As the next Education Ministry curriculum guidelines have been announced, which is the largest revision ever made in the post war period, the time is coming to start the new curriculum based on “qualification and competence.”  It is emphasized in mathematics more than ever to cultivate the general-purpose competence by making the “mathematical perspectives and ways of thinking” work as it is expected to enhance the mathematical activities being aware of its involvement in the actual society throughout each school stage.  This research study aims at shedding light on the concrete features of the critical thinking the elementary school students in the upper grades demonstrate by paying attention to the critical thinking competence as the general-purpose competence and developing and practicing arithmetic classes to foster such competence.  To achieve those, this research, based on the perspective of critical mathematics education by Skovsmose (1994), focused on the socially openended problem (Baba, 2009) as a methodological aspect.  During the session “Purchasing of a car”, which we devised, students’ various values were expressed and we observed our students making full use of their diverse critical thinking consisting of mathematical judgments and social value judgments so as to get a solution.  In the problem given, mathematical tools such as tables and formulas were used by elementary school students.  This mathematical tool was used to integrate various social values and mathematical models based on the values. This suggests that the lesson practice featuring socially open-ended problem was successful in terms of fostering critical thinking skills in students.  While we acknowledge the existence of diverse values and the mathematics used with those values, fair critical thinking of students should be further cultivated.  In addition, in revealing the social values of children, it was suggested that, when socially open-ended problem is given to children, children are required to grasp the context of the problem as their own affairs.  For future work, the development of multifaceted methods to assess the critical thinking of students are required.