New Methods of Teaching Mathematics in High Schools and Universities

In this paper, we show a new approach in math teaching. The thing that makes this method different from the older ones is the way the notions are defined. Thus, we start with a practical problem from Physics, Chemistry, Biology, etc. and we try to get a formula to solve that problem. At a moment, we stop the try, because of a lack of theoretical notion. Then, it follows a paragraph in which we define the mathematical notion that we need to solve the given problem. Some properties of the notion and useful formulas are given. After that, we go back to the practical problem and, using the new defined mathematical notion, we solve the problem. We use this technique to define very important mathematical notions, as: derivatives, Riemann integral and differential equations. With these tools, some important problems from the real life can be solved.