How should students tackle trigonometric equations?
Trigonometry is a very difficult subject to many. It doesn't come easy because it's a different side to math than ever seen before. Most trigonometry questions are basically a puzzle. Just like a puzzle, there needs to be a way of thinking that is very systematic, yet open minded. As in a puzzle where you start with the edge pieces, in trigonometry you start with writing down the trig equations so you can have a visual. You then solve a puzzle by trying different systematic approaches like organizing by color. In trig, the types of questions should be organized by the student and they should have systematic approaches already in their head before attempting the actual questions.
Why is Calculus such an important math subject?
Calculus it is by far the most type of math to understand how the world works. It can simply help you find out how much you car accelerates or even just the distance you have traveled. Calc can also be as complicated as Einstein's theory of relativity. Using math to optimize the way the way you solve the world's problems is an incredible thing. It is crucial in mostly all of the technical majors and needs to be learned the correct way. If it is not, the student will struggle in many other classes that follow. The basics of Calculus aren't hard to learn if you are instructed in the right way. I learned Calculus only four years ago and I think that puts me a large advantage to help whatever student I am tutoring. I remember the struggles I had and what helped me get past those to be able to strive in the class.
What makes Algebra different from any math before it's time and why is it so important?
Algebra is first time students are introduced to the thought that letters and symbols can be used to represent numbers. This is a hard concept to learn because for the first time, there are values on both sides of the equation. Algebra is by far the most important math subject to learn in depth and master at an early age. It is the basis of every other math class. Even at the magnitude of solving high level engineering problems with calculus, the hardest part can be knowing how to solve the algebra and making sure it's done flawlessly. Learning the basics of algebra are where people can screw up most. The basics need to be covered and tested rigorously. Once this is done, the student will strive in the subject.