The Psychology of Number and Its Applications to Methods of Teaching ArithmeticD. Appleton, 1895 - 309 halaman |
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Halaman vii
... idea that it is necessary to elimi- nate the ratio idea by changing one of the terms of the fraction to a qualitative unit and by this to change the thought to that of a simple number . Thus halves and quarters and cents and dimes are ...
... idea that it is necessary to elimi- nate the ratio idea by changing one of the terms of the fraction to a qualitative unit and by this to change the thought to that of a simple number . Thus halves and quarters and cents and dimes are ...
Halaman viii
... idea , one sees how fallacious are those theories which seek to lay a basis for mathematics by at first producing a clear and vivid idea of unity - as though the idea of quantity were to be built up on this idea . It is shown that such ...
... idea , one sees how fallacious are those theories which seek to lay a basis for mathematics by at first producing a clear and vivid idea of unity - as though the idea of quantity were to be built up on this idea . It is shown that such ...
Halaman ix
James Alexander McLellan, John Dewey. a qualitative idea , and does not become quantitative until it is conceived as composite and made up of con- stituent units homogeneous with itself . The true psychological theory of number is the ...
James Alexander McLellan, John Dewey. a qualitative idea , and does not become quantitative until it is conceived as composite and made up of con- stituent units homogeneous with itself . The true psychological theory of number is the ...
Halaman xiii
... ideas of rhythm , of balance , of measure , in moral and æsthetic culture . That the Greeks also kept their arithmetical ... idea of balance , of compensation , is more than formal . Number represents , as is shown in the following pages ...
... ideas of rhythm , of balance , of measure , in moral and æsthetic culture . That the Greeks also kept their arithmetical ... idea of balance , of compensation , is more than formal . Number represents , as is shown in the following pages ...
Halaman 24
... idea of their number ; there may be clear and adequate percepts of the things quite unaccom- panied by definite numerical concepts . No such con- cepts , no clearly defined numerical ideas , can enter into consciousness till the mind ...
... idea of their number ; there may be clear and adequate percepts of the things quite unaccom- panied by definite numerical concepts . No such con- cepts , no clearly defined numerical ideas , can enter into consciousness till the mind ...
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Istilah dan frasa umum
abstrac abstract activity addition and subtraction apples applied arithmetic cent centimetre child complete conception conscious constructive counting cube cube root decimal decimetre defined denominator denotes derived unit digits divided divisor dollar educational equal example exercises factor facts feet figures five foot four frac fractions FRANK VINCENT fundamental given quantity gives greatest common measure groups hundred hundredths ical idea of number inches interest least common multiple magnitude means measured quantity measuring unit ment mental method metic metre mind minor units minuend multi multiplicand multiplication and division nature numbers expressed numerical ideas numerical operations numerical value objects perfect conception primary unit principle psychical psychological pupil quan quotient rational recognition recurring decimal relation remainder result simply square root subtrahend symbols taken teacher teaching tens things tion tiple tity unit of measure unit of reference unity ured vague whole numbers yard
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Halaman 243 - ... can be expressed as integers, namely, 4 cents, 4 feet, 4 pounds, and so on, with kindred ideas and operations. 3. The Primary Practical Principle in Fractions. — It is clear that this complete expression for the number process is the fundamental principle employed in the treatment of fractions : if both terms of a fraction be multiplied or divided by the same number, the numerical value of the fraction will not be changed. This principle is usually " demonstrated " ; it is, however, involved...
Halaman 206 - The process of solving equations depends upon the following principles, called axioms : 1. If equals be added to equals, the sums are equal. 2. If equals be subtracted from equals, the remainders are equal. 3. If equals be multiplied by equals, the products are equal. 4. If equals be divided by equals, the quotients are equal. 5. Like powers or like roots of equals are equal. NOTE. Axiom 4 is not true if the divisor equals zero.
Halaman 5 - ... of commodities; just as a knowledge of anatomy, physiology, pathology has transformed medicine from empiricism to applied science, so a knowledge of the structure and functions of the human being can alone elevate the school from the position of a mere workshop, a more or less cumbrous, uncertain, and even baneful institution, to that of a vital, certain, and effective instrument in the greatest of all constructions — the building of a free and powerful character. Without the assured methods...