| 1. |
- Lindegren, Cecilia, et al.
(författare)
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Förståelse för tal i bråkform
- 2012
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- En undersökning om elevers förståelse för tal i bråkform genomfördes i form av diagos på 78 elever i årskurs 6. Lösningsstrategier som eleverna använder kan bidra till förståelse av elevers lärande om bråk i matematik.
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| 2. |
- Sönnerhed, Wang Wei, 1968-
(författare)
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Mathematics textbooks for teaching : An analysis of content knowledge and pedagogical content knowledge concerning algebra in Swedish upper secondary education
- 2011
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. Similarly, what is missing from the textbook may not be presented by the teacher. The study is based on an assumption that pedagogical content knowledge is embedded in the subject content presented in textbooks. Textbooks contain both subject content knowledge and pedagogical content knowledge. The primary aim of the study is to explore what pedagogical content knowledge regarding solving quadratic equations that is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content related to solving quadratic equations from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom. The study concerns a teaching perspective and is intended to contribute to the understanding of the conditions of teaching solving quadratic equations. The theoretical framework is based on Shulman’s concept pedagogical content knowledge and Mishra and Koehler’s concept content knowledge. The general theoretical perspective is based on Wartofsky’s artifact theory. The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The study contains four rounds of analyses. The results of the first three rounds have set up a basis for a deep analysis of one selected textbook. The results show that the analyzed Swedish mathematics textbooks reflect the Swedish mathematics syllabus of algebra. It is found that the algebra content related to solving quadratic equations is similar in every investigated textbook. There is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula, which implies that classroom teaching may focus on quadratic formula. Factorization method is presented for solving simple quadratic equations but not the general-formed quadratic equations. The study finds that the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models that can be traced back to the history of algebra. These four geometrical models are applied for illustrating algebra rules and construct an overall embedded teaching trajectory with five sub-trajectories. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the pedagogical content knowledge related to quadratic equations.
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| 3. |
- Sönnerhed, Wang Wei, 1968-
(författare)
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Mathematics textbooks related to algebra content
- 2012
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Ingår i: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. - Linköpings universitet. - 9789197393485 ; , s. 209-210
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 4. |
- Sönnerhed, Wang Wei, 1968-
(författare)
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Three different methods for solving quadratic equations
- 2011. - 1:1
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Ingår i: Voices on learning and instruction in mathematics. - Göteborgs universitet : Nationellt centrum för matematikutbildning (NCM). - 9789185143207 ; , s. 275-285
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 5. |
- Wang Wei, Sönnerhed, 1968
(författare)
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Quadratic equations in Swedish textbooks for upper-secondary school
- 2021
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Ingår i: LUMAT. - 2323-7112. ; 9:1, s. 518-545
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Tidskriftsartikel (refereegranskat)abstract
- This paper analyzes the content and tasks involving quadratic equations in eight mathematics textbooks published during the period 2000-2012 at the uppersecondary level in Sweden. The study applies the theoretical hypothetical learning trajectory (HLT) framework combining conceptual and procedural knowledge. The analysis includes horizontal and vertical dimensions within an HLT. The aim is to explore embedded HLTs and learning opportunities from both dimensions in these textbooks. A total of 250 examples and 1,068 tasks have been examined. Results show that all the textbooks contain algebra identities and four different methods for solving quadratic equations as well as their applications as a core hypothetical learning trajectory but differ in how an HLT starts and ends. Geometrical representations for some algebra identities and completing the square are widely used in both theoretical presentations and tasks, which implies that conceptual learning is encouraged among the Swedish textbooks. At the same time, procedural knowledge is still emphasized as a basic but important learning process. © 2021 University of Helsinki. All rights reserved.
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