| 1. |
- 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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| 2. |
- 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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| 3. |
- Asami-Johansson, Yukiko, et al.
(författare)
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Comparing mathematics education lessons for primary school teachers : case studies from Japan, Finland and Sweden
- 2020
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; 51:5, s. 688-712
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to investigate and compare lessons given in primary school teacher education in Japan, Finland and Sweden. We analyse one lesson from each country and compare them using a common framework. Chevallard’s anthropological theory of the didactic (ATD) is used to frame this analysis and in particular to model teacher educators' didactic organization of the lessons. The focus is on how the didactic organizations of the teacher educators relate to the mathematical and didactic organizations of primary school. Based on official documents and viewpoints of the teacher educators, we also discuss how the contents and descriptions of the national curricula, and the different traditions of the teaching practices in each country, influence the didactic organizations found in the lessons.
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| 4. |
- Attorps, Iiris, et al.
(författare)
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Generating the patterns of variation with GeoGebra : the case of polynomial approximations
- 2016
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Ingår i: International Journal of Mathematical Education in Science and Technology. - 0020-739X .- 1464-5211. ; 47:1, s. 45-57
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students’ learning opportunities in the study group compared with the control group.
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| 5. |
- Bengmark, Samuel, 1965, et al.
(författare)
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Success-factors in transition to university mathematics
- 2017
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211. ; 48:7, s. 988-1001
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Tidskriftsartikel (refereegranskat)abstract
- This study examines different factors' relative importance for students' performance in the transition to university mathematics. Students' characteristics (motivation, actions and beliefs) were measured when entering the university and at the end of the first year. Principal component analysis revealed four important constructs: Self-efficacy, Motivation type, Study habits and Views of mathematics. Subsequently, orthogonal partial least squares (OPLS) analysis was used for measuring the constructs' ability to predict students' university mathematics grades. No individual constructs measured at the time of entrance predicted more than 5% of the variation. On the other hand, jointly they predicted 14%, which is almost in pair with upper secondary grades predicting 17%. Constructs measured at the end of the first year were stronger predictors, jointly predicting 37% of the variation in university grades, with Self-efficacy (21%) and Motivation (12%) being the two strongest individual predictors. In general, Study habits were not important for predicting university achievement. However, for students with low upper secondary grades, the textbook and interaction with peers, rather than internet-based resources, contributed positively to achievement. The association between Views of mathematics and performance was weak for all groups and non-existing for students with low grades.
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| 6. |
- Bergqvist, Tomas, 1962-, et al.
(författare)
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Upper secondary students’ task reasoning
- 2008
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Informa UK Limited. - 0020-739X .- 1464-5211. ; 39:1
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Tidskriftsartikel (refereegranskat)abstract
- Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and guided reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer.
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| 7. |
- Bergsten, Christer, 1949-, et al.
(författare)
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Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries
- 2015
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Ingår i: International journal of mathematical education in science and technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211. ; 46:7, s. 979-990
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Tidskriftsartikel (refereegranskat)abstract
- This study forms part of a collaboration project between universities in South Africa and Sweden in which we investigate whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than a traditional more procedurally oriented way of teaching. In this paper, we report in some detail from two interviews with professional engineers, selected to represent two different ‘poles’ of engineering work. The aim was to explore different kinds of arguments regarding the role of mathematics in engineering work, as well as some common across contexts. Both interviewees feel that conceptual mathematics is more important for engineering work, although the role of the procedural aspect was seen by one of the interviewees also to be important, but in a very intricate way.
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| 8. |
- Bergström, Tove, et al.
(författare)
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The importance of flow for secondary school students’ experiences in geometry
- 2023
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; 54:6, s. 1067-1091
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Tidskriftsartikel (refereegranskat)abstract
- This article is intended to contribute to greater knowledge regarding the importance of flow and the time used to perform an activity, with a focus on students’ mathematical experiences of 3D bodies. Thirty-one 9th-grade students took part in the study. Flow and variation theory was used in the analysis of lesson observations, submission tasks, audio recordings, logbooks, tests and nationwide tests. The results indicate that the selected mathematics problem is characterized by seven components, which serve as the basis for identifying intended critical aspects; a variation is evident in the balance between skills and challenges that is characterized by the critical aspects that the students discern; a variation is evident in the experience of flow that is dependent upon the students’ approach to their work on various activities; the students’ mathematical experiences are based, both short- and long-term, on discerned critical aspects and on the time spent on the activity that generates flow. Theoretical contributions as well as implications for teaching are presented at the end of the article.
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| 9. |
- Bergwall, Andreas, 1972-
(författare)
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Proof-related reasoning in upper secondary school : characteristics of Swedish and Finnish textbooks
- 2021
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; 52:5, s. 731-751
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Tidskriftsartikel (refereegranskat)abstract
- Despite the central role of proofs in mathematics, research often shows that school textbooks offer limited support for the teaching and learning of proof-related reasoning. This study contributes to this field of research by studying Swedish and Finnish upper secondary textbooks on logarithms and combinatorics. Justifications in expository sections are analysed and students' tasks are categorized according to the type and nature of reasoning they require. The findings imply that opportunities to learn proof-related reasoning are few, and are more oriented towards deductive reasoning in Finnish textbooks and towards empirical reasoning and conjecturing in Swedish textbooks. The results are discussed in relation to similar studies from both Scandinavian and United States contexts, and address future research and development of the theoretical framing of proof-related reasoning.
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| 10. |
- Bergwall, Andreas, 1972-
(författare)
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Topic-specific characteristics of proof-related reasoning
- 2023
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211.
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Tidskriftsartikel (refereegranskat)abstract
- Students’ difficulties with proofs are well documented. To remedy this, it is often recommended that reasoning and proving be focused on in all grades and content areas of school mathematics. However, proofs continue to have a marginal place in many classrooms, or are only given explicit attention in courses in Euclidean geometry. Geometry is also the most common topic for educational research on reasoning and proving. This paper compares what four other topics in secondary school mathematics – logarithms, primitive functions, definite integrals, and combinatorics – can offer in terms of opportunities to learn proof. The types and natures of reasoning in expository sections and students’ tasks in 11 Swedish and Finnish textbooks are analysed in search of similarities and differences between these topics. The results are accounted for with special focus on opportunities for reasoning about general cases. Finally, the findings are discussed in relation to mathematical aspects of the four analysed topics.
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