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- W605890 abstract "This study explores difficulties that prospective elementary mathematics teachers have with the concepts of ratio and proportion, mainly when they are engaged in solving problems using algorithm procedures. These difficulties can be traced back to earlier experiences when they were students of junior and high school. The reflection on these difficulties by student teachers, comparing to informal ways of solving the problems is a fundamental step of the pre-service programme in which they are involved. In this communication I also present and discuss an attempt to promote development of prospective teachers’ own knowledge of ratio and proportion as well as their awareness of the pupils’ difficulties on this subject. Teacher education programmes should provide both a profound mathematics understanding of the basic concepts of mathematics and the capacity of future teachers to be aware of the difficulties and the misconceptions of the students (e.g. National Council of Teachers of Mathematics, 1989, 1991, 2001), in order to enable future teachers to create adequate learning situations for their students. One of the basic concepts of the Portuguese elementary mathematics curriculum (grades 6-9) is the proportionality concept, which has been an obstacle to the learning of Mathematics. Most of the teachers teach this theme in a very formal way, emphasising the memorisation of the rules. Researchers on proportional reasoning have been looking for children’s strategies and errors (e.g. Hart, 1984, Lamon, 1993, Vergnaud, 1988). Vergnaud has mainly distinguished two kinds of strategies to solve situations involving direct proportions: the scalar operator “within” the same magnitude and the functional (across the measures) “between” the two magnitudes. Teachers should be aware of their own strategies and errors when they are dealing with situations of proportionality both direct (isomorphism of measures) and “inverse” (product of measures). They need to understand the differences between these two structures, respecting the invariance and the Cartesian graphs and to know what is the model that is underlying a specific problem. In this study I will focus on the procedures and on the reasoning of future teachers in solving proportionality problems in the context of a teacher education programme. I begin by providing a short explanation of the programme inasmuch as it seems important to understand the process that prospective teachers followed until being prepared to elaborate lessons for their future pupils to teach ratio and proportion. THE TEACHER EDUCATION PROGRAMME" @default.
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- W605890 date "2003-07-01" @default.
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- W605890 title "Prospective Elementary Teachers' Misunderstandings in Solving Ratio and Proportion Problems." @default.
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