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- Bråting, Kajsa, Docent, 1975-, et al.
(author)
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Exemplifying different methodological approaches of analysing textbooks in mathematics
- 2022
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In: The relation between mathematics education research and teachers' professional development. - Göteborg : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 1651-3274. - 9789198402452 ; 16, s. 125-129, s. 125-129
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Conference paper (peer-reviewed)abstract
- In this symposium, we will discuss different ways of analysing mathematics textbooks from a methodological point of view. The discussion will be based on examples from five separate ongoing analyses of Swedish textbooks divided into two methodological approaches; one where analysis is conducted within an established theoretical framework, and one where analytical tools are constructed through combining aspects of different theories. The symposium will be held at the conference MADIF-13.
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| 3. |
- Palm Kaplan, Kristina
(author)
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International large-scale assessments and mathematics textbooks in a curriculum reform process : Changes in lower secondary school algebra in Sweden 1995–2015
- 2019
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Doctoral thesis (other academic/artistic)abstract
- Reforming a curriculum entails more than simply launching new steering documents: it includes the development of new materials, evaluation of reform and identification of needs for further action. Drawing from algebra material surrounding the 2011 Swedish curriculum reform, this thesis contributes to understanding the process of curriculum reform concerning mathematics textbooks and international large-scale assessments.Two analytical frameworks are applied to algebra tasks in six mathematics textbooks from three series, published in 1995–2015, and algebra items from four consecutive TIMSS tests in 2003, 2007, 2011 and 2015. These frameworks are a Systemic Functional Linguistics-framework based on a social-semiotic perspective and a framework adapted from different views on school algebra. They are used in order to understand algebra characteristics in terms of school algebra discourses and algebraic activities. Additionally, the relationship between Swedish students’ results on TIMSS’ algebra-items and algebra characteristics of the test items is explored statistically. The findings are viewed against the test structure over time.The results show that five school algebra discourses are identified in both materials: the symbolic, arithmetical, geometrical, (un)realistic and scientific discourse. However, in the TIMSS tests, a relational discourse was further identified. The materials comprise the same algebraic activities, although in somewhat different proportions. The major change in textbooks is conservative since it is an increase of the (un)realistic discourse, which concerns features that may have been prevalent in the Swedish syllabus already a hundred years ago. This discourse may also be interpreted as a transformation of a reform idea in the syllabus, on mathematical literacy, into quite superficial everyday connections.A comparison of the materials show that the algebra characteristic which increases most in textbooks, decreases in TIMSS. Further, students with high achievements on TIMSS perform significantly better on test items with algebra characteristics that decrease in proportion, compared with those which increase in proportion. Relatively seen, the difficulty of the tests for these students thus increases over time. This implies that the validity of interpreting TIMSS results as a knowledge trend is lessened. It is therefore less relevant to use TIMSS results for evaluating and identifying needs for further action. It is suggested that conclusions about student achievements in algebra should not be drawn based on the validity of interpreting and using the aggregate of TIMSS results in mathematics. Also, policy makers should pay more attention to how TIMSS results are used as a base for curricular reform and evaluation.
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| 6. |
- Bråting, Kajsa, 1975-, et al.
(author)
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Algebra för lärare
- 2017. - 1
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Book (other academic/artistic)
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| 7. |
- Bråting, Kajsa, 1975-
(author)
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Ambiguities of fundamental concepts in mathematical analysis during the mid 19th century
- 2012
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In: Foundations of Science. - : Springer. - 1233-1821 .- 1572-8471. ; 17:4, s. 301-320
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Journal article (peer-reviewed)abstract
- In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke's (Hist Math 20(3):265-284, 1993) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Bjorling's general view of real- and complexvalued functions. We argue that Bjorling had a tendency to sometimes consider mathematical objects in a naturalistic way. One example is how Bjorling interprets Cauchy's definition of the logarithm function with respect to complex variables, which is investigated in the paper. Furthermore, in view of an article written by Bjorling (Kongl Vetens Akad Forh Stockholm 166-228, 1852) we consider Cauchy's theorem on power series expansions of complex valued functions. We investigate Bjorling's, Cauchy's and the Belgian mathematician Lamarle's different conditions for expanding a complex function of a complex variable in a power series. We argue that one reason why Cauchy's theorem was controversial could be the ambiguities of fundamental concepts in analysis that existed during the mid-nineteenth century. This problem is demonstrated with examples from Bjorling, Cauchy and Lamarle.
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| 8. |
- Bråting, Kajsa, 1975-, et al.
(author)
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Development of algebraic thinking : opportunities offered by the Swedish curriculum and elementary mathematics textbooks
- 2019
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In: Nordisk matematikkdidaktikk, NOMAD. - 1104-2176. ; 24:1, s. 27-49
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Journal article (peer-reviewed)abstract
- In search of the reasons for Swedish students’ low achievement in algebra in inter-national and national evaluations, we investigate how the development of algebraic thinking is addressed in the Swedish national mathematics curriculum and two widely used mathematics textbook series for grades 1–6 in Sweden. The analytical tool used is based on the classification of ”big ideas” which research has shown as important for developing pupils’ algebraic understanding in early school grades. The results show that functional thinking, expressions, and equations are well represented topics both in the curriculum and the textbooks; however generalized arithmetic is a topic that is poorly developed in both the curriculum and the textbooks.
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