| Abstract |
The great role in the process of mathematical knowledge mastering, forming of knowledge, abilities and experiences, necessary for studying mathematics and using it in practice for preparing students to practical activity psychologists, didactics and Methodists conduct to education tasks effective using [1, p. 133]. Tasks of mathematics education at the same time appears in two aspects: as the facility and as the aim of education.
On the opinion of A.S. Krygovski, «principle of teaching mathematics with the help of tasks is an obvious movement to mathematics essence itself. Tasks solving- is the most effective form not only for development of students’ mathematical activity, but also for knowledge, experiences, methods and mathematical application mastering»[2, p.20].
The notion «task»itself is very polyhedral. The detailed analysis of attends to define the notion «task» is situated in U.M.Kolyagin [3] and L.M. Fridman [4]. They point to single tasks definition absence because of investigating this notion from different points of view: logical, mathematics, cybernetic, psyche, pedagogic. On the basis of the investigations of this question analysis one can pick out two approaches of task definition. The majority of the authors include the subject into task notion itself [5,6,3,7].
All investigators think that exercises are the main qualities for forming abilities and experiences. «Exercises-N.M.Savin points-are planned-organized made action (of brain or practical) with the aim of mastering it or making the quality higher» [11, p. 108]. During the exercises the action not only secures but also improves. That is why the indispensable clause of the reasonable mastering of the knowledge about action ways and forming the abilities and experiences at the private themes is planning-organized doing exercises for instance such themes like «identical transformation of reasonable expressions, proving of trigonometric identities, transformation with logarithm formulas».
At the basis of the exercises like a method there is using the mechanisms of conventional reflexes formation. As a result of the exercises the action qualitevly changes, becomes more complete. Its doing begins to come true with less spending of volitional sources and weakening of students’ arbitrary attention on doing another more difficult study action. «Automation of basis reception of control making and action regulating - L.B. Itelson points makes the mind free for vaster taking action clauses into account. One gets an opportunity arbitrary to control the actions’ speed, to fit them for changing tasks, move to new situations and details.» [11, p. 154].
On the opinion of G.I. Sarantchev the task can be discerned like the way of exercise giving in the conception frames of the task as the situation which includes as the aim as clauses in which it should be reached because student’s interaction with many tasks makes the exercises.
Mathematical abilities and experiences are formed mainly during tasks solving process. Moreover it is made according to chosen model of the education process (KNOWLEDGE- ABILlTlES-EXPERIENCES-ABILITIES) and stages of abilities and experiences forming.
The didactical aim of abilities forming should be formed at the time of first tasks solving, doing first exercises for new reception, algorithm, and some tasks’ class solving method mastering. While solving these tasks students should be able to use the just learned material, use the general algorithm and way in definite situation. The first tasks of this kind are nesessary to solve with the whole explanation of all new moments in solving, with detailed recording on the board. It helps to form conscious abilities which as known are formed considerably faster and have greater firmness.
Mathematical experiences forming should be a didactic aim not of separate tasks but of carefully thought out system. It is caused by the fact that experiences are formed on the basis of consciously got abilities and experiences by the way of iteratively repeating operations, actions, algorithms.
So the tasks system directed to forming the experiences among students and satisfying definite demands is the basis facility for forming experiences among students.
On the basis of psychologists’ and deducts’ investigations analysis it was picked out that the structure of experiences forming should be reflected in the system to make this system an effective quality for process of forming experiences of full value control.
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