| 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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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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| 5. |
- 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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| 6. |
- 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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| 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. 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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| 8. |
- 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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