In the past, teaching objectives in Mathematics were limited to having students’ memorized facts and obtain skill in manipulating and calculating numbers. Memorizing of rules and mechanical manipulation of numbers were considered sufficient. Today we emphasize skill in compilation as well as skill in mastery of ideas and understanding of operations.
The application of knowledge and facts to new situations is the best criterion of effective learning and application needs clear understanding, close study and concentrated attention. Hence the teacher of mathematics has to develop all these habits and attitudes in the pupils. There should be no insistence upon memorizing facts. So the chief value of mathematical study is that it trains in the use of reasoning power. Hence in teaching, the teacher should emphasize thinking and reasoning, rather than memory work and rote learning.
To the students, the solving of a difficult problem is a discovery and constitutes training in such work. The chief aim of teaching mathematics is to develop these faculties that lead to discovery and inventions.
The famous pedagogue Schultze remarks, “Mathematical study trains the students in systematic and orderly habits and the pleasure connected with the successful conquering of a difficulty stimulate will power.” It also cultivates the power of attention for in mathematics, the slightest slack in attention is ruinous. Mathematics makes constant demands upon imagination.