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A project of university preparatory course in mathematics for high school students (zero-year)

...what an unhappy man I must now have been, if I had not acquired in my youth some fund and taste of learning. What could I have done with myself at this age, without them?

(Lord Chesterfield's Letters TO HIS SON).

I. Grounds of the topicality of the problem

As the international experience shows, the secondary school math program itself gives sufficient knowledge in the sense that it provides familiarity with the basics of the elementary mathematics and acquirement of habits for a wide circles of pupils. However, this knowledge and habits prove to be insufficient for a smooth passage to successful studying at universities.
Because of that, an enormous number of students of all the courses where mathematical disciplines are present, in fact have problems with mastering these disciplines from the very beginning of their studying at university. As a result, they fail to pass exams. The plucks accumulate and do not give a chance to graduate in time and start working in the field of his choice.

The rise of the problem just in studying mathematical disciplines when passing to university education is not casual. This is caused by the structure itself of the discipline. The fact is that at secondary school the mathematics is usually studied on a comprehensible elementary level when the material is given in terms of concrete categories and notions, often without strict proofs of statements, while familiarity with some basics of the "higher" mathematics is occasional and is mostly given on a level of "recipes".

The passage itself from the elementary mathematics to the "higher" mathematics is a fundamental jump in the manner of comprehension, being in fact the step into the field of abstract thinking, where it is necessary to absorb a big portion of new abstract ideas and comprehend demonstrations on a new, more complicated level. If a student has gaps in understanding demonstrations of mathematical statements on an elementary level, the process of learning a new material often becomes unsuccessful.

It is obvious that there is a need of some supplementary structures in the organization of the education process which could provide a possibility for students to be ready to comprehend mathematical disciplines at universities.

As the practice shows, a possibility to use service of private tutors does not solve the problem, being an individual undertaking.

A structure which could be helpful in solving the problem has to be based on the idea of a step-by-step integration between elementary mathematics of secondary school and mathematical disciplines of universities for those secondary school graduates who wish to continue their education.

The realization of this idea must be made by a specially elaborated program and may be done by acting university professors who have an experience of teaching students and knowing well by their own practice the main stumbling-blocks in the process of learning mathematical disciplines.

`It is considered as expedient to organize at the university a special course of weekly mathematical classes by a specially prepared program for students of upper school, who wish to continue their education at the university, as well as for those who already graduated upper school and wish to deepen their knowledge of mathematics to continue the education.

II. "Zero-year"

"Zero-year" is an annual course of weekly classes at the university by a specially elaborated program for all comers.

The main objective of "zero-year" is preparation of students to be for their future mathematical education at the university.

"Zero-year" functions on commercial base with a differentiated fees for school students and working comers. The principle of fees is elaborated on the bases of the existing laws.

"Zero-year"- classes are carried out every year between April 1 and Mat 1 (of the next year) with the break for August. This period is chosen with the aim that the graduates of the 12-th year could finish the complete suggested course before the their exams.

Announcement about the enrollment and the registration of entrants to "zero-year" is made between January 5 and February 25 of every year.

In March the groups are formed and the problem of time table and classrooms is solved depending on number of registered students.

III. The program of the realization of the course in essence

  1. There is developed a program of the course of mathematics for 100 hours intended for students of upper school or for any person who graduated school and wishes to put in good order his knowledge of elementary mathematics.
    The program includes the main parts of the elementary mathematics with the analysis, algorithms and conclusions adapted to categories of university courses.
  2. Within the framework of the university, there are developed training aids for students of "zero-year" with respect to the whole program, where there is given the essence of the material, solution of problems with the realization of the suggested algorithms and typical examples are given for self-instruction.
  3. Every week, university professors provide one (2-3 hours) lesson according to the timetable. At these lessons a professor exposes in detail the topic of the lecture, shows the main ideas and algorithms of solving problems, solves typical examples and suggest a homework for self-instruction.

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