7/2/2023 0 Comments Equal definition in math3 + 5 = _ + 2) in Grades 1–3 and equations and expressions in Grades 4–6. ( 2018) found that Swedish textbooks are rich in tasks using equalities, for example, open number sentences (e.g. As part of this research project, Hemmi et al. Possible causes for the lack of improvements among Swedish students are studied in an ongoing research project in which Swedish school algebra is characterized, by analyzing steering documents and textbooks and by conducting focus group interviews with teachers (Bråting, Madej & Hemmi, 2018). However, we have not yet seen any improvements to Swedish students’ algebraic skills, at least if we consider the results of the TIMSS evaluations. Recently, a new version of the textbook was published (Häggström, Kilhamn, & Fredriksson, 2019). Hence, early algebra and algebraic thinking is part of “Algebra for all,” but it also includes traditional algebraic content like formal equation solving. In this textbook, algebra is described by using Usiskin’s (1988) four aspects of algebra and Linchevski’s ( 1995) definition of pre-algebra. The aim of the textbook was to make algebra available to all, that is, all mathematics teachers and all students (Bergsten et al., 1997). A specific algebra textbook adapted to teacher education (Bergsten, Häggström, & Lindberg, 1997) was published in the 1990s, and has been used at several universities. Furthermore, in-service programs for teachers have been implemented and since the 1990s there has been a strong emphasis on the “Algebra for all” movement, ensuring that all students have the opportunity to study algebra (Hemmi, Bråting, & Lepik, 2020). Inspired by the early algebra movement, Sweden has revised its national curriculum and today algebra is introduced already in Grade 1 with, for example, the importance of the equal sign forming part of the core content in Grades 1–3 (Swedish National Agency of Education, 2018). In recent decades, several efforts have been made in Sweden to improve students’ algebraic knowledge. Even in 1995, when Swedish students performed the best ever on the TIMSS, their results in algebra remained poor (Hemmi et al. In international evaluations, such as the TIMSS, 1 Swedish students’ results in algebra have been below average since the 1960s (Murray & Liljefors, 1983 Swedish National Agency of Education, 2008, 2012, 2016a). In Sweden, which is the context of this study, algebra has always been problematic for students. In recent years, research has shown that it is possible to teach algebra already in earlier grades by, for example, using mathematical relations and patterns to develop algebraic thinking (Kieran, Pang, Schifter, & Fong Ng, 2016). This emphasizes the importance of research on mathematics education in general, and specifically on the teaching and learning of algebra. Brandell, Hemmi & Thunberg, 2008 Hemmi, Bråting, Liljekvist, Prytz, Madej, Pejlare & Palm Kaplan, 2018). Profound knowledge in algebra is important for higher studies in mathematics (e.g.
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