No. Teaching breadth of topics involves more than just teaching obviously useful information. The problem stems from our ability to evaluate what is actually us

No. Teaching breadth of topics involves more than just teaching obviously useful information. The problem stems from our ability to evaluate what is actually useful. Let me give a direct example you may not have considered, and an interesting hypothesis. Perhaps most importantly, we live in a democracy. This means that people vote for the direction of our government. When doing so, many different issues are considered. Of these, most are probably outside the area of ones expertise. How can we expect good decisions made by people ignorant of the subjects in question? So we teach basic science, basic math, history, english, and the arts to everyone. This way our population has at least a small amount of knowledge to fall back on when needed. On a less concrete topic, there is much speculation about the effects of learning on brain structure. Despite not remembering much mathematics, for instance, how do we know that learning mathematical concepts did not leave a lasting effect on the brain? What about the lessons we learn from history class? We might not directly associate with them when making everyday decisions, but is it not possible that learning those lessons contributed to our current thought processes? In summary, it is very difficult to quantify exactly what you retain from education and even harder to identify specific ways in which it helps you or helped to shape your mind. Thus, it is best to err on the side of caution and teach as much as we can.