The Reorganization of Mathematics in Secondary Education |
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Page 2
... examination . Chapter VI contains lists of propositions and constructions in plane and in solid geometry . The propositions are classified in such a way as to separate from others of less importance those which are regarded as so ...
... examination . Chapter VI contains lists of propositions and constructions in plane and in solid geometry . The propositions are classified in such a way as to separate from others of less importance those which are regarded as so ...
Page 39
... examination board.2 ] * Linear equations in one unknown .. Simple formulas - their meaning and use .. * Ratio and proportion .. * Negative numbers - their meaning and use .. * Quadratic equations in one unknown .. The linear function ...
... examination board.2 ] * Linear equations in one unknown .. Simple formulas - their meaning and use .. * Ratio and proportion .. * Negative numbers - their meaning and use .. * Quadratic equations in one unknown .. The linear function ...
Page 40
... examination board . A list of propositions and constructions has however been prepared , and is given in the next ... examinations based on the old and on the new definitions , so far as differences between them may make this desirable ...
... examination board . A list of propositions and constructions has however been prepared , and is given in the next ... examinations based on the old and on the new definitions , so far as differences between them may make this desirable ...
Page 43
... examinations form the only or prevailing mode of admission , inevitably direct their instruction toward the entrance examination . This remains true even if only a small percentage of the class intends to take these examinations , the ...
... examinations form the only or prevailing mode of admission , inevitably direct their instruction toward the entrance examination . This remains true even if only a small percentage of the class intends to take these examinations , the ...
Page 44
... Examination Board , has often been excessive . As a result , teachers preparing pupils for these examinations have inevitably been led to devote an excessive amount of time to drill in algebraic technique , without insuring an adequate ...
... Examination Board , has often been excessive . As a result , teachers preparing pupils for these examinations have inevitably been led to devote an excessive amount of time to drill in algebraic technique , without insuring an adequate ...
Common terms and phrases
ability aims algebraic technique Analytic geometry angles are equal applications arcs Ball High School Binomial theorem bisector Chapter chord circle college entrance examination college-entrance requirements complete report concepts congruent connection constructions courses in mathematics definitions demonstrative geometry desirable drill in algebraic E. H. Moore elementary algebra elementary calculus elementary mathematics exponents figures formulas fractional functional fundamental operations geometric progressions graphic representation graphs ideas importance included angle instruction interest intuitive geometry involving J. W. Young junior high school large number linear equations material mathe matics meaning measured methods metic national committee needs numerical trigonometry organization parallel parallelogram parallelopiped perpendicular plane geometry polygon practical present principles problems propositions pupils quadratic equation quadratic function quantities questions recognized recommended relations relationships right triangles secondary education secondary school segments sides significant similar simple solid geometry square straight line student tangent teachers of mathematics teaching theorems tion topics
Popular passages
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.