Tuesday, June 8, 2021

On the Role of Mathematics in the Education of Schoolchildren

 The main reason for this is that we have a lot of experience in the field of science. So, let us distinguish the following blocks: natural science, exact sciences, linguistic, social sciences, creative. And let's see what tasks in each of the subjects included in them are solved by mathematics.

1. Natural sciences: biology (solving genetics problems), geography (determining location in Cartesian and polar coordinate systems), physics (solving any problems, including graphs), chemistry (making equations and chains of chemical reactions).

2. exact sciences: algebra (all), geometry (solving graphical, planimetric and stereometric problems), computer science (making algorithms and programs), drawing (depicting stereometric figures and their parts).

3. social science: history (dates of events, number of participants), social studies (charts, graphs), economics (calculating percentages), economic geography (percentages and proportions).

4. Linguistic: foreign language (structure of language grammar), literature (dates, poetry), Russian (spelling and pronunciation of numerals).

5. Creative: fine arts (proportions, stereometric representation of bodies and objects), music (solfeggio, composing melodies with the help of electronic technical means), physical education (team games).

Do my Math Homework

The scheme (see appendix) will help us to visualize these connections.  From the diagram we can see that almost all school disciplines, in one way or another, are related to mathematics, and this relationship is mutual. Consequently, mathematics is by nature a science of application. This is perfectly confirmed by the statement. S. Sobolev: "There are many sciences, and all sciences are closely linked. It is impossible to study chemistry without knowing physics, biology without knowing chemistry, geology without knowing biology... But there is one science, without which no other is possible. This is mathematics. Its concepts, notions, and symbols serve as the language in which the other sciences speak, write, and think... It predicts and predicts far ahead and with great accuracy the course of things." [1, p.5] However, the last part of the statement speaks about the independence of mathematics as a science, about its leading role in the field of knowledge.

 The study of mathematics is directly related to the creative development of the child's personality, i.e. the fulfillment of the main pedagogical task. Indeed, mathematics develops memory, horizons, logic, analytical thinking, spatial thinking and imagination. So, mathematics fully shapes the future specialist, and in any area of application of accumulated knowledge. This means that the level of training in mathematics in secondary school should meet certain criteria, which would be the starting point for further training of a specialist, such as in high school. But it is well known that at present the level of training in schools has decreased significantly (and not only in mathematics). This has become a serious problem for teachers of higher education institutions, as students no longer understand the courses offered to them in professional disciplines.

 One of the solutions to this problem was proposed to take the USE using the test system.

It is believed that this unified approach to testing knowledge will make it possible to accurately determine the level of preparation of each graduate. It is not the task of the author of this article to analyze the positive and negative aspects of the USE. In this case, the only important thing is that the test with the help of the USE includes several sections of varying degrees of difficulty, and this gives, at first glance, an objective assessment of the overall level of a graduate's mathematical knowledge. But it turns out that "Unified" does not at all mean that all tasks in a certain block are of the same difficulty in different cities. For example, it was found that for students in St. Petersburg and Moscow they differ significantly, and for St. Petersburg the tasks turn out to be of higher complexity. This has been demonstrated by the practice of the USE over at least the last two years.

  The latest results of the GIA clearly show that in the Algebra section students do not perform well enough on the topic "Percentages" and "Solving Problems with Equations", and in the Geometry section - on the topic "Circle". In addition, the fact that the hours (one hour per week or 35 hours per year) for the mathematics program have been reduced, provided that the program itself has not been reduced, is credible.

 So the question arises: "Should we include in the mathematics program for secondary schools sections of mathematics that were traditionally studied in universities, and universities of technology?" For example, random variables, integrals, factorials. Of course, those who have already studied these sections at school will find it easier to study in the future.  But what about those who go to the humanities or are not going to study further? Do they have to master complex sections of mathematics, and, in the case of poor mastering, lower the grade for the mandatory exam?  And this circumstance is a significant argument in making a negative decision on this (already accepted) proposal. In addition, the refusal