The Teaching of Elementary MathematicsMacmillan, 1902 - 312 páginas |
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Términos y frases comunes
algebra angle applied arith axiom Beman and Smith's Cantor century chapter child circle common considered counting course decimal definition Diophantus elementary algebra elementary geometry equal equation Euclid example factoring figures Fitzga fractions Geschichte give given grades greatest common divisor Greek Greek Mathematics Hence highest common factor Hindu numerals idea importance interest Jänicke Laisant Leipzig logic mathe mathematician mathematics Mathématique matics matter means measure ment merely method metic metric system modern multiplication negative number number space objects Pestalozzi plane plane geometry postulate practical present problems propositions proved pupil quadratic quadratic equations question ratio reasons for teaching recognized rectangle result rules schools simple solid geometry solution solve square root statement straight line student suggested symbols taught teacher teaching arithmetic text-books theorem theory things tion to-day triangle true Unterrichts usually write
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Página 275 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth ; or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth ; or, if the multiple of Book V.
Página 229 - Here, then, is the dominating value of geometry, its value as an exercise in logic, as a means of mental training, as a discipline in the habits of neatness, order, diligence, and, above all, of honesty. The fact that a piece of mathematical work must be definitely right or wrong, and that if it is wrong the mistake can be discovered, may be made a very effective means of conveying a moral lesson. Without this aim well in mind, the teacher is like...
Página 142 - Roots and squares are equal to numbers: for instance, 'one square, and ten roots of the same, amount to thirty-nine dirhems'; that is to say, what must be the square which, when increased by ten of its own roots, amounts to thirty-nine? The solution is this: you halve the number of the roots, which in the present instance yields five. This you multiply by itself; the product is twenty-five. Add this to thirty-nine; the sum is sixty-four. Now take the root of this, which is eight, and subtract from...
Página 41 - Now, what I am venturing to maintain is that the individual should grow his own mathematics, just as the race has had to do. But I do not propose that he should grow it as if the race had not grown it too.
Página 301 - The best we can say of the work is that it is more interesting than any novel." — Queen's Quarterly. " After having read this admirable work, I take great pleasure in recommending it to all students and teachers of mathematics. The development and progress of mathematics have been traced by a master pen. Every mathematician should procure a copy of this book. The book is written in a clear and pleasing style." — DR. HALSTED, in American Mathematical Monthly, " A scholarship both wide and deep...
Página 80 - Grube considers the numbers from 1 to 10 sufficient to engage the attention of a child (of six or seven years) during the first year of school. " In regard to extent, the scholar has not, apparently, gained very much — he knows only the numbers from 1 to 10. But he knows them."* The Germans " make haste slowly," but in elementary education they beat us in the race.
Página 27 - In the first place, it guarantees a vividness and permanency of impression which the usual methods can never produce. Any piece of knowledge which the pupil has himself acquired, any problem which he has himself solved, becomes by virtue of the conquest much more thoroughly his than it could else be.
Página 60 - Your committee believes that, with the right methods and a wise use of time in preparing the arithmetic lesson in and out of school, five years are sufficient for the study of mere arithmetic — -the five years beginning with the second school year and ending with the close of the sixth year; and that the seventh and eighth years should be given to the algebraic method of dealing with those problems that involve difficulties in the transformation of quantitative indirect functions into numerical...
Página 31 - And here give me leave to take notice of one thing I think a fault in the ordinary method of education; and that is, the charging of children's memories...
Página 1 - Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father but by me.