The Teaching of Elementary MathematicsMacmillan Company, 1900 - 312 páginas |
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Página x
... recently made the criti- cism that Kant was not justified in supposing that mathematical and philosophical necessary reasoning are distinguished by the circumstance that the former uses construction or diagrams . Mr. Peirce holds that ...
... recently made the criti- cism that Kant was not justified in supposing that mathematical and philosophical necessary reasoning are distinguished by the circumstance that the former uses construction or diagrams . Mr. Peirce holds that ...
Página xiv
... Recent writers CHAPTER V - • PAGE 71-97 THE PRESENT TEACHING OF ARITHMETIC . — Objects aimed at . The number concept . The great question of method . The writing of numbers . The work of the first year . The time for beginning the study ...
... Recent writers CHAPTER V - • PAGE 71-97 THE PRESENT TEACHING OF ARITHMETIC . — Objects aimed at . The number concept . The great question of method . The writing of numbers . The work of the first year . The time for beginning the study ...
Página 11
... recently come to light . The oldest deciphered work on mathematics is a papyrus manuscript preserved in the British Museum . It was copied by one Ahmes ( Aahmesu , the Moonborn ) , a scribe of the Hyksos dynasty , say between 2000 and ...
... recently come to light . The oldest deciphered work on mathematics is a papyrus manuscript preserved in the British Museum . It was copied by one Ahmes ( Aahmesu , the Moonborn ) , a scribe of the Hyksos dynasty , say between 2000 and ...
Página 17
... recent American and German text - books , coming to a settlement in two countries at least . England , more conserva- tive , and France , less open minded in her lower schools , still attempt to draw a rigid line between algebra and ...
... recent American and German text - books , coming to a settlement in two countries at least . England , more conserva- tive , and France , less open minded in her lower schools , still attempt to draw a rigid line between algebra and ...
Página 20
... recent discussions is given in Knilling , R. , Die naturgemässe Methode des Rechen - Unterrichts in der deutschen Volksschule , II . Teil , München , 1899 . speed in simple fundamental processes have been underestimated , the 20 THE ...
... recent discussions is given in Knilling , R. , Die naturgemässe Methode des Rechen - Unterrichts in der deutschen Volksschule , II . Teil , München , 1899 . speed in simple fundamental processes have been underestimated , the 20 THE ...
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Términos y frases comunes
algebra America angle applied arith axiom Beman and Smith's Cantor century chapter child circle common considered counting course decimal definition difficult Diophantus elementary algebra elementary geometry equal equation Euclid example factoring figures Fitzga fractions German Geschichte give given grades greatest common divisor Greek Greek Mathematics Hence highest common factor Hindu numerals idea interest ject knowledge Laisant Leipzig mathe mathematician Mathématique matics matter means measure merely method metic metric system modern multiplication negative number Paris Pestalozzi plane plane geometry postulate practical present problems 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 usually valuable write
Pasajes populares
Página 287 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the...
Página 288 - ... 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...
Página 152 - 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 21 - ... 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 42 - 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 228 - 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 90 - 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 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.