In the master's thesis I outline some of the important aspects of learning with understanding: understanding a mathematical concept, assessing understanding, the image and the definition of mathematical concepts, graphic organiser as a tool for facilitating understanding mathematical concepts. In particular I focus on the theory of Tall an Vinner on concept image, its structure, consistency, and the discrepancy between the concept definition and the concept image, i.e. the cognitive processes used to understand them.
In the thesis I also consider graphic organiser as a tool for improving understanding concepts, the usage of graphic organiser, including its usage in solving problems, and the reasons for appropriateness of its introduction into mathematics classes in Slovenia.
In the empirical part of the master's thesis I present a pilot research establishing whether the use of graphic organiser in teaching improves pupils' understanding of direct proportionality. In particular I consider whether pupils that use graphing organiser exhibit a better concept image of direct proportionality with respect to those that do not use it. Furthermore I analysed five graphic organisers on the topic of direct proportionality from a random sample of pupils.
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