Mathematical thinking is an abstract way of thinking, through logical reasoning and strict proof to understand and solve problems. Understanding mathematical ideas and applying them to practical problems requires the following steps:

First of all, we need to understand the basic concepts and principles of mathematics. This includes the properties of numbers, operation rules and geometric figures. These basic concepts and principles are the basis for understanding and solving mathematical problems.

Secondly, we need to learn to solve problems by mathematical methods. This includes induction, deduction and reduction to absurdity. These methods can help us to understand and solve problems from different angles.

Then, we need to learn to apply mathematical ideas to practical problems. This requires us to combine abstract mathematical concepts and principles with practical problems and describe and solve practical problems through mathematical models. For example, we can use calculus to study the laws of motion of objects and probability theory to study the laws of random events.

Finally, we need to improve our mathematical thinking ability through a lot of exercises. This includes solving various math problems, taking part in math competitions and reading math books. Through these exercises, we can better understand and master mathematical ideas and improve our ability to solve practical problems.

Generally speaking, to understand mathematical ideas and apply them to practical problems requires us to have a solid basic knowledge of mathematics, master a variety of mathematical methods, be good at combining abstract mathematical concepts and principles with practical problems, and improve our mathematical thinking ability through a large number of exercises.