Abstract
The process of mathematical problem solving can be seen as a continuation of construction and reconstruction of a mathematical model, since we must check up whether the mathematical model reflects the mathematical aspects of a real world problem correctly and whether the outcome resulting from the operation of the mathematical model is suitable for the real world problem. Observing some lessons given via problem solving, we can conclude that inquiries about the value, validity and an extent of applicability of the mathematical model including the critical point of view to the model give rise to zigzag path between the real world problem and the mathematical world. Making the inquiries to the model constitutes one of the domains of mathematical activity-the meta domain of mathematical activity-and the domain is characterized as the following: (1) the meta domain depends rather on the series of problems than on a student as a problem solver and it consists of factors that affect the process of problem solving, (2) the teacher needs to develop questions based on the problems that activate the meta domain of students, (3) the meta domain of each student can be enriched through the internalization of the inquiries made by the teacher and other students.
