Understanding mathematical concepts promotes creativity in solving mathematical problems. Anyone who understands math can correctly work the problems at the level of their understanding; however, it is possible to do math, even advanced math and especially with a calculator, and yet not understand any of it. Understanding offers alternatives to problem solving, and insight into the problem itself, especially when applied to physics. Confidence also is concomitant with understanding. ...
Understanding mathematical concepts promotes creativity in solving mathematical problems. Anyone who understands math can correctly work the problems at the level of their understanding; however, it is possible to do math, even advanced math and especially with a calculator, and yet not understand any of it. Understanding offers alternatives to problem solving, and insight into the problem itself, especially when applied to physics. Confidence also is concomitant with understanding. Whether one is going on a job interview or selling his/her services as an entrepreneur, confidence shines forth and paves the way for success either way.
I have been tutoring math for 10 years. To me math is an intellectual technique for finding buried treasure. That treasure may be discovering the informational density stored in the geometric structure of DNA, or it may be in discovering that the rotational energy of the sun is much greater than the energy of its luminosity, but whatever you are searching to discover mathematically, it often is astounding, and to me very exciting. So is math boring? No, not if you understand it and know what can be done with it. Is putting men on the moon boring? Are skyscrapers, bridges, cell phones, rockets, and saving money in business boring? Could any of these things been accomplished without mathematics. I remember a problem in a business textbook in which the manufacturer would save $250,000 per year by shipping most of its product from the warehouse furthest from the shipping destinations. It does not make sense but that is what the linear programming (a mathematical technique) procedure revealed.
Personally, mathematics has revealed to me some concept of God's omnipotence and omniscience. It is His language, and--as to be expected--it serves both humanity and animals in unimaginable ways. It has made possible the labor-saving devices, advances in medical equipment, and communications we all enjoy, and from which we derive much benefit. It has been a conduit to make America opulent so that we have a $300 billion industry for charity alleviating starvation, homelessness and sickness.