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The object of this report is to give an account, in such a form as to allow comparisons, of the instruction in mathematics in the Lower and Middle Commercial and Industrial Schools in the countries reporting to the International Commission on the Teaching of Mathematics.

The data of this report have been taken entirely from the reports of the international commission, except in the cases of Great Britain, Germany and the United States. In these cases certain other sources of information, such as official school reports, have been consulted.

The countries included in this report are Austria, Belgium, Denmark, Finland, France, Germany, Great Britain, Holland, Hungary, Italy, Japan, Russia, Spain, Sweden, Switzerland, and the United States.

The reports of the international commission give a very brief treatment of the commercial and industrial schools in certain countries, and consequently the discussion of the schools of those countries is brief in the present report.

The first part of this report consists of an account of the schools considered, arranged according to countries. This account contains, so far as the facts are available, a brief statement of the organization of each type of school, the entrance requirements, length of the course, by whom supported, aim of the school and of the mathematical instruction, courses of study in mathematics, methods of instruction in mathematics, preparation of the teachers, examinations, and present tendencies.

The second part gives in tabular form, so far as the facts are available, for each type of school in each country the following facts: The number of years of previous school attendance required for entrance; the approximate age at entrance; the number of years in the course; the number of hours a week spent in the school; the number of hours a week given to the study of mathematics; the course of study in mathematics.

There is given, finally (pp. 94-96), a list of the kinds of schools here considered and the terms used as equivalents in this report.

An account of the teaching of mathematics in the commercial and industrial schools of the United States is given in the Reports of Committees I, II, III, IV, and V of the American Subcommission of the International Commission. As these reports are readily available,1 it has been thought necessary in the present report to give only a brief summary of this work and to refer to the original committee reports for further details.

1 In the bulletin series of the U. S. Bureau of Education. See Nos. 6-9, 12, 13, 16, of 1911, and 2, 4, 13, 14, 29, of 1912.

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