The misuse of Logic

A Google search of the word logic turns out 130,000,000 results. Ronald Munson, in his book The Element of Reasoning, defines logic as a "Branch of philosophy concerned with the distinction between correct and incorrect reasoning. It commonly comprises both deductive and inductive arguments." Logic is taught in math classes, in writing courses, and even in physical education, and yet some have not understood it. Everyday Americans use logic to form opinions, having been trained in public school to do so. However, Americans also misuse logic, having been trained to do so by their post-modern society.
Monday through Friday from 1-6pm I work at an after-school program for the YMCA with fourth and fifth graders. I see the homework they have and how they must use problem-solving skills to solve problems; basically they are using logic to figure out a correct solution. There are steps and directions to these problems clearly written out at the top of their worksheet. The children are well versed in solving these problems and yet do not apply what they learn to their lives on the playground. These children have been taught more than just problem solving, they have been taught to compartmentalize their lives so that it does not occur to them to use what they learn in one part of their life, the classroom, to another part of their life, the playground. On the playground they interact socially. They act and react to each other, forming opinions on the fly without fully observing any given situation. This gets the children into trouble. They assume that they can fully understand another persons meaning without making sure. So fights break out and the students resort to hitting because they do not understand how to apply the problem solving skills they've learned in class to the social interaction they encounter in the world.
Even though these children are young and have not fully developed emotionally or intellectually, they are a microcosm of America. Their parents are not much different. Adults in America seem to know how to solve other people's problems but cannot solve their own. Often we form opinions and beliefs based on what fundamental values we hold, thus making the world into black and white, or right and wrong solutions. We do not use the logic we learned in public school to see that much of the world is grey. By logically following correct steps to a solution, avoiding fallacy, there come problems in society which result in more than one solution, or which are unsolvable if one considers all of the variables.
As Americans we must realize that we come from multiple backgrounds and multiple forms of logic. What may be a logical answer for one must not always be logical for another. As Christians we can not always logically scream out dogma in our search for the absolute truth of God. As both Christians and Americans we have the responsibility of setting an example of right logic, and also of interacting with the right logic of those with varying opinions, for example Muslim Americans. We must seek not to force our Christian American logic on others, but come to a common ground that will allow for both solutions to exist, without hitting each other like fourth graders. After all, America is still a Democracy, not a Theocracy.