The Teaching Objectives in a First Course in the Calculus

Abstract

There is a great deal being said nowadays about course objectives. It is said that the objectives for any course in the curriculum should be clearly defined and that teacher and student alike should be conscious of these objectives at all times. This concern has lead to a re-examination of the objectives for courses taught by the writer. This paper is particularly concerned with the objectives for a first course in differential and integral calculus. Stated briefly, the question at hand is this what are my objectives in teaching a first course in the calculus? Three major objectives are found to be inherent in this case. These are: (1) to give the student an understanding of the fundamental concepts of the calculus and a point of view relative to the historical background out of which these concepts grew; (2) to develop proficiency in the manipulative skills of differentiation and integration; and (3) to develop abilities in making practical applications of the principles learned. A few words will be said about each of these objectives relative to the methods used in attempting to realize them. It is hoped that the following statements will arouse some interest and will bring forth some comments as well as criticisms from individuals more experienced than the writer. In this way the writer, and possibly others, may be greatly helped in setting up goals toward which to work.