1, problem definition

The first step of horizontal mathematicization is to define the problem clearly. At this stage, we need to clarify the objectives, constraints and limiting factors of the problem. Through the accurate definition of the problem, the problem can be concretized and quantified, which provides the basis for the subsequent mathematical modeling.

Step 2 collect data

Before mathematical modeling, we need to collect relevant data. Data can come from experiments, surveys, statistics, literature and other channels. The collected data should be accurate, comprehensive and reliable to ensure the reliability and feasibility of the mathematical model.

Step 3 build a model

Establishing mathematical model is the core link of horizontal mathematicization. When establishing the model, it is necessary to choose appropriate mathematical methods and tools according to the characteristics of the problem. Common mathematical methods include linear programming, nonlinear programming, dynamic programming, graph theory and so on. By establishing a mathematical model, practical problems can be abstracted into mathematical problems, which can be described and solved by mathematical language.

4. Solve the model

After the mathematical model is established, it needs to be solved. There are many ways to solve the model, which can be solved by mathematical software, programming language or manual calculation. In the process of solving, variables in the model need to be substituted for optimization according to the objective function and constraints of the model.

5. Verify the model.

After the model is established and solved, it needs to be verified. The purpose of verifying the model is to test the validity and accuracy of the model. Compared with the actual data and the existing research results, the stability of the model is verified. If the verification result of the model accords with the actual situation, it shows that the model is feasible and effective.

Transverse mathematization

The idea of mathematization was first put forward by Hans Friedenthal, a famous Dutch mathematics educator, in his book Mathematics as an Educational Task in 1973. The basic educational proposition of this book is that mathematics should belong to everyone and we must teach it to them.

But he also pointed out that every educated person learns mathematics with his own unique mathematical reality. Mathematical reality here refers to people's overall understanding of objective things by using mathematical concepts and methods, including both the reality of the objective world and the knowledge acquired by the educated by observing these objective things with their own mathematical ability, including the objective world and students' mathematical knowledge and experience.