The Psychology of Number and Its Applications to Methods of Teaching ArithmeticD. Appleton, 1905 - 309 páginas |
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abstrac abstract activity addition and subtraction apples apply arithmetic cent centimetre child complete conception conscious constructive counting cube decimal decimetre defined denominator denotes derived unit digits divided divisor dollar Education equal example exercises FABIAN WARE factor facts feet figures five foot four frac fractions FRIEDRICH FROEBEL fundamental given quantity gives greatest common measure groups hundred hundredths idea of number inches interest least common multiple magnitude means measured quantity measuring unit ment mental method metic mind minor units minuend multi multiplicand multiplication and division nature numbers expressed numerical ideas numerical operations numerical value objects practice 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 Thomas Platter tion tiple tity unit of measure unit of reference unity ured vague yard Young and Jackson
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Página 245 - ... 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...
Página v - There is no subject taught in the elementary schools that taxes the teacher's resources as to methods and devices to a greater extent than arithmetic, and none that is more dangerous to the pupil in the way of deadening his mind and arresting its development, if bad methods are used.
Página 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.
Página 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...
Página 4 - To the educator, therefore, the only solid ground of assurance that he is not setting up impossible or artificial aims, that he is not using ineffective and perverting methods, is a clear and definite knowledge of the normal end and the normal forms of mental action. To know...