In the introduction to a lesson a teacher will often differentiate between the “situation or original problem presented firstly by the teacher” and “the problem truly recognized by the children themselves based on the situation or original problem presented firstly by the teacher.” By referrinHowever, the interpretation of the words “task” and “problem” can very widely, and some teacher refer to the former as the “problem” and the latter as the “task.”g to the former as a “task” and the latter as a “problem.”Either way, one is still a mere starting point which is simply given by the other person.The other is a authentic aim which children strongly desire to seek out solution for themselves.This is the essential difference between “task” and “problem.”This article sets aside the issue of this diversity in definitions for the sake of convenience, referring to the former as a “task” and the latter as a “problem.”For instance, the “Meate (aim)” of arithmetic lessons in Japanese the elementary school would correspond to the latter “problem” in this article.