Mathematics, like any other subject, is important to the extent to which it supports and contributes to the purposes of general education. For children are sent to school in order that they become useful members of the community and contribute to the welfare of society. The mathematics
referred to in this article designates that subject matter and training which is important to the entire school population, as distinguished from the advanced mathematics needed for professional and technical education. It is mathematics that aids in the preparation of pupils for efficient participation in the activities in which they engage later as adults, and for the assumption of their share of social responsibility.
From the beginning of American high school to the present time, the teachers of mathematics have insisted that the learner may be benefited vastly from devoting their study to this subject. However, the pupil populace of the early high school differed from those in the present day in that its members belonged to a rather small and select group. The boys came to school to prepare themselves for leadership in the community. They planned to be ministers, doctors, or engineers, which naturally made mathematics an important part of their education. The girls, not to be outdone, preferred the same kind of education. Pupils took schoolwork seriously. Neither pupils nor parents were critical about the courses prepared and recommended by the teachers. With the growth of the schools, the high school population kept on increasing and toward the end of the nineteenth century, approximately half a million pupils were enrolled. Now they formed no longer a select group and differed widely in interest, industry, and ability. Many “took” mathematics who were not interested and considered it a useless study. Many others were not able to do the work prescribed in the mathematical courses. This part of the school population kept on increasing and created serious problems for the teachers and administrators. The question was raised whether schools should insist that these pupils take the mathematics presented in the courses in algebra and demonstrative geometry. If not, the teachers faced the problem of formulating a more suitable curriculum, one more attractive and profitable.
The Joint Commission of the Mathematical Association of America and the National Council of Teachers of Mathematics of 1940 made a study of the problem and reached the conclusion that mathematics is in fact important in general education because the average citizen of today needs considerable mathematical knowledge in the activities and experiences of everyday life, and because mathematics supplies a means of understanding important aspects of the world. A similar view on the importance of mathematics in general education is expressed by the Commission on Post-War Plans in 1944 and 1945. It recommends a course that develops “mathematical competence” for the ordinary affairs of life as a part of general education, appropriate to the major fraction of the high school population. As a matter of fact, the citizen of today will not be able to escape the grasp of mathematics in their daily lives. She/He must balance her/his budget, adjust expenses to her/his income, and compute taxes. His ability to understand them depends on his mathematical education.
Mathematics is a way of thinking and can be taught as such. It continually exhibits the processes of thinking in correct simple form and frowns upon hit-or-miss methods. It stresses thinking in terms of relationships that exist between facts. The technique of thinking which it uses is the same as that employed in the experiences and relations involved in the social and economic problems encountered by adults in everyday life.
Mathematics lends itself readily to training in reasoning. In daily life, situations constantly arise in which people must proceed with caution and must make careful use of the principles and processes of correct reasoning. They must be able to separate facts from assumptions and to draw correct inferences from them. The reasoning so characteristic of mathematics is essentially the type required in non-mathematical situations where conclusions are to be drawn from given assumptions. Mathematics trains in the process of drawing correct conclusions. This gives it the right to an important place in the curriculum of the schools.