## The Psychology of Number and Its Applications to Methods of Teaching Arithmetic |

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abstract activity actual addition already amount applied arithmetic attention become begin carry cent child clear common complete conception conscious constructive cost counting defined definite denoting digits direct divided division divisor dollar educational equal exact example exercises expressed fact factor feet figure five foot four fractions fundamental given gives groups hundred idea inches interest involved kind learned least less magnitude means meas measured quantity measuring unit mental method mind minor multiplicand multiplication nature necessary numerical value objects once operations original practice present primary unit principle problem psychological pupil ratio reason recognition reference relation remainder repeated represents result root seen sense separate simply square stage subtraction taken teacher teaching tens things third tion true unit of measure unity ured vague whole yard

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Página 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...

Página 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.

Página 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.

Página 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.

Página 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...

Página 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...

Página 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...

Página 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.

Página 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...

Página 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...