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Mathematics and the Philosophy of Education

Math_lecture_at_TKKI remember the first days of my training to compete as a debater back in high school. The class started by teaching the fundamental rules of tournament rounds, and how they functioned. We all learned the time limits and conventions to the rounds and how each of them progressed. We learned the structure to a typical speech and what good argumentation looked like. After a long while, as I grew more comfortable and experienced, I started experimenting with debate theory and tinkering with the reasoning behind the fundamentals that I now knew by rote.

This process followed standard educational practice. When learning a subject, the fundamentals must be taught and memorized. The student must become incredibly familiar with them before getting into the theories behind the basic facts. This is the way humans learn. When one is a child, one observes constantly, looking for the simple “what” of the world. ┬áBefore we can begin to discover the concept of gravity, we must first identify the apple and the ground on which it falls. The point is, particulars can only be truly analyzed after the universals are fully and thoroughly understood.

You may be wondering why I am spending time explaining basic, straightforward educational norms. All of the above argumentation shouldn’t really be drawing that much fire, it seems like the obvious way of teaching most subjects. Yet, in this world where reason is denied in the place of tolerance and the very basic truths of the universe are questioned daily, there are those who would dissent. And these people are not mere eccentrics who dwell on the fringe of society, being paid little heed. No, those who disagree are, in fact, those who are developing national educational standards, with great influence. I think we shall see that the madmen have taken over the asylum by the end of this piece.

The Common Core stems from a noble goal. The idea is that students across the country are currently receiving a poor education and are falling behind in international competitiveness; thus, the American public education model must change. This line of thought is valid so far. However, like the vast majority of noble goals, those who seek to implement them end up throwing out the baby with the bathwater. Education should be reformed, but not at the cost of replacing current standards with abject idiocy.

I will explain myself. The Common Core sets new standards on educational theory and hopes that the results will be a better educated populace. One of the main areas they seek to reform, for example, is mathematics. They strive for a greater understanding by students of math, and the reasoning behind it. To achieve this, the standards call for more education on the explanation of concepts, rather than having students memorize principles. The website specifically states: “Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.”

The problem with using this approach to math specifically is that math is based entirely on objective fact. We use personal explanations and discernment when dealing with the application of wisdom to various situations. We use hard logical arguments when dealing with hard data (i.e., mathematical concepts) and for very real reasons don’t rely on personal explanations. A mathematical proof is either true or it isn’t. We don’t have the luxury (or curse, depending on how you look at it) of “deciding” whether the proof makes sense. Our ability to communicate well is based on how accessible we can make our ideas. Our ability to reason well is based on how well we can apply universals to particulars.

If I am teaching a foreigner about American football, I will not begin by explaining the tuck rule. I will begin by explaining the way the field is set up and how a team operates and scores points. Then I would demonstrate basic offensive and defensive strategies. Only after that could I even begin to delve into the theory behind the game that led to implementation of the tuck rule. The universals must be understood before the particulars make sense.

I applaud the Common Core for wanting students to be able to really understand mathematical concepts without resorting to mere memorizing mnemonic phrases. However, this is only possible for the children who have first internalized and learned by heart these concepts, probably not elementary students. Humans simply cannot understand the “why” if they have not already memorized the “what”. There is a logical flow of universals to particulars, and not the other way around. Students should have their times tables down before they can theorize about why exactly they work the way they do. Not that they shouldn’t understand the why, but it comes after the what.

Beyond bad educational theory, the worldview behind the Common Core standards is deeply flawed. And the effects will be devastating. The next generation will grow up understanding that the basic facts and laws governing the world aren’t important, their own explanations for them are. This destroys the one of the main ideas of education thus far: teaching the universals of human behavior, mathematical concepts, scientific phenomena, etc. and then discussing how they apply in particular situations. Instead, each particular will be discussed, and students will be asked to come up with a way that it can be rationalized.

When a man kills another man, outside of wartime or without the benefit of a trial, this action is known as murder. Murder is always wrong. We know this because of our understanding of the universal sacredness of human life. The particular circumstances don’t necessarily matter. The Common Core is symptomatic of a new push to remove the profundity of universals from the human mind and move in the direction of personal justification. The students educated in this manner will have a much more difficult time arriving on a standard of morality for society, if they are interested in one at all. If my reasons for murdering my neighbor happened to be better liked in a courtroom than the opposing argument, then I may very well go free. A world in which universals are no longer applied or valued is a world in which order dies.

I highly doubt this is what the creators of the Common Core had in mind when developing the curriculum. They more than likely truly believe that they are accomplishing good. The problem is, they have fallen prey to their own philosophy. They look at the particular problem: falling international competitiveness for American schools, and try a particular solution without examining the universal principles behind good education. The question is: if the leaders in American thought can be so shortsighted about an issue as fundamental as education, where else is the country failing?

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