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1.	Ahl, Linda Marie, 1970, et al. (author) A framework for analyzing progress in concept knowledge in mathematics textbooks 2021 In: Bringing Nordic mathematics education into the future. Preceedings of Norma 20. The ninth Nordic Conference on Mathematics Education Oslo, 2021. - Göteborg : SMDF. - 1651-3274. Conference paper (peer-reviewed)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.

Ahl, Linda Marie, 1970, et al. (author)
A framework for analyzing progress in concept knowledge in mathematics textbooks
2021
In: Bringing Nordic mathematics education into the future. Preceedings of Norma 20. The ninth Nordic Conference on Mathematics Education Oslo, 2021. - Göteborg : SMDF. - 1651-3274.
Conference paper (peer-reviewed)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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