A change toward new mathematics has been gradually taking place over a period of years in most mathematics courses.
The goal of the new mathematics is to provide the student with an understanding of enough basic principles so that he can visualize the science of mathematics as a logical structure built on basic principles. In the past, different branches of mathematics have appeared to be unrelated, isolated, and without any common relationships.
New mathematics emphasizes the basic patterns and structures of operations or isolated rules and techniques which apply to very few situations.
Stress is placed on the self-discovery of generalizations which can be applied to many situations. Along with the broad concepts which link all branches of mathematics, the ability to think logically, organize, analyze, and arrive at reasonable solutions is also emphasized.
If a student forgets the method of solving a problem, his background from new mathematics enables him to reason out techniques, rather than referring to rules.
While new mathematical students reason out problems, students of the old mathematics often perform operations without knowing the reasons for application of the operations.
New mathematics produces independent thinkers who are capable of coping with new situations which they have never encountered before.
New mathematics is more difficult to learn than the older mathematics because more logical thinking from the lack of set guidelines is required. Although a student must work harder to learn math, he can easily change to different branches of mathematics because he possesses the basic ideas of that specific branch.
Since structure and pattern are emphasized, some people feel that students do not receive an adequate amount of drills on the computational work which is important to the application of mathematics in industry.
Stress is still placed upon problem solving, but emphasis is on understanding rather than on mere memorization. Application of basic principles learned in the new mathematics gives the student more flexibility in solving problems.