This paper aims to investigate and to clarify the facts of female mathematics teachers, who succeeded in the Examination for Teachers' Licences which was held by the Ministry of Education, before World War II. First, since the curriculum of girls’ high schools was composed for making good wives and wise mothers, many of the girls did not deeply study mathematics compared with boys who were studying in middle schools. Therefore the applicants of mathematics in this examination were much less than that of sewing or Japanese, which were considered to be suited to girls. Next, since this examination was very difficult for even many male applicants, some of successful female applicants were often made news items of the newspaper. And two female successful applicants entered the course of mathematics at the university, because a qualification for entering the university was given to a successful applicant In addition, one of them acquired a doctorate of mathematics as a Japanese woman for the first time. Moreover, many of the successful applicants met excellent mathematics teachers by chance, or they were brought up in the intellectual family background. Finally, the following was found out in this investigation: Interesting a student in mathematics and making a student to keep up it depended on whether a student met high-quality mathematics teachers.

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The entrance examination problems (Mathematics) of the Higher Schools are analyzed in this paper. The problems contained the four subjects on mathematics, those are : arithmetic, algebra, geometry and trigonometry. (1) The arithmetic problems were contained at about 23-26% of the rates in the beginning, but they disappeared in 1910-1927 and were set again only 1% after 1928. I think there are two causes. First, those problems lost the social contexts and secondly, they were included in algebra. (2) The trigonometric problems were contained at about 20-28% of the rates in the beginning, but they disappeared in 1919-1927 and were set again only 2% after 1928. It was because an examination could be taken for the Higher Schools after completion of the fourth grade of Junior Higher School. In that age, the trigonometry was treated in the fifth grade. (3) There were some assertions of the International Reformation Movement in Mathematical Education. The principle of mixed course which is one of those assertions permeated gradually in the entrance examination problems (Mathematics) of the Higher Schools. We can point out two examples about the permeation. The first example is that arithmetic was included in algebra and the second example is the increase of the problems about the length, area and volume in geometry. It means that arithmetic, algebra and geometry are mixed. (4) In contrast to the principle of mixed course, the functional idea didn't permeate so much. The problems of functions were set about 9%of the rates in 1926–1927 and after 1928, about 5% of the rates. In contrast, the problems of equations were set about 26%of the rates in 1926–1927 and after 1928, about 36%of the rates.

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The Imperial College of Engineering, Kobu Daigakko, is a predecessor of the College of Engineering of the University of Tokyo, and was established in 1873 under the name of Kogakuryo to educate engineers for service in the Department of Public Works, Kobusho. All professors were invited from the United Kingdom. It was a six-year college of technical education. Theory and applications, teaching and learning at school and practical training outside school were unified together in the curriculum. It was an ambitious attempt to establish a technical institution, and it was succeeded. Mathematics was divided in two parts: Elementary Mathematics and Higher Mathematics, and the main contents of the latter were analytical geometry, differential and integral calculus and differential equations. The curriculum, syllabus and examination papers recorded in the “Calendar” of the College, as well as the “Catalogue of Books in the Library of the College” give us information about the actual state of mathematics education at the College. For instance, the examination papers show that mathematics taught there is a ‘regular’ one and not the one which is merely application-oriented, and the level of mathematics taught at this College has been raised year by year.

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