Reflection on Mathematics' Role in Citizenship

In Elaine Simmit's article she discussed the potential problems with associating mathematics as a mere collection of facts; as black and white. Surely no pure mathematician would ever contend with these notions. Mathematics is built on a foundation that EVERY statement can only take on exactly one of two values: true and false. All of mathematical logic is built around this concept and all theorems proven is based on this essential assumption. Essentially, assuming the 'universal' axiom that a statement is something that is either true or false (but not both) and a given set of axioms, all mathematical theorems may be proven. While this is essential to building rigor in mathematics it is problematic in mathematics education. The problem is the lack of emphasis that PURE MATHEMATICS need not translate or apply to REAL LIFE situation. For example, there can be no doubt that a sequence of independent and identically distributed random variables with finite mean converge in mean almost surely, it is NOT without doubt that a given sequence of random variables in real life SATISFY the conditions for the theorem. Thus it is important for us educators to identify the APPLICATION of mathematics in real life situation. This is already strongly advocated in, for example, social studies classrooms where there is a strong emphasis on analysis of current events and to unfold the intricacies of modern society and politics. This is not done in mathematics. When thinking of 'real life' problems in mathematics we usually associate extremely trivial things like finding the correct amount of change. This is tantamount to being able to read road signs as 'reading in real life'. While not a FALSE statement this obviously does not achieve the objective. Students are not challenged and don't learn anything. Instead, students need to be implored to discover more sophisticated applications of mathematics, for example how survey companies collect data, how data collected from the census is analyzed by the government and how does this influence public policy, the soundness of using 'average income' as a barometer to judge the social well-being of a community, etc. These will ultimately produce a more engaged learning environment and produce better, more quantitatively literate citizens.