Research on the validity and Effectiveness of Two-Axes Process Model of Understanding Mathematics

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As a result of this research, we find out the followings. First, we can exemplify the validity and effectiveness of the "two-axes process model" of understanding mathematics by the case study of the elementary school mathematics class. Second, we might be able to characterize such a teaching and learning of mathematics that enables children to understand mathematics deeply and in their meaningful way as the dialectic process of children's individual and social constructions in their classroom. In order to realize such mathematics classroom, it is suggested that a teacher should make a plan of teaching and learning mathematics in the light of "two-axes process model", and embody it with teaching materials of a topic in due consideration both of the objectives and the actual state of children. The teacher also should play a role as a facilitator for the dialectic process of individual and social constructions through a discussion with children and among them.There are two important features of teacher's role in the process of teaching and learning mathematics. The one is related to children's individual construction and it is to set the problematic situation where children are able to have their own learning tasks and encourage them to have various mathematical ideas and ways individually. The other is related to children's social construction and it is to encourage and allow them to explain, share and discuss their various mathematical ideas and ways socially in the classroom.