| 1. |
- Aguilar, Mario Sanchez, et al.
(författare)
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Towards Characterization of Scale and Scaling in Implementation Research within Mathematics Education
- 2023
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Ingår i: Implementation and Replication Studies in Mathematics Education. - 2667-0135 .- 2667-0127. ; 3:1, s. 99-122
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Tidskriftsartikel (refereegranskat)abstract
- Scale and scaling are central concepts in projects aimed at implementing innovations for improving mathematics education. This study aims to provide conceptual clarity on the notions of scale and scaling in mathematics education research. The meanings of these terms are handled tacitly, and there is diversity in how they are used in the literature. To address this, we gathered opinions from experienced researchers in the area of the large-scale implementation of educational innovations, and we also conducted a literature review of articles explicitly addressing aspects of scale and scaling in mathematics education. We analyzed the content of these sources using Coburn’s (2003) conceptualization of scale. Our findings provide insight into how experts define and understand the concepts of small scale, large scale, at scale and scaling, and how these concepts relate to the four dimensions of scale proposed by Coburn. This study contributes to developing a more precise and nuanced understanding of scale and scaling in mathematics education research by offering an operational distinction between small-scale, large-scale, and medium-scale project implementation. This distinction is based on three key factors: the contact factor, the material factor, and the organizational factor.
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| 2. |
- Ahl, Linda Marie, 1970, et al.
(författare)
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A framework for analyzing progress in concept knowledge in mathematics textbooks
- 2021
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Ingår i: Bringing Nordic mathematics education into the future. Preceedings of Norma 20. The ninth Nordic Conference on Mathematics Education Oslo, 2021. - Göteborg : SMDF. - 1651-3274.
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Konferensbidrag (refereegranskat)abstract
- In this paper we report on a framework for analyzing progress in concept knowledge as represented in textbooks. The framework is based on theories of Vergnaud, combined with a theory of Bruner. Two Swedish textbook series are analyzed with respect to how they introduce mathematical content and how it supports the progress of concept knowledge throughout school years. The analysis is restricted to the conceptual field of quotient constructions. We classified representations in terms of situational, iconic and symbol system representations. Results show that the investigated textbooks provide students with the same limited explanations in iconic representations of quotient constructions from year 3, when it is introduced, to year 9. We argue that our theory for progress in concept knowledge, together with our framework for analyzing progress, can be used by teachers and curriculum developers to organize instruction.
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| 3. |
- Ahl, Linda Marie, 1970-, et al.
(författare)
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Bill's Rationales for Learning Mathematics in Prison
- 2021
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Ingår i: Scandinavian Journal of Educational Research. - : Informa UK Limited. - 0031-3831 .- 1470-1170. ; 65:4, s. 633-645
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Tidskriftsartikel (refereegranskat)abstract
- This paper reports on a case study of a student's rationales for learning mathematics. We operationalize Stieg Mellin-Olsen's educational concept of rationales for learning and apply the concept on data consisting of three semi-structured interviews with a student in the Swedish prison education program. Our analysis shows that the student's rationales vary in character over time as a reaction to his educational contexts. We conclude that Mellin-Olsen's construct of rationales is useful for understanding students' changing motivation in relation to the teaching and to the practice of mathematics the teaching entails. Teachers may use the concepts from our analysis as cognitive tools, related to students' rationales for learning. By identifying students' different rationales, opportunities arise for an individualized instructional design.
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| 4. |
- Ahl, Linda Marie, 1970, et al.
(författare)
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Implementation Research in Mathematics Education: A Systematic Mapping Review
- 2023
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Ingår i: Implementation and Replication Studies in Mathematics Education. - : Brill Academic Publishers. - 2667-0135 .- 2667-0127. ; 3:2, s. 135-199
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Tidskriftsartikel (refereegranskat)abstract
- We present the results of a systematic literature review of research articles that self-identify as describing the implementation of innovations from mathematics education research in educational practice. We classified 103 articles according to study type, the type of teaching/learning phenomenon the implementation targeted, and whether the innovation carrier was a curriculum reform, professional development, or a curriculum resource. We found that interest in implementation research increased from a modest number of published studies prior to 2003 to a peak in 2021. Other results highlight that projects that targeted teaching in line with the U.S. National Council of Teachers of Mathematics process standards were dominant when curricular reform acted as a carrier. Planning and design aspects of such projects were rarely reported, and projects were rarely discussed theoretically. Instead, such projects were commonly researched by studying teachers’ reform enactment. We discuss the consequences of this imbalance.
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| 5. |
- Ahl, Linda Marie, 1970, et al.
(författare)
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New Demands on the Symbols and Formalism Competency in the Digital Era
- 2023
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Ingår i: Uffe Thomas Jankvist & Eirini Geraniou (eds.), Mathematical Competencies in the Digital Era. - Cham : Springer International Publishing. - 9783031101403 ; , s. 159-176
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Bokkapitel (refereegranskat)abstract
- Theoretical aspects of symbol systems and the theories of conceptual fields and representation by Vergnaud are used to unpack the symbols and formalism competency. We illustrate how mathematical symbols are initially used as labels for phenomena in concrete situations or through iconic representations. Later, however, developing mathematical symbols and formalism competency involves making an epistemological shift, where the situational or iconical grounding for the formalism must be replaced by a grounding involving relations in symbol systems. The introduction of digital tools, for example, programming, can complicate the relationship between grounding situations and formalism and hence needs specific didactical attention.
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| 6. |
- Ahl, Linda Marie, 1970, et al.
(författare)
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Polysemy and the role of representations for progress in concept knowledge
- 2021
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Ingår i: Sustainable mathematics education in a digitalized world. Proceedings of MADIF 12. - Göteborg : SMDF. - 1651-3274. - 9789198402445
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Konferensbidrag (refereegranskat)abstract
- Mathematics is a polysemic enterprise, where the same name is given to different things. Polysemy is present whenever mathematical patterns identified in different circumstances share the same structure. This structure will be subsumed under the same mathematical symbolism. Therefore, it is of interest to theorize upon progress in concept knowledge, with respect to the polysemic nature. We argue that progress in concept knowledge involves an epistemological shift that occurs when the meaning introduced by situations and iconic representations is replaced by meaning residing in non-iconic representations that exists independent of the situations and iconic representations. Our theorization can be used in teaching design and by curriculum developers.
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| 7. |
- Ahl, Linda Marie, 1970-, et al.
(författare)
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The role of language representation for triggering students’ schemes
- 2018
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Ingår i: Perspectives on professional development of mathematics teachers. - Gothenburg : Swedish Society for Research in Mathematics Education. ; , s. 49-59
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Konferensbidrag (refereegranskat)abstract
- Schemes were Piaget’s most important concept. Through work of Vergnaud, schemes were connected to representations and theoretical models from Piaget were connected to principal insights from Vygotsky. We suggest that the scheme concept can be elaborated further by detailing the relationship between schemes and semiotics. We consider a case of an adult student’s work on a situation involving average speed. Linguistic representations in the problem formulation triggers two separate schemes for the student, one associated to the speed concept and one to the arithmetic average. By identifying exemplary phenomena in the presented case, we show how previous theory connecting schemes and representations can be extended to allow alternative explanations for a well-known class of students’ errors.
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| 8. |
- Ahl, Linda Marie, 1970, et al.
(författare)
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The role of language representation for triggering students’ schemes
- 2018
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Ingår i: Perspectives on professional development of mathematics teachers. Proceedings of MADIF11: the eleventh research seminar of the Swedish Society for Research in Mathematics Education, Karlstad, January 23–24 2018.
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Konferensbidrag (refereegranskat)
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| 9. |
- Ahl, Linda Marie, 1970, et al.
(författare)
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Why is calculating the average speed difficult?
- 2018
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Ingår i: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education.
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Konferensbidrag (refereegranskat)
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| 10. |
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| 11. |
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| 12. |
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| 13. |
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| 14. |
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| 15. |
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| 16. |
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| 17. |
- Koljonen, Tuula, et al.
(författare)
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Evaluating the enactment of a scripted teaching model
- 2023
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Ingår i: Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). - Budapest : Eötvös Loránd University and ERME.
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Konferensbidrag (refereegranskat)
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| 18. |
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| 19. |
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| 20. |
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| 21. |
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| 22. |
- Teledahl, Anna, 1972-, et al.
(författare)
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Defining and measuring quality in students' mathematical writing: a systematic literature review
- 2024
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Ingår i: MATHEMATICS EDUCATION RESEARCH JOURNAL. - 1033-2170 .- 2211-050X.
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical communication, encompassing writing in, about, and for mathematics, is a critical competency. Defining excellent mathematical writing standards, however, remains challenging. To address this, we conducted a systematic review of 48 scholarly works on quality in mathematical writing. Our findings reveal mathematical writing for different purposes under scrutiny, including general mathematical writing, proof writing, reflective writing, expository writing, and descriptive writing during problem solving. To assess quality, researchers explore a variety of facets, such as syntax and semantics. Progression pathways vary, with both quantitative and qualitative evaluations-analysing text structure, writing style, and the use of different semiotic elements. It seems that in mathematics education, a consensus on quality measurement remains elusive. Proof writing is a notable exception. Among reviewed articles examining proof writing, a common set of standards emerges and provides valuable guidance. We propose that mathematical writing, perhaps especially in the context of reporting solutions in problem solving, can draw from proof writing standards. 'Good' mathematical writing would then require students to focus on (1) defining assumptions and assigning variables; (2) producing a coherent narrative, including relevant calculations (semantic issues); (3) using correct language, representations, and mathematical symbols (syntax issues); and (4) attending to what is appropriate in the context.
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| 23. |
- Teledahl, Anna, 1972-, et al.
(författare)
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Quality in students’ writing in mathematics
- 2022
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Ingår i: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). - : ERME / Free University of Bozen-Bolzano.
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Konferensbidrag (refereegranskat)
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| 24. |
- Teledahl, Anna, et al.
(författare)
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Writing down the Solution Separate from Solving the Problem
- 2023
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Ingår i: For the Learning of Mathematics. - 0228-0671. ; 43:2, s. 41-46
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Tidskriftsartikel (refereegranskat)abstract
- In this article we aim to discuss how teaching, focused on developing students’ ability to write this latter type of mathematical text, can be designed.
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| 25. |
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| 26. |
- Boesen, Jesper, 1971, et al.
(författare)
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Améliorer l'enseignement des mathématiques : le cas de la Suède
- 2009
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Ingår i: Revue internationale d'éducation - Sevres. - 1254-4590. ; :51, s. 91-101
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- In this article a Swedish Action Plan for Mathematics is presented, why was it initiated, what was its main goals and - in some detail - how to attain these goals. As both a mean for and as a consequence of the Action Plan’s intention to raise both individual students’ and public interest in mathematics the authors propose an enriched view of what mathematics for schooling can be. To conclude they list what has been done since the Action Plan was presented and exemplifies with some ongoing initiatives. Finally they relate some of the key aspects of the intentions of the Action Plan to the wider scope of science teaching.
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| 27. |
- Boesen, Jesper, 1971, et al.
(författare)
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Developing mathematical competence: From the intended to the enacted curriculum
- 2013
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Ingår i: Journal of Mathematical Behavior. - : Elsevier BV. - 0732-3123 .- 1873-8028. ; 33:1, s. 72-87
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Tidskriftsartikel (refereegranskat)abstract
- This study investigates the impact of a national reform in Sweden introducing mathematical competency goals. Data were gathered through interviews, classroom observations, and online surveys with nearly 200 teachers. Contrasting to most studies of this size, qualitative analyses were conducted. The results show that teachers are positive to the message, but the combination of using national curriculum documents and national tests to convey the reform message has not been sufficient for teachers to identify the meaning of the message. Thus, the teachers have not acquired the functional knowledge of the competence message required to modify their teaching in alignment with the reform. The results indicate that for complex reform messages, such as the competency message, to have intended impact on classroom practice, special attention needs to be put on the clarity of the message. To have high-stakes tests, for example, does not alone seem to be sufficient. © 2013 Elsevier Inc.
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| 28. |
- Boesen, Jesper, 1971, et al.
(författare)
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National-scale professional development in Sweden: theory, policy, practice
- 2015
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Ingår i: ZDM - the International Journal on Mathematics Education. - : Springer Science and Business Media LLC. - 1863-9690 .- 1863-9704. ; 47:1, s. 129-141
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Tidskriftsartikel (refereegranskat)abstract
- From 2012 to 2016 all teachers of mathematics, in primary through to upper secondary and adult education, in Sweden are to be given the opportunity of receiving state-coordinated professional development (PD), generally involving around one meeting per week for a year. We examine the ways in which this programme and its content are research-based by analysing the design principles of the PD and its content via a review of the underlying documents. We find that the research base for the design of the PD decisions is formulated only partly explicitly in the documentation, as is the case for the content. Nevertheless, the principles still largely conform to internationally recognised research-based models for PD and teacher change. In the discussion we propose that a relatively open design process, involving many stakeholders with knowledge of both theory and practice rather than an analytical examination of previous research, has contributed to the adoption of this format for the PD programme. © 2014, FIZ Karlsruhe.
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| 29. |
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| 30. |
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| 31. |
- Eriksson, Kimmo, et al.
(författare)
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Cultural Variation in the Effectiveness of Feedback on Students' Mistakes
- 2020
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Ingår i: Frontiers in Psychology. - : Frontiers Media SA. - 1664-1078. ; 10
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Tidskriftsartikel (refereegranskat)abstract
- One of the many things teachers do is to give feedback on their students' work. Feedback pointing out mistakes may be a key to learning, but it may also backfire. We hypothesized that feedback based on students' mistakes may have more positive effects in cultures where teachers have greater authority over students, which we assume to be cultures that are high on power distance and religiosity. To test this hypothesis we analyzed data from 49 countries taking part in the 2015 wave of the TIMSS assessment, in which students in the 4th and 8th grades were asked whether their teachers in mathematics and science told them how to do better when they had made a mistake. For each country we could then estimate the association between the reported use of mistake-based feedback and student achievement. Consistent with our hypothesis, the estimated effect of mistake-based feedback was positive only in certain countries, and these countries tended to be high on power distance and religiosity. These results highlight the importance of cultural values in educational practice.
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| 32. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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Higher-achieving children are better at estimating the number of books at home: Evidence and implications
- 2022
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Ingår i: Frontiers in Psychology. - : Frontiers Media SA. - 1664-1078. ; 13
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Tidskriftsartikel (refereegranskat)abstract
- The number of books at home is commonly used as a proxy for socioeconomic status in educational studies. While both parents' and students' reports of the number of books at home are relatively strong predictors of student achievement, they often disagree with each other. When interpreting findings of analyses that measure socioeconomic status using books at home, it is important to understand how findings may be biased by the imperfect reliability of the data. For example, it was recently suggested that especially low-achieving students tend to underestimate the number of books at home, so that use of such data would lead researchers to overestimate the association between books at home and achievement. Here we take a closer look at how students' and parents' reports of the number of books at home relate to literacy among fourth grade students, by analyzing data from more than 250,000 students in 47 countries participating in 2011 PIRLS. Contrary to prior claims, we find more downward bias in estimates of books at home among high-achieving students than among low-achieving students, but unsystematic errors appear to be larger among low-achieving students. This holds within almost every country. It also holds between countries, that is, errors in estimates of books at home are larger in low-achieving countries. This has implications for studies of the association between books at home and achievement: the strength of the association will generally be underestimated, and this problem is exacerbated in low-achieving countries and among low-achieving students.
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| 33. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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Socioeconomic Status as a Multidimensional Predictor of Student Achievement in 77 Societies
- 2021
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Ingår i: Frontiers in Education. - : Frontiers Media SA. - 2504-284X. ; 6
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Tidskriftsartikel (refereegranskat)abstract
- We reassess the relation between students' socioeconomic status (SES) and their achievement by treating SES as multidimensional instead of unidimensional. We use data from almost 600,000 students in 77 countries participating in the 2018 PISA assessment of student achievement in math, science, and reading. The composite measure of SES that PISA uses can be broken down into six component variables that we here use as simultaneous predictors of achievement. This analysis yields several new insights. First, in the typical society, two predictors (books at home and parents' highest occupational status) clearly outperform the rest. Second, a new composite measure based only on these two components often reveals substantially larger achievement gaps than those reported by PISA. Third, the analysis revealed remarkable differences between societies in the relation between achievement and wealth possessions. In most societies, the independent effect of wealth possessions on student achievement was zero or even slightly negative-but in the least developed societies it was strongly positive. These findings have implications for how SES achievement gaps should be measured and interpreted.
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| 34. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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Using TIMSS items to evaluate the effectiveness of different instructional practices
- 2019
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Ingår i: Instructional Science. - : Springer Science and Business Media LLC. - 0020-4277 .- 1573-1952. ; 47:1, s. 1-18
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Tidskriftsartikel (refereegranskat)abstract
- Can instructional quality be measured using TIMSS items on how often certain instructional practices are used in the mathematics classroom? We focused on three instructional practices that have been the topics of longstanding debates in the educational literature: memorizing formulas, listening to the teacher, and relating mathematics to daily life. In a multi-level multiple regression analysis, we examined how class-level responses to these items predicted mathematics achievement. In Sweden, across four waves of TIMSS, relating to daily life was a negative predictor of achievement, whereas memorizing formulas and listening to the teacher were positive predictors. This was also the typical pattern of results across all countries participating in two waves of the international TIMSS. Our findings are in line with certain positions on the abovementioned debates. Although conclusions are limited by the correlational nature of the data, we argue that TIMSS is a promising tool for evaluating the effectiveness of different instructional practices. We also suggest several improvements.
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| 35. |
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Förskolans matematik
- 2013
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Samlingsverk (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract
- Denna bok i NämnarenTema-serien behandlar förskolans matematik. Artiklarna är samlade under rubrikerna Leka, Räkna, Mäta, Lokalisera, Konstruera och Förklara. Dessa sex matematiska aktiviteter har beskrivits av Alan Bishop och återfinns i bakgrundstexterna till förskolans reviderade läroplan. I denna bok ges konkreta exempel på hur dessa aktiviteter kan komma till uttryck i förskolans verksamhet. Varje aktivitet är också beskriven med en kort in ledande text.
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| 36. |
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| 37. |
- Helenius, Ola, 1970
(författare)
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A stakeholder analysis of the development of a large scale professional development program.
- 2021
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Ingår i: Implementation and Replication Studies in Mathematics Education. - : Brill. - 2667-0135 .- 2667-0127. ; 1:2, s. 227-256
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Tidskriftsartikel (refereegranskat)abstract
- The development of a large-scale professional development project for Swedish mathematics teachers is retrospectively examined. By referring to documentation produced by stakeholders in the development process, the stakeholder’s design recommendations and underlying assumptions on teacher development are described. Seeing the development as a co-determination process explains how research-based principles appearing early in the process gradually change to become something different in the end, without the reasons for this shift ever being explicitly discussed in stakeholders’ documentations. It is discussed whether the distributed way of constructing the program might cause difficulties in sticking to an explicit theory of change.
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| 38. |
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| 39. |
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| 40. |
- Helenius, Ola, 1970
(författare)
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Explicating professional modes of action for teaching preschool mathematics
- 2018
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Ingår i: Research in Mathematics Education. - : Informa UK Limited. - 1479-4802 .- 1754-0178. ; 20:2, s. 183-199
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Tidskriftsartikel (refereegranskat)abstract
- Play-based preschool pedagogy usually relies on informal teaching while policy trends and some research call for increased formalisation of the pedagogy. Using Bernstein's concepts of classification and framing, this article characterises mechanisms that link evaluation of preschool to the push towards the formalisation of teaching in preschool. Moreover, it is suggested how preschool teaching of mathematics can be conceptualised in a way that widens the pedagogical responsibilities of the teachers to include a broader range of social activities than typically expected. These responsibilities concern how teachers are involved in pedagogical situations, if situations are planned and if the mathematics is a pedagogical goal in the situation or instrumental in some other activity. It is argued that a practice built on these principles could both honour well-developed play-based preschool practices and provide a structure for teaching preschool mathematics in which using traditional child-teacher interaction is only one of many options.
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| 41. |
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| 42. |
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| 43. |
- Helenius, Ola, 1970
(författare)
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Godkänt är inte bra nog
- 2014
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Ingår i: Origo. - 2000-1940. ; 2014:2
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 44. |
- Helenius, Ola, 1970
(författare)
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Hedda mäter
- 2012
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Ingår i: Nämnaren. - 0348-2723. ; :2012:2
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Barn lär sig mäta när de deltar i sammanhang där mätning har en central roll. Att mäta växter som växer är fascinerande. I artikeln möter vi Hedda som tar hjälp av vinkelhake, linjal, tumstock och kartongark när hon ska mäta sina växter och dokumentera tillväxten.
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| 45. |
- Helenius, Ola, 1970, et al.
(författare)
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Hur många ryms i klassrummet? En introduktion till areabegreppet
- 2005
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Ingår i: Nämnaren. - 0348-2723. ; :2005:4
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Area är ett begrepp som tar sin utgångspunkt i en konkret problemställning om storleksbestämning av ytor. Vid introduktion av areabegreppet kan det vara lämpligt att fundera på vilka egenskaper ett sådant storleksmått bör ha.
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| 46. |
- Helenius, Ola, 1970, et al.
(författare)
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IKT i matematikundervisningen
- 2015
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Ingår i: Skolverket , 2015. , 5 s.. ; Lärportalen för matematik Grundskola åk 7-9
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 47. |
- Helenius, Ola, 1970
(författare)
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IKT inte självklart i matten
- 2013
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Ingår i: Origo. - 2000-1940. ; :2013:1
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 48. |
- Helenius, Ola, 1970
(författare)
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Information från NCM: Leken i förskolans läroplan
- 2012
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Ingår i: Nämnaren. - 0348-2723. ; :2012:4
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Lek är ett av de mest fundamentala begreppen i förskolans läroplan. Ett medvetet bruk av leken för att främja varje barns utveckling och lärande ska prägla verksamheten i förskolan, heter det bland annat. Det betyder givetvis att de av förskolans mål som handlar om matematiken också måste ses ur ett perspektiv där lek och lärande går hand i hand.
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| 49. |
- Helenius, Ola, 1970
(författare)
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Kompetenser och matematik
- 2006
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Ingår i: Nämnaren. - 0348-2723. ; :2006:3, s. 11-15
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Att försöka skapa strukturer i vad det innebär att kunna matematik är en mångårig internationell trend. Denna artikel anknyter till Vad är kunskap i matematik i förra numret. Här presenteras idéer från den danska rapporten Kompetencer och Matematiklæring. Åtta delkompetenser som tillsammans utgör den totala matematiska kompetensen bildar ryggrad i de danska tankarna.
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| 50. |
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