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  • 1.
    Gunnarsson, Robert
    et al.
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Hernell, Bernt
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Sönnerhed, Wang Wei
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    On the use of emphasizing brackets when learning precedence rules2012In: Evaluation and comparison of mathematical achievement: Dimensions and perspectives: Proceedings of Madif 8 / [ed] C Bergsten, E Jablonka, M Raman, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2012, p. 209-210Conference paper (Refereed)
  • 2.
    Gunnarsson, Robert
    et al.
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Hernell, Bernt
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Sönnerhed, Wang Wei
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Useless brackets in arithmetic expressions with mixed operations2012In: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education / [ed] T.Y. Tso, The International Group for the Psychology of mathematics Education , 2012, p. 2-275-2-282Conference paper (Refereed)
    Abstract [en]

    There can be different intentions with brackets in mathematical expressions. It has previously been suggested that mathematically useless brackets can be educationally useful when learning the order of operations in expressions with mixed operations. This paper reports how students (12-13 years) deal with the implicit mental conflict between brackets as a necessary part of the order of operations and brackets to emphasize precedence. The students taking part in this quasi-experimental study were instructed on the order of operations, but were also indirectly exposed to different use of brackets. It is concluded that emphasizing brackets impede the transfer from a left-to-right computation strategy to the use of precedence rules.

  • 3.
    Lindegren, Cecilia
    et al.
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Welin, Ida
    Sönnerhed, Wang Wei
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Förståelse för tal i bråkform2012Other (Other academic)
    Abstract [sv]

    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. 

  • 4.
    Sönnerhed, Wang Wei
    Institutionen för pedagogik, kommunikation och lärande, Göteborgs universitet.
    Mathematics textbooks for teaching: An analysis of content knowledge and pedagogical content knowledge concerning algebra in Swedish upper secondary education2011Licentiate thesis, monograph (Other academic)
    Abstract [en]

    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.

  • 5.
    Sönnerhed, Wang Wei
    Institutionen för pedagogik, kommunikation och lärande, Göteborgs universitet.
    Three different methods for solving quadratic equations2011In: Voices on learning and instruction in mathematics / [ed] Jonas Emanuelsson, Laura Fainsilber, Johan Häggström, Angelika Kullberg, Berner Lindström, Madeleine Löwing, Göteborgs universitet: Nationellt centrum för matematikutbildning (NCM), 2011, 1:1, p. 275-285Chapter in book (Other academic)
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