For the first question, since we thought that no objective criteria for observing such behavior patterns existed, we sent a questionnaire to mathematics education leaders throughout Japan to gather opinions on this issue. Most concrete comments gathered could be summarized as follows: In facing a problem situation, the students can mathematize the situation and deal with it, or in other word, In analyzing a problem situation, the students bring forth an (important) aspect of the problem into their favored way of thinking by mobilizing their repertoire of learned mathematics, reinterpreting it to deal with the situation mathematically, and then applying their preferred technique