Variationens betydelse för elevernas lärande. Relationen mellan en funktions graf och grafen till funktionens derivata
Sammanfattning: The significance of variation for students’ learning – The relationship between a graph and its derivative graph The concept of derivative is multifaceted and can be described in a variety of representations. Nevertheless, students ́ knowledge of the concept is often restricted to a set of loosely connected algebraic actions and many students facing a graph express the need for a formula in order to use the differentiation rules. In previous research, students ́ capability to change between representations is highlighted as very important. This view was established several decades ago but how to design instruction in the most appropriate way, to make it possible for the students to achieve this capability, still needs to be explored. The aim of this licentiate thesis is to describe how students ́ learning of the relationship between a graph and its derivative graph can be related to instruction. The methodological approach is Learning Study, an iterative and cyclic process where researchers and teachers cooperate in designing, implementing, revising and analysing th e outcomes of a lesson plan. The study is conducted at a Swedish upper secondary school and comprises 68 students, aged 17-18 years, attending four different programmes. In a Learning Study, the points of departure are previous research results and the participating students ́ initially expressed perceptions. To examine the latter, qualitative interviews with six students were conducted. Based on the insights from the interviews and the previous research results, a lesson plan was designed and during this process, Variation Theory was used as a theoretical framework. According to Variation Theory, learning is equivalent to discerning critical aspects of a phenomenon and for this to occur; the patterns of variation and invariance created during the instructions are determinant.
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