The majority see the obstacles; the few see the objectives; history records the successes of the latter, while oblivion is the reward of the former.
Alfred Armand Montape
There is no doubt that higher education and research are a moving force for innovations and country development. Increased international cooperation, the need to establish new business contracts and their effective maintenance require specialists who can solve different professional problems independently. Technical universities should prepare engineers with a high enough level of knowledge about modern technologies and foster a love for lifelong learning. To achieve these goals, universities use various innovative teaching methods and approaches. Problem-based learning is one of them. In general, it includes:
- problem identification;
- avoidance of giving ready-made answers;
- interaction between learners and the teacher;
- teacher guidance and coaching of the problem-solving;
- teaching within a context [12, 14, 15].
Problem-based learning is indented to the acquisition of new knowledge through the solution of theoretical and practical tasks. The majority of scholars agree that problem-based learning includes several stages:
- general awareness of the problem;
- analysis of the problem;
- solution (development, justification of a hypothesis, its sequential check);
- decision verification [4, 7, 10, 11].
Considering advantages of problem-based learning, researchers state that it:
- stimulates interest in cognitive activity;
- exercises the capacity for work and encourages to learn new materials when solving problems;
- develops abilities to formulate the problem;
- develops problem-solving and critical thinking skills;
- enables to see events multi-dimensionally and with a deeper perspective;
- contributes to the development of creative skills;
- develops time management skills;
- develops the ability to respond to unexpected situations [13, 15].
Problem-based learning is aimed at preparing students for future problems in their learning environment and producing appropriate solutions to problems [11].
When choosing tasks, a teacher should remember that they should:
- be realistic;
- be open-ended, imply a “multiple-choice”;
- evoke curiosity.
The successful use of problem-based learning requires the correspondence of the tasks to students’:
- intellectual abilities;
- individual peculiarities and age interests;
- knowledge of the subject.
Problem-based learning anticipates:
- teacher-learner, learner and learner exchanges;
- teacher guidance;
- rich material and research;
- friendly learning environment;
- theoretical or practical tasks which suppose the acquisition of new knowledge and skills.
Problem tasks set learners before certain difficulties demanding considerable mental effort leading to a solution. They are directed at placing a learner in a difficult situation which he has to overcome. The majority of exercises presented in teaching materials and textbooks for mathematics are tasks oriented towards thinking rather than simple sample training [5, 9].
Problem tasks at lessons of mathematics favour the formation of logical, creative thinking, teach to reformulate, uncover logical connections between theories, generalize studied material, develop mathematical thinking alongside the knowledge and contribute to the practical use of mathematics [2]. The use of these tasks encourages cognitive development, trains to identify, generalize, specialize and clarify problems [6].
Besides the use of problem tasks at lessons of mathematics contributes to the formation of intellectual abilities, research skills, abstraction and generalization skills, encourages inquisitiveness, curiosity and independence [1, 3, 8].
Problem-based learning enables practical application of knowledge, advances the role of creative and cognitive work. However, it should be noted that a teacher can’t use only one method, he should combine elements of different methods to achieve greater results while teaching his subject.
Nowadays much attention is paid to the development of a strong creative personality, the ability to solve problems independently and find ingenious solutions. Problem-based learning in teaching mathematics helps to solve unconventional tasks, develops high level of critical thinking skills, motivates leaning and prepares to meet everyday challenges.
References:
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