## The Reorganization of Mathematics in Secondary Education |

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ability aims algebra angle applications arcs arithmetic attempt base calculus changes Chapter circle committee common complete computation concepts connection considerable considered constructions continue corresponding courses definitions demonstrative dependence desirable discussion effective elementary entrance equal equations examination exponents expression fact figures finding formulas fractional functional fundamental geometry give given grades high school ideas importance included instruction interest intuitive involving junior later less limited linear material mathematics meaning measured mentioned methods national committee necessary needs organization parallel period perpendicular plane polygon possible practical preparation present principles problems processes proportional propositions pupils quadratic quantities questions reason recognized recommended referred relations relationships representing requirements respectively result secondary school selection sides significant similar simple solid square standard student suggested symbol tables teachers teaching theorems tion topics triangle trigonometry understanding unknowns various

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Page 51 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.

Page 9 - It must be conceived throughout as a means to an end, not as an end in itself.

Page 52 - The sum of the face angles of any convex polyhedral angle is less than four right angles.

Page 43 - 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 40 - 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 52 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°.

Page 7 - The acquisition, in precise form, of those ideas or concepts in terms of which the quantitative thinking of the world is done.

Page 16 - 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 9 - The primary 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 51 - If two planes are perpendicular to each other, a straight line drawn in one of them , perpendicular to their intersection, is perpendicular to the oth'er.