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length should be 280 times 1 yard; when comparing the width. that the length should be i sixth of the first result; and when comparing the depth, that the length should be 3 fourteenths of
3 the second result; and that the true multiplier of the equals is 280 X % X 14, or 1o. So with all problems in proportion.
(6) A bookseller sold a lot of books on commission, at 20 per cent., and remitted $160 as net proceeds; for how much were the books sold ? Form--100%
20%, or 80% - $160.
100% = $200. (7) A man bought Michigan Central at 120, and sold at 124; what per cent of the investment did he gain ?
Form—120 = 100%.
124 - · 120, or 4 313%. (8) What is the Amt. of $804.25 for 1 yr. 5 mo. 10 da, at 8% ? The mind by inductive reasoning discovers that the interest at 4% for i fourth of a year (90 da.), at 5% for i fifth of a year (72 da.), at 6% for sixth of a year (60 da.), etc., is 1 % of the priacipal. In comparing the corresponding terms, it sees they are alike, excepting the times, and that the ratio between these only need be determined.
I year + 5 mo. = 17 mo.
$897.29, Amt. The reader should not understand that all of the above form should be written whenever an example in Interest is solved. The first five equations, in a short time, could be thought merely, and only the last two written. What the pupil needs is more time devoted to reasoning and less to the written expression.
(9) A boy being asked his age, said that 3 fourths of 80 was 2 fifths of 10 times his age; what was his age ? Form- of 10 times his age, or 4 times his age = 34 of 80 yr. or 60 yr.
i time his age = 15 yr. (10) A horse tied to a stake can graze to the distance of 40 ft from the stake; on how much surface can he graze?
Form—The area of a circle whose radius is 12 of a ft. =.7854
The area of a circle whose radius is
Since similar surfaces are to each other as the squares of their like dimensions, the second circle is 802 times the first.
(u) The surface of the planet Mercury contains about 28274400 square miles; what is its diameter ? Form—The diameter of a sphere whose surface is 3.1416 sq.
= I mile. The diameter of a sphere whose surface is 28274400 miles =
= 3000 miles. The surface of the larger sphere is 9,000,000 times as large as that of the small sphere; hence the diameter is 3000 times as long as the diameter of the small sphere.
It can be seen now that the reasoning described above and the simple form given apply to all examples in which one equation, known or stated, serves as the basis for finishing another equation; and in all problems which are a combination of such problems; or, in other words, about nine-tenths of arithmetic.
METHOD OF GEOGRAPHICAL INSTRUCTION.
BY HEINRICH MATZAL.
[Translated from the German by Howard Sandi on.]
And what in wavering vision hovers,
(GOETHE, Faust, Prologue in Heaven. EMPIRICAL PART.
The sources of all knowledge are experience and reflection. To both also we shall have to address ourselves. Accordingly, to experience for the first.
Now, as is known, the so called pedagogical experience is a peculiar thing. We know well, what we ourselves and others do; but only in rare cases do we win a sufficiently certain, clear and definite knowledge of what has been gained through that work. And even in these few favorable cases, very many questions remain unanswered.
Either the aim of our efforts was not gained: then we have learned that we should have proceeded. But how ?
Or the aim was accomplished. But even then—always, as above supposed, we would know that through doing, and only through that, it might have been gained-even then the question yet remains whether that procedure was really best adapted to the end; whether other ways, better, shorter, might not have led more certainly to the end.
Briefly: every individual finds by accurate reflectir n his pedagogical experience interwoven with the accidental and the arbitrary-of others and of self; the latter is the worse, because the more difficult to be perceived—to such a degree, that he can not at all seek here the leading point of view for an earnest pedagogical procedure, if he desires to think clearly and to act conscientiously.
The case stands otherwise if we raise ourselves above the standpoint of individual experience.
It is not left with the individual teacher in public instruction, and only with this will this work employ itself, to proceed wholly and entirely according to his best knowlege and conscience. The leading officials (educational] determine the aim of education, and prescribe also the system of instruction, more or less in detail
These norms perform them also in didactical literature, an important role partly as matter of fact with which one must deal, partly as objects of criticism.
A third thing is, in this connection, easily overlooked, namely this, that here also experiences are, and, in truth, a general experience which, formed during long periods of time and from widely differing communities offers in its behalf a guaranty that in it the accidentality and the arbitrariness of the individual experience shall have been, at least in part, neutralized.
Of similar worth are the conclusions of the meetings of directors [conventions of superintendents, etc.) in the province of the Prussian kingdom, which have several times employed themselves with the geographical instruction in the Prussian higher schools.
Finally, several geographical conventions also, have made, in
the course of the last decade, geographical instruction the subject of their deliberations, and have preserved the results of these deliberations in a series of theses.
Now in the following, a synopsis of such material shall first be given. Yet in this it seems neither necessary nor possible to bring under consideration the geographical instruction of all civilized lands; it will be more profitable to lay stress upon only some states as representative and to treat these therefore so much the more amply. As such I choose for Germany, Prussia; for foreign lands, Belgium.
PSYCHOLOGY IN THE INSTITUTE.
MR. EDITOR :--It is generally admitted, now, that all true methods of instruction are based upon psychological principles; and that a clear understanding of the mind processes in learning is indispensable to the teacher: but it is a debatable question whether much that is given in Institutes under the name of psychology has any practical bearing on the work of the ordinary common school teacher. Why is it that these psychologicaldidactic workers must define everything in a scientific manner before they can say anything practical about it? Often, they take up nearly the whole time in making definitions and elaborately discussing them. The more they define and discuss, the duller and more disgusted we become. Take for example the following definition of language:
"In general, language is the self-active statement of the peculiar interior become exterior, the representation of it by the exterior, as the breaking of a thing makes known its innermost."
Now, Mr. Editor, of what advantage is this to a teacher who has to teach grammar, and who has not spent years in the study of the interior and the exterior ? If our psychological instructor explains such a definition the chances are, he'll use so many technical terms and queer expressions (to us) that “the plainer he gets, the more we don't understand.”
Every teacher believes that cheerfulness should pervade the school work from first to last, but of what earthly use can a teacher make of the following definition of cheerfulness :
" Cheerfulness is the not-brokenness of emotional character with reference to a view of life."
This is too elevated, or too spiritooal, or too something for a great many of us. After we have heard such a definition discussed for forty minutes on a hot August afternoon, our view of life is not as cheerful as it was, and we have no emotional character left. It is broken. We are sleepy, and sometimes we sleep. “God bless the man who first invented sleep!”—"Nature's sweet restorer." This definition and the “discussion" that fol. lows it does not help us to go into District School house No. 2, surrounded by a muddy country and many other unpleasant things, and make things cheerful.
This psychological worker of ours never looks at a thing. He views an object in space and in time. When these and other different views are taken he does not think about it, he ponders it, or considers it. When this is done he names it an object object or a subject-object, owing to how he views it. We have heard the word “differentiation” used somewhere in connection with insti. tute work, but don't know just where.
Spirit, environment, individualize, generalize, induction, deduction, come in for their share of attention and get it from our terminological worker, but not from the majority of the teachers.
These terms and phrases used by our psychological-pedagogical-thought man we suppose are valuable to those who understand them. They probably express the most in the fewest words; but as the majority of us do not understand them our worker speaks to us in an unknown tongue. Is the Institute the place for this kind of work ?
We would not have this class of workers stay away from our Institutes. They are valuable men. They are close thinkers. They know more than we do, Mr. Editor. What we wish them to do is to forget their psychology when they talk to us and give us some helpful instruction in plain United States language. Lead us to see how the mind of the child acts in learning arithmetic; in learning grammar; in learning to read, etc. Show us what we can do for the child that will enable him to do for himself. Have us see why we do thus and so, but don't ask us to speculate. The weather is too hot, We will buy a book and read it as carefully as we can during the long winter evenings.