums to empirical data
- 2002
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 126:1, s. 31-61
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Tidskriftsartikel (refereegranskat)abstract
- Exponential sum models are used frequently: in heat diffusion, diffusion of chemical compounds, time series in medicine, economics, physical sciences and technology. Thus it is important to find good methods for the estimation of parameters in exponential sums. In this paper we review and discuss results from the last forty years of research. There are many different ways of estimating parameters in exponential sums and model a fit criterion, which gives a valid result from the fit. We find that a good choice is a weighted two-norm objective function, with weights based on the maximum likelihood (ML) criterion. If the number of exponential terms is unknown, statistical methods based on an information criterion or cross-validation can be used to determine the optimal number. It is suitable to use hybrid Gauss–Newton (GN) and quasi-Newton algorithms to find the unknown parameters in the constrained weighted nonlinear least-squares (NLLS) problem formulated using an maximal likelihood (ML) objective function. The problem is highly ill conditioned and it is crucial to find good starting values for the parameters. To find the initial parameter values, a modified Prony method or a method based upon rewriting partial sums as geometrical sums is proposed.
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| 10. |
- Norén, Eva, et al.
(författare)
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Algebra tasks in a word problem and non-word problem context – a multilingual project
- 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
- Many students see algebra as a difficult topic. For second language speakers there might also be difficulties comprehending an algebra task linguistically correct. The authors suggest studying how knowledge in algebra and linguistic registers in mathematics interplay for both newly early arrived immigrants compared to first language speakers. We suggest the tools for such a study to be measuring achievement and solution strategy while varying the text intensity and mathematics register in algebra problems for students with different length of experience of Swedish language in school year 9. We want to discuss design of test instrument and methods for background data collection.
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