The most striking characteristic of technological as of other forms of education in the United States from the international standpoint is doubtless its extreme range of variation and the impossibility of framing general statements and definitions which shall be free from numerous exceptions. For the purposes of the present report a technological school or department may he defined as one giving systematic instruction in engineering and other forms of applied science to students entering the institution at the average age of 18 or 19, usually on the completion of a high-school course four years in length. The technological instruction aims to qualify its graduates both for immediate usefulness in junior positions in the various branches of engineering, in technical chemistry, in architecture, and for ultimate professional responsibility proportionate to individual capacity, etc. There is danger that in a university the balance may not always be evenly held between the interests of the academic and the technological students, or there maybe an excess of emphasis on abstract science, or the professional spirit of the technological student may suffer impairment from the distractions of academic athletics, etc. An interesting review of present conditions, and particularly of current criticism of the teaching of mathematics to students of engineering, may be found in the reports of the joint meeting of the section on mathematics and on mechanical science and engineering of the American Association for the Advancement of Science and the Chicago section of the American Mathematical Society. The object of that 1908 report was to present a synopsis of those fundamental principles and methods of mathematics that should constitute the minimum mathematical equipment of the student of engineering. The United States Commissioner of Education, in December, 1909, issued a detailed questionnaire on the teaching of mathematics to a large number of representative colleges of liberal arts and universities. Topics addressed in this questionnaire included: (1) General information; (2) Organization; (3) Curriculum; (4) Aims and methods of teaching--examinations; and (5) Preparation of teachers. (Contains 3 footnotes.) [Best copy available has been provided.]