Looking to the aims of teaching mathematics it can be
seen that more focus is laid to the higher level of objectives underlying the
mathematics subject, like critical thinking, analytical thinking, logical
reasoning, decision-making, problem-solving. Such objectives are
difficult to
be achieved only through verbal and mechanical methods that are usually used in
the class of mathematics. The verbal method of instruction gives all importance
of speech and texts, to the book and to the teacher. From an historical point
of view this method was majorly used until the end of the nineteenth century.
In one of these verbal methods teachers are simply satisfied with giving the
mathematical rules to pupils and having them memorize it.
They justify this method by saying pupils would not
understand explanations. Their task is to transmit to their pupils the
knowledge which was accumulated over the centuries, to staff their memory while
asking them to work exercises, e.g. the rule of signs and formulas in algebra,
students memorize this and remember it! Another verbal method involves
explanation. Teachers who use this method assume that the mental structure of
the child is same as the adult’s. but a development stage according to Piaget
is a period of years or months during which certain developments take place.
Teachers think teaching must imply logia, and logic being linked to
language, or at least to verbal thought, verbal teaching is supposed to be
sufficient to constitute this logic. This method leads to series of
explanations and students at the initial steps of logical explanations trying
to understand and group but slowly the gap is created between the explanations
transmitted by teacher and received by students which leads to poor
understanding on part of students and they develop a fear of the subject:
“MATHSPHOBIA”. The education commission (1964 – 66) pointed/points out that “in
the teaching of mathematics emphasis should be more on the understanding of
basic principles than on the mechanical teaching of mathematical competitions”.
Commenting on the prevailing situation in schools, it is observed that in the
average school today instructions still confirms to a mechanical routine,
continues to be dominated by the old besetting evil of verbalism and therefore
remains dull and uninspiring.
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