The Psychology of Number and Its Applications to Methods of Teaching ArithmeticD. Appleton, 1895 - 309 halaman |
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Halaman v
... fundamental and true form of all quantity , number included . The differential of x and the differential of y are ratios . The authors of this book have presented in an admirable manner this psychological view of number , and shown its ...
... fundamental and true form of all quantity , number included . The differential of x and the differential of y are ratios . The authors of this book have presented in an admirable manner this psychological view of number , and shown its ...
Halaman viii
... fundamental 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 ...
... fundamental 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 ...
Halaman 19
... fundamental process . But , in the second place , this " faculty " psy- chology is not merely negatively useless for the edu- cator , it is positively false , and therefore harmful in its effects . The psychical reality is that ...
... fundamental process . But , in the second place , this " faculty " psy- chology is not merely negatively useless for the edu- cator , it is positively false , and therefore harmful in its effects . The psychical reality is that ...
Halaman 20
... fundamental interest and purpose which underlie this classification are discovered and appealed to , the subject which deals with it can not be presented along the lines of least resistance and in the most fruitful way . This discovery ...
... fundamental interest and purpose which underlie this classification are discovered and appealed to , the subject which deals with it can not be presented along the lines of least resistance and in the most fruitful way . This discovery ...
Halaman 30
... fundamental error - the failure to grasp clearly the place which dis- crimination occupies as the transitional step in the change of a vague whole into a coherent whole . In the ordinary methods of teaching number , for example , both ...
... fundamental error - the failure to grasp clearly the place which dis- crimination occupies as the transitional step in the change of a vague whole into a coherent whole . In the ordinary methods of teaching number , for example , both ...
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Istilah dan frasa umum
abstract activity addends addition and subtraction apples applied arithmetic begin cent centimetre child complete conception constructive correlative counting cube cube root decimal decimetre defined denominator denoting derived unit digits divided dividend divisor dollar educational equal exact example fact factor feet figure five foot four fractions fundamental given quantity gives grasp greatest common measure groups hundredths ical idea of number inches interest involved 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 oranges primary unit principle psychical psychological pupil pure number quan quotient ratio recurring decimal relation remainder result simply square root stage of measurement subtrahend symbols taken teacher teaching tens things tion tiple tity unit of measure unity ured vague yard
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Halaman 211 - ... that to take a half, a third, a fourth ... an nth of any quantity, it is only necessary to divide by 2, or 3, or 4 ... or n; that if, for example, 16 cents, or 16 feet, or 16 pounds has been divided into four parts, the counts of the units in each case are one, two, three, four, or one fourth, two fourths, three fourths, four fourths ; that each of these units — fourths — is measured by other units, and can be expressed as integers, namely, 4 cents, 4 feet, 4 pounds, and so on, with kindred...
Halaman iii - 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.
Halaman 172 - 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 280 - Pres. G. Stanley Hall, Clark University. " It is to my mind the most stimulating book that has appeared for a long time. The conception here set forth of the function of the school is, I believe, the broadest and best that has been formulated. The chapter on Illustrative Methods is worth more than all the books on ' Method ' that I know of. The diagrams and tables are very convincing. I am satisfied that the author has given us an epoch-making book.
Halaman 33 - If every human being could use at his pleasure all the land he wanted, it is probable that no one would ever measure land with mathematical exactness. There might be, of course — Crusoe-like — a crude estimate of the quantity required for a given purpose ; but there would be no definite numerical valuation in acres, rods, yards, feet. There would be no need for such accuracy. If food could be had without trouble or care, and in sufficiency for everybody, we should never...
Halaman 3 - ... 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...
Halaman 2 - To say that the purpose of education is "an increase of the powers of the mind rather than an enlargement of its possessions"; that education is a science, the science of the formation of character; that character means a measure of mental power, mastery of truths and laws, love of beauty in nature and in art, strong human sympathy, and unswerving moral rectitude; that the teacher is a trainer of mind, a former of character; that he is an artist above nature, yet in harmony with nature, who applies...
Halaman 280 - A book I wish I could have written myself; and I can think of no single educational volume in the world-wide range of literature in this field that I believe so well calculated to do so much good at the present time, and which I could so heartily advise every teacher in the land, of whatever grade, to read and ponder."—Pres.
Halaman 50 - That which fixes the magnitude or quantity which, in any given case needs to be measured is some activity or movement, internally continuous, but externally limited. That which measures this whole is some minor or partial activity into which the original continuous activity...
Halaman 260 - B would be undertaking an equivalent if he would* agree (for himself and his heirs) to pay to B (and his heirs) $6 at the end of each year, for all time. This $6 supposed paid at the end of each year is called an annuity ; as it runs for all time, it is called a perpetual annuity, and is said to begin now, though the first payment is made at the end of the first year. The $100 is very properly called its cash value, and the relation of the $100 to the annuity of $6 is plainly that of principal to...