Our society is increasingly dependent on technologies such as in the life sciences and information technologies. The technologies create alternatives and the choice among alternatives is guided by what the individual values. On the other hand, Bishop (1991) pointed out the danger that the general public and students understand that mathematics learning is regarded in many countries as being unreal and value-free, mainly because of the abstract nature of mathematics. This gap between social reality and students’ perceptions deprives many students of a willingness and positive attitudes towards problem-solving in mathematics. This chapter proposes a new approach to dealing with social values through problem-solving. Baba (2007, 2009) has named this type of problem “socially open-ended problem” which elicits students’ social values by extending a traditional open-ended approach (Shimada 1977). This chapter describes some basic ideas and discusses how the social values are treated while dealing with socially open-ended problems.