The phases for teaching do not mean that teachers have to teach mathematics step by step. For example, the phase of independent solving does not mean that all children have to solve the task in this phase even if the teacher supports the children's work. Children who cannot solve the given task can learn from their friends how to solve it in the phase of explanation and discussion. At the end, children who have failed still have the chance to apply learned ideas to the task for
further development. Basically, before the class, the teachers develop the lesson plans for supporting the children in each phase and set the decision-making conditions for observing, assessing, and supporting the children. In Part II, the assessment to develop mathematical thinking in the teaching process is explained for each lesson plan.