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# Abstracts

## How to teach students analyse

Raspopova N.S.

Russia, 423823, Naberezhnye Chelny, Sunny Boulevard, 1, apartment 65

1 pp. (accepted)

HOW TO TEACH STUDENTS ANALYSE

The traditional system of teaching mathematics includes lectures, practical exercises and control knowledge in the form of colloquiums, tests and examinations. The number of classroom hours has been steadily declining, and the main burden shifts to the independent work of students. And many first-year students are not ready to it. Transition to Unified State Examination, an exception of oral examination in mathematics in the school led to that students have no skills of studying of a theoretical material. For example, they don't understand that it is impossible to prove truth of the statement by one numerical example, that at first it is necessary to formulate definitions, and only then to prove the theorems connected with these concepts, etc. More than a modest number of lecture hours leads to the fact that only a portion of the material can be given with the proof. Therefore it is necessary to choose such small sections in which it is possible to carry out the strict proofs relying on entered definitions. Very desirable to lead counter examples, showing the need for all conditions of the theorem. Conducting colloquiums for small topics, starting with the first month of study at the University, helps in the formation of a culture of logical construction, which is one of the most difficult and important tasks in the first year.

At one time, the inability of students to analyze the results of solving the task after a two-year standard course of mathematics was opening for me. It seemed that this skill should come to them automatically. It turns out that this skill also the need to purposefully teach. Now, starting from the first theme linear algebra, homework assignments include the theoretical level. For example, the product of two matrices is a matrix of size 2 * 2. What can be said about the number of rows and columns of the matrices of factors? What happens with the determinant of the matrix, if places for the three rows of the matrix change? And if for four?

Excellent opportunities for analysis of the results and impact of the problem parameters on the result are incorporated in the course «operations Research». The decision of tasks on the computer enables the student to quickly check the fidelity of the formulated hypotheses. For example, in the problem of equipment replacement, you can explore the effect of changes in the purchase price of the new equipment on profit and usage of the equipment. In the problem of maximal flow on the network, you can analyze bandwidth of which arc makes sense to increase, if you know the costs and benefits for incrementing the throughput of all the arcs on a unit.

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