The following subjects were discussed by Educational psychologists, Mathematicians, and School teachers. The organizer of this symposium intends, through all the propositions and discussions, to make clear some points on mathematics teaching by examining the acceptance of such hypothesis as follows: 1. Children's learning in school is the core of the whole human learning activities. Therefore, the learning psychology or the educational psychology which dose not cover that field can be called "pseudo-learning psychology" or "non-educational psychology". 2. Children's learning activities in school are the products of teaching activities. Therefore, the most effective method for studying the children's learning process is the action-research with the teaching strategy which evokes a certain purposive activity. 3. The concept that children's learning activities in school is only due to the developmental stage like age or grade, etc, is far from a proper and effective theorization. For, such a view ignores the relation between learning activities and subject matters, and also abandons the effort to operate teaching activities. 4. Children's learning in school is never the same as putting data or informations into a computer, but it is to reconstruct the rule-systems. 5. The problems in early-mathematics teaching can be understood and solved only through the study of class activities.