Problem-based teaching is one of contemporary teaching systems. Theoreticians concerned with the area agree on the following: it is fastest way of learning, thinking, and enterprise, it revolves around an unknown situation that requires resolution, it assumes that the problem is resolved by understanding the relationship between the given and the assigned, it causes spiritual turmoil in a student, which becomes spiritual tranquility upon the resolution of the problem, by which new knowledge is acquired and applied in newly-created situations, and it helps students prepare for research activities on their own. Due to its advantages (great motivational power, intensification of cognitive activities in students, increased teaching efficiency, generating creative forces in students at acquiring new knowledge, creating new generalisations, a wide scope of various forms of teaching organisation, encouraging students to conduct research on their own etc), problem-based teaching is widely used, in particular in teaching mathematics. It seems that it increases the efficiency of teaching this subject, it develops cognitive abilities and application and transfer of knowledge in students, and it allows students to discover on their own what has already been discovered in mathematics by applying the very same procedures as a scientist themselves. The paper deals with the notion of problem-based teaching, its characteristics, levels, and stages, as well as its application in teaching mathematics.
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