The Teaching of Elementary Mathematics

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Macmillan, 1900 - Mathematics - 312 pages

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Page 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...
Page 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...
Page 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...
Page 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,...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 1 - Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father but by me.

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