The Teaching of Elementary MathematicsMacmillan Company, 1900 - 312 páginas |
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Términos y frases comunes
algebra America angle arith axiom Beman and Smith's Cantor century chapter child circle common computation considered counting course decimal definition difficulty 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 interest ject knowledge Laisant Leipzig mathe mathematician mathematics Mathématique matics matter measure merely method metic metric system modern multiplication negative number objects Paris Pestalozzi plane plane geometry postulate practical present problems propositions proved pupil quadratic quadratic equations question reasons for teaching recent Rechenunterrichts Rechnen result rules Schmid schools simple solid geometry solution solve square root statement straight line student symbols taught teacher teaching arithmetic text-books theorem theory tion to-day triangle true Unger Unterrichts valuable write
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Página 283 - ... 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 311 - Philadelphia Evening Bulletin. " We have nothing but commendation to bestow." — Scientific American. " 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 oi 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...
Página 148 - 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 38 - 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 17 - ... billions (the English thousand millions), (2) addition and multiplication of integers, of decimal fractions with not more than three decimal places, and of simple common fractions, (3) subtraction of integers and decimal fractions, and (4) a little of division. Of applied arithmetic we need to know (1) a few tables of denominate numbers, (2) the simpler problems in reduction of such numbers, as from pounds to ounces, (3) a slight amount concerning addition and multiplication of such numbers,...
Página 224 - I judge that the sum of the interior angles of a triangle is two right angles, the "is" of my judgment expresses the necessary intellectual connection between the two terms connected.
Página 86 - 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 23 - 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 27 - 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 311 - DR. HALSTED, in American Mathematical Monthly. " A scholarship both wide and deep is manifest." — Journal of Education. "A clear, concise, and critical account. Its style is so clear, concise, and so enlivened by anecdote as to interest even the young reader.