Why does math work, or Conceptual/Interesting Math Resources

[BlueVanMeer]

I am a sophomore in high school and have heard about how great and majestic math is, so I decided to get a piece of the action. However, I struggle to see the "great and majestic" part (though I really am trying). Granted, math isn't my strongest subject (it could be said that it's my weakest), so I've been perusing the internet for some math help that teaches conceptually not procedurally, for I've heard the former is much more fascinating and will help me get a better grip on the subject. That leads me to another point: I don't understand the "whys" of mathematics. For instance, I know that the lattice method of solving multiplication works, but I have no clue as to the "inbetween." Now that I'm learning things such as various quadratic formulas, the problem has gotten much worse.

 

[Stephen Tashi]

What's great or majestic is probably a matter of taste. In my opinion, there are two somewhat contradictory aspects that make mathematics impressive. On the one hand there is the "power" of mathematics. Often "power" amounts to being able to solve and calculate things by various algorithms and manipulations without thinking about the details and the "why"s of the situation. On the other hand there is the logical precision of mathematics, which does involves understanding the "why"s. The traditional way to teach math is a compromise between these two aspects. Knowing all the precise (an sometimes hair splitting) logic behind mathematics is considered a topic for advanced students - say college seniors or graduate students. So you aren't going to be taught that way as a sophomore in H.S. People's standards for thinking they understand something get stricter as they study more advanced topics. A beginning algebra student may think he understands why x + x = 2x. But that level of understanding may not be sufficient to write a proof in a college course in abstract algebra.

If you aren't happy with how well you understand H.S. level math, I suggest you study an introductory book on mathematical logic. (However, don't neglect your regular courses if you do that.)