A brief course in the teaching process

by George D. Strayer

a. The practical value. Whatever pretends to be practical in arithmetic should really be so.

b. The question of “mental discipline.” The rise of this doctrine. The results of a psychological study of the question. The tangible part of “mental discipline.”

c. The interest in the subject for its own sake. The game element of mathematics. The historical development of the science of arithmetic from the primitive game.

References: Smith, The Teaching of Arithmetic, chap. ii, to the chapters of which no further reference will be made, this syllabus being merely a synopsis of that work. Teaching of Elementary Mathematics, pp. 1-70. Young, The Teaching of Mathematics, New York, 1907, pp. 41-52, 202-256. On the historical side, consult Fink, History of Mathematics, Chicago, 1898. Ball, Short History of Mathematics, New York, 1908. Cajori, History of Elementary Mathematics, New York. Jackson, The Educational Significance of Sixteenth Century Arithmetic, New York, 1906. Branford, A Study of Mathematical Education, Oxford, 1908.

III. What Arithmetic should include

1. From the Practical Standpoint.

a. The utilities of arithmetic overrated. A detailed consideration of the various topics usually studied.

b. The effect of tradition upon the matter of arithmetic.

2. From the Standpoint of Mental Discipline. Discipline a Matter of Method rather than one of Topics.