YearbookNational Council of Teachers of Mathematics, 1927 |
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Ability addition amount analysis analytic geometry angles apparent-quotient rule calculus carried cent child column combinations computation course of study crutch curriculum decimal develop diagnostic tests difficulty discussion dividend divisor drill Education eighth grade elementary algebra equations errors example exercises facts figures formulas fractions functions G G G give given graph habits high school mathematics important increase-by-one rule instruction interest intuitive geometry junior high school learning long division material matics means measure method metic minuend monomial multiplication ninth grade plane geometry possible practice present problem solving processes pupils Pythagorean Theorem quadratic quadratic equations ratio reading sampling senior simple situations skills solid geometry solution subtraction tables taught teacher teaching textbooks texts theorems tion topics Trial div triangle trigonometry True quot true quotient understand unit-skills University of Iowa verbal problems vocabulary whole numbers zero
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227. lappuse - Two angles of a triangle being given, or merely their sum, the third will be found by subtracting that sum from two right angles. Cor.
179. lappuse - ... 2. Interlacing of branches. This means that there is no part of mathematics that is not related to all the other parts. For example, the equation a2 + b2 = c2 is a statement that is related to arithmetic, algebra, geometry, and trigonometry. 3. The relation of mathematics to allied subjects. This means, for example, that the subject of latitude and longitude in geography is closely related to intuitive geometry, arithmetic, trigonometry, and analytic geometry ; that a subject like physics could...
278. lappuse - ... exercise further the spatial imagination of the student and to give him both a knowledge of the fundamental spatial relationships and the power to work with them. It is felt that the work in plane geometry gives enough training in logical demonstration to warrant a shifting of emphasis in the work on solid geometry away from this aspect of the subject and in the direction of developing greater facility in visualizing spatial relations and figures, in representing such figures on paper, and in...
109. lappuse - The correct placing of partial products in the multiplication of two numbers of two or more figures is a specific case. (2) If a process does recur in the same manner, but is so little used in after life that any formal method of solution would be forgotten, then the teacher should
257. lappuse - 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.
109. lappuse - The division of a fraction by a fraction is frequently taught both " mechanically " and " by thinking it out." (4) "When a process or relation is likely to be expressed in a variable form, then the child must be taught to think through the relations involved, and should not be permitted to treat it...
263. lappuse - The school must be thought of primarily not as a place where certain knowledge is learnt, but as a place where the young are disciplined in certain forms of activity — namely, those that are of greatest and most permanent significance in the wider world.
279. lappuse - ... the (right circular) cylinder, cone and frustum, based on an informal treatment of limits; the sphere, and the spherical triangle. c. Spherical geometry. d. Similar solids. Such theorems as are necessary as a basis for the topics here outlined should be- studied in immediate connection with them. Desirable simplification and generalization may be introduced into the treatment of mensuration theorems by employing such theorems as Cavalieri's and Simpson's, and the Prismoid Formula; but rigorous...
280. lappuse - ... elementary calculus is sufficiently easy, interesting, and valuable to justify its introduction, special pains should be taken to guard against any lack of thoroughness in the fundamentals of algebra and geometry. No possible gain could compensate for a real sacrifice of such thoroughness. • It should also be borne in mind that the suggestion of including elementary calculus is not intended for all schools nor for all teachers or all pupils in any school. It is not intended to connect in any...
154. lappuse - The situation that needs to be met may best be illustrated by the case of algebra. Our elementary algebra is, in theory and symbolism, substantially what it was in the seventeenth century. The present standards of drill work, largely on non-essentials, were set up about fifty years ago.