The Teaching of Elementary MathematicsMacmillan, 1902 - 312 σελίδες |
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Σελίδα vi
David Eugene Smith. Several years ago the author set about to find some- thing of what the world had done in the way of making and of teaching mathematics , and to know the really valuable literature of the subject . He found , however ...
David Eugene Smith. Several years ago the author set about to find some- thing of what the world had done in the way of making and of teaching mathematics , and to know the really valuable literature of the subject . He found , however ...
Σελίδα vii
David Eugene Smith. reader wishes . Where a quotation seemed to lose some- thing by being put into English , the original has been placed in a footnote . By these references the reader is put in touch with those works which the author ...
David Eugene Smith. reader wishes . Where a quotation seemed to lose some- thing by being put into English , the original has been placed in a footnote . By these references the reader is put in touch with those works which the author ...
Σελίδα 5
... thing for its own sake , but for what it contained for him in a practical way . Hence the Assyrians and Arabs and related peoples have no national epos and no enduring art.2 But they found in arithmetic a subject usable in trade , and ...
... thing for its own sake , but for what it contained for him in a practical way . Hence the Assyrians and Arabs and related peoples have no national epos and no enduring art.2 But they found in arithmetic a subject usable in trade , and ...
Σελίδα 25
... things , has a value difficult properly to appreciate . He is not sure that every flower has petals , that every animal needs oxygen , that " most unkindest " is bad grammar , or that Columbus was the real discoverer of America ; but he ...
... things , has a value difficult properly to appreciate . He is not sure that every flower has petals , that every animal needs oxygen , that " most unkindest " is bad grammar , or that Columbus was the real discoverer of America ; but he ...
Σελίδα 31
... thing I think a fault in the ordinary method of education ; and that is , the charging of children's memories , upon all occasions , with rules and precepts , which they often do not understand , and constantly as soon forget as given ...
... thing I think a fault in the ordinary method of education ; and that is , the charging of children's memories , upon all occasions , with rules and precepts , which they often do not understand , and constantly as soon forget as given ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
algebra American angle applied arith arithmetic axiom Beman and Smith's Cantor century chapter child circle common considered counting course cube decimal definition Diophantus elementary algebra elementary arithmetic elementary geometry equal equation Euclid exercise factoring figures Fitzga fractions Geschichte give given grades greatest common divisor Greek Greek Mathematics Hence highest common factor Hindu numerals History idea interest Jänicke Laisant Leipzig logic mathe mathematician mathematics Mathématique matical matter measures merely method Methodik metic modern multiplication negative number number space objects Pestalozzi plane plane geometry polygon postulate practical present problems proof propositions proved pupil quadratic quadratic equations question reason recent Rechenunterrichtes Rechnen recognized result rules simple solid geometry solution solved square root statement straight line student symbols taught teacher teaching text-books theorem theory Tillich tion to-day triangle Unterrichts usually write
Δημοφιλή αποσπάσματα
Σελίδα 233 - ... 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...
Σελίδα 21 - Children should be led to make their own investigations, and to draw their own inferences. They should be told as little as possible, and induced to discover as much as possible.
Σελίδα 195 - 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...
Σελίδα 126 - 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...
Σελίδα 15 - ... 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,...
Σελίδα 34 - 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.
Σελίδα 184 - 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.
Σελίδα 82 - 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.
Σελίδα 21 - 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.
Σελίδα 23 - 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...