Practical Research on Improving Primary School Mathematics Lessons Based on the Two-Axes Process Model of Understanding Mathematics

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As a result of this research, the followings are found out. First, the "two axes process model" of understanding mathematics can be embodied and used for improving primary school mathematics lessons as the teaching and learning mathematics in a classroom by analyzing mathematics curriculum and teaching materials. Second, we can identify and refine the three principles and three methods for designing lessons based on the "two-axes process model" of understanding mathematics;Principle 1 [Understanding mathematics as a complex and dynamic process], Principle 2 [Setting up hierarchical levels and learning stages], Principle 3 [Emphasizing both activities of individual and social construction], Method 1 [Clarifying hierarchical levels of understanding], Method 2 [Assessing students' level of understanding], and Method 3 [Embodying learning stages]. Third, these principles and methods are used as effective guidelines for a teacher when he/she improving mathematics lessons in order to deepen his/her students' understanding of mathematical concepts, properties and relations through the long-going and intensive "lessen study" with teachers in a school. Fourth, the "two axes process model" of understanding mathematics and its principles and methods can be applicable in pre-service teacher training and in-service teacher education at primary school level for improving their mathematics lessons.