Exploring Basic Components of the Process Model of Understanding Mathematics for Building a Two Axes Process Model
The purpose of this study is to make clear what kind of characteristics a model of understanding mathematics should have so as to be useful and effective in mathematics education. The models of understanding presented in preceding papers are classified into two large categories, i. e. "aspect model" and "process model". Focusing on the process of understanding mathematics, reflective thinking plays an important role to develop children's understanding, or to progress children's thinking from a level to a higher level of understanding. As a theoretical framework, a process model consisting of two axes is presented for further studies. The vertical axis in the model implies levels of understanding and the horizontal axis implies learning stages. At any level of understanding, there are three stages, i. e. intuitive, reflective and analytic stage.