What goals should we achieve in mathematics education?

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Educating in mathematics is a teaching challenge at all levels, since there is a perspective that it is difficult to learn, however that perception can be broken as long as we can analyze the tools, methods and teaching approaches that can help facilitate the teaching-learning process, especially so that what the student learns can be put into practice.

What goals should a mathematics educator pursue?

There are no unified objectives in this case, since everything will depend on the context in which the educational act takes place, however there are some proposals that I believe should be considered and which I will explain below:

[1] Teaching arithmetic, algebra, geometry and trigonometry for the basic levels of education:

If the objective is that students can perform academically at all levels, then they should be prepared in basic and fundamental areas so that when they are at a higher level they only have to learn new concepts, since many concepts of mathematics at the university level need mathematical artifices as a tool that have their basis in arithmetic, and that many times as educators we cannot focus on developing logical-mathematical thinking in students since we have to spend time correcting the basic learning deficiencies in the student.

[2] Focus our teaching on the abstract mathematical aspects:

From my experience at the university level, I have realized that the student in mathematics has his first experiences in visualizing abstract mathematical topics only when he reaches the university, which I consider a big mistake, from an early age and at basic levels of education the student should experience a teaching in abstract topics such as set and function, But above all, in any subject, demonstrations of theorems and corollaries should be contemplated in order to develop in the student a critical interest in the abstract, and when higher levels of mathematics education are reached, we can focus on new concepts having a solid base in the abstract of mathematics.

[3] Teaching geometry within an axiomatic system:

I still have memories of when I studied basic and high school, where the topics of geometry were treated from an elementary perspective as area calculations, perimeters, volumes, among others, however the simplicity of mathematics sometimes lies in aspects that although abstract give answers to everything we know today in geometry and are the basis for understanding basic principles of what is the point, the line and the plane.

It is Euclidean geometry that teaches us about these topics within an axiomatic set whose basis of understanding is based on a deductive reasoning of axioms, theorems and corollaries.

It is known that delving into these topics at lower levels can be very difficult for students to learn, however they can be incorporated as educational complements for the learning of mathematics students.

Conclusion

Many of the objectives expressed and explained by me in this post are intended to generate a reflective character for all people interested in the field of mathematics education, in that the teaching of many abstract topics at lower levels should be seen as an introduction to these topics, since the levels of mathematics learning are taught at their corresponding age, in different sequences depending on the environment and the educational model you want to implement.

However, each educational experience sets precedents to make proposals and define objectives that help us to see mathematics as a powerful tool of knowledge and that it is not difficult to learn as long as basic learning is incorporated in the lower levels.

References

Didactics of mathematics. Search for relationships and contextualization of problems.