The Reorganization of Mathematics in Secondary Education (part I): A Report, Part 1 |
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aims algebraic technique analytic geometry applications arcs arithmetic binomial theorem calculus candidate Chapter chord circle College Entrance Examination college entrance requirements computation congruent connection constructions definitions demonstrative geometry desirable E. H. Moore elementary algebra Entrance Examination Board exponents figures formulas fractions functional geometric progression given point grades graph graphic ideas important included instruction intuitive geometry involving J. W. Young junior high school linear equations logarithms material mathe matics meaning measure methods metic National Committee numerical trigonometry organization parallel parallelepiped perpendicular Plane and Solid plane geometry practical present edition principles prism problems proof propositions pupil quadratic equations quantities questions recommended regular polygons relations relationships right triangles secondary education secondary school sides similar simple sine skew lines solid geometry solution square standard student symbol tangent teachers of mathematics teaching tests theorems tion topics transfer trigonometric functions trigonometry unknown
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Page 15 - It must be conceived throughout as a means to an end, not as an end in itself.
Page 67 - A unit represents a year's study in any subject in a secondary school, constituting approximately a quarter of a full year's work.
Page 72 - PLANE GEOMETRY: The usual theorems and constructions of good text-books, including the general properties of plane rectilinear figures; the circle and the measurement of angles; similar polygons; areas; regular polygons and the measurement of the circle. The solution of numerous original exercises, including loci problems. Applications to the mensuration of lines and plane surfaces.
Page 14 - ... purposes of the teaching of mathematics should be to develop those powers of understanding and of analyzing relations of quantity and of space which are necessary to an insight into and control over our environment and to an appreciation of the progress of civilization in its various aspects, and to develop those habits of thought and of action which will make these powers effective in the life of the individual.
Page 5 - This commission, therefore, regards the following as the main objectives of education: 1. Health. 2. Command of fundamental processes. 3. Worthy home membership. 4. Vocation. 5. Citizenship. 6. Worthy use of leisure. 7. Ethical character.
Page 26 - We therefore recommend a reorganization of the school system whereby the first six years shall be devoted to elementary education designed to meet the needs of pupils approximately 6 to 12 years of age; and the second six years to secondary education designed to meet the needs of pupils of approximately 12 to 18 years of age.
Page 11 - The acquisition, in precise form, of those ideas or concepts in terms of which the quantitative thinking of the world is done.
Page 16 - The primary and underlying principle of the course should be the idea of relationship between variables, including the methods of determining and expressing such relationship. The teacher should have this idea constantly in mind, and the pupil's advancement should be consciously directed along the lines which will present first one and then another of the ideas upon which finally the formation of the general concept of functionality depends.
Page 34 - Factoring. The only cases that need be considered are (i) common factors of the terms of a polynomial; (ii) the difference of two squares; (iii) trinomials of the second degree that can be easily factored by trial. (c) Fractions. Here again the intimate connection with the corresponding processes of arithmetic should be made clear and should serve to illuminate such processes. The four fundamental operations with fractions should be considered only in connection with simple cases and should be applied...
Page 41 - PLAN A. First year: Applications of arithmetic, particularly in such lines as relate to the home, to thrift, and to the various school subjects; intuitive geometry. Second year: Algebra; applied arithmetic, particularly in such lines as relate to the commercial, industrial and social needs.