Konferensbidrag WALS 2017 –
av Constanta Olteanu, Linnéuniversitetet
Many students in upper secondary school and at university have difficulties with the distinction between the concepts of equation and function. Research has found that if students do not acquire sufficient understanding they tend to compartmentalise their knowledge and may later experience difficulties when addressing mathematically related problems. In addition to that, if they do not understand, the mathematical skills/knowledge remains within the mathematics classroom, so that there is a struggle to make connections with real life experiences.
In this presentation the focus is to present a theoretical argument for these difficulties, with some examples. The presentation illustrates how teachers make use of a learning theory, the variation theory, as well as their own professional expertise and collaboration to help students improve their understanding of the structure sense of function and equation. A learning study involves a group of teachers who undertake theoretically grounded collaborative action research in their own practice. The primary role of the researcher in a learning study is to have a professional dialogue with the teachers and to provide professional support when necessary. Furthermore, the major focus of a learning study is on the objects of learning, i.e., on what students are expected to learn, rather than on the teaching arrangements. The object of learning in this study is the understanding of the structure sense of equation and function.
According to the variation theory, in order to help students appropriate certain objects of learning, certain patterns of variation and invariance that are co-constituted by the learners and the teacher are necessary. To exemplify this, the presentation focuses on learning studies conducted in mathematics in Sweden. The results show that there was a marked improvement in students’ mathematical understanding after learning studies grounded on the variation theory were introduced. The results also show that professional learning through collaborative action research supported the teachers to further develop their own knowledge of mathematics, their understanding of students’ thinking and how a variation theoretic approach to mathematics teaching can contribute to students’ learning.
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