Chapter II: Part 2

The common jig-saw puzzle maps have value if accurately cut. A splendid game for learning the states of the United States, their shape, size and relative position, can be made at home. Lay a map of the United States on a piece of good cardboard, trace the outline of each state and then cut them out on the state lines with a sharp knife. Have the child first learn to name the states by seeing the blank pieces of irregularly shaped cardboard. Then let him learn to put the pieces together, naming the states as he does so. This plan can be followed in studying the counties in your state or the countries in a continent.

The Blank Map

Another helpful method is to draw an outline map of the United States on blank paper, drawing in each state. This can best be done by using impression paper. Now have the child take the map with the outlines of the states and write in the name of each.

The Geography Game

Have cards cut on the lines of the different states of the United States. You can use the ones made for the puzzle map above. On each state card place three spots in the location of the capital and two principal cities. Prepare a series of three cards about 2×3 inches for each of the states, and on each print the name of one of the three cities mentioned so that for each state there is a book of four cards, the plain outline card of the state, a card bearing the name of the capital, and a card for each of the two principal cities. Below the name of the city can be drawn an object, or a word which will indicate the approximate population of the city, by the Number Code. Make a similar set of four cards for each state, the state cards to be cut on the map outline, but not to have the name of the state on them; nothing but three spots in the location of the cities mentioned.

Some states can best be made in a group because of their comparative size. Vermont and New Hampshire can be on one card; Massachusetts, Connecticut and Rhode Island on another, and Maryland and Delaware another. Only three cities should be marked on the cards of these groups, always using the capitals of the states.

The state cards and the city cards should be shuffled separately, the state cards laid to one side as a draw pile, and the city cards divided among the players. The first player draws a state card and lays it on the table and has the first opportunity to play with it any city card he holds. The player to the left has the next turn, and so on, until someone has laid down the last of the three city cards belonging to this state card and takes the book. The one playing the last city card is entitled to the book and has the privilege of drawing the next state card. The one securing the largest number of books wins.

Any player playing a wrong city card on a state card must forfeit the card to the one who started with the state card.

This game requires that the players recognize the state by its outline and know the name of the capital and the two principal cities of the state, and of course, in which state each city card belongs.

The same game can be arranged for the countries of Europe, South America or any other continent. The card can bear the names of the capital, the principal river and mountain range, or the capital and two principal cities.

Following the Travelers

Have the child follow the travelers in the following stories by actually seeing the geographical formations as they are named. Then have him repeat the itinerary by referring to the picture of the geographical formations. You will find that he can visualize the isthmus, plateau, etc., only after having clear knowledge of what each is. This repeated visualization will make a lasting impression upon his mind.

The Story

A man and a boy were out sailing when a strong wind blew them ashore on a POINT, opposite a small ISLAND. They dragged their boat across an ISTHMUS and soon reached the PENINSULA, where they landed in a BAY. They started out in opposite directions looking for drinking water. The boy followed up a RAVINE and found himself on a PLATEAU. He became lost in a SWAMP and came out on a PRAIRIE, and inquired at a village where he found that he could return by following a RIVER through the VALLEY. He made a raft and floated down the river until he was stranded on a DELTA. He waded ashore and was soon back at his boat.

The man climbed a MOUNTAIN and looked out over the DESERT, where he saw an OASIS. Then he climbed over a CLIFF and followed a CANYON back to the BAY.

The Travel Game

Give the child the blank outline of the country in which you are going to tell the story of your travel. Have him locate on the blank map each city you visit and draw a line from one to the other showing the route which was followed.

An example: England. I went to England and landed at Liverpool. I went by rail from there to London, stopping one day at Gloucester. From London I went by water to Portsmouth.

In this story you can ask the child to tell you what kind of houses the inhabitants live in. You can take a ship and be collecting a cargo at the ports. Ask the child what local products are most easily found, and other questions which will show what these people export. Also the customs and commerce of the country in which the story is located can be discussed.

STUDYING HISTORY

The study of history is largely a matter of Remembering What You Read. Children who have difficulty in remembering what they read, as a rule, do not like to study history. The lesson made into a visual picture will fix the points in mind with one reading, but this reading must not be careless or hasty. Help the child to read slowly and to pause long enough to make a mind's eye picture of each circumstance and change. It will be helpful to take a piece of paper and draw the scene of the battle. Mark in roughly the hills, mountains and rivers. Show the positions of the opposing armies, then roughly sketch the changes which take place. This drawing will help you to make a definite picture impression.

Take advantage of the pictures on the page of the book. The child's mind will naturally associate with the picture the many circumstances happening before and after, if he hears or reads them while the picture is visible.

For example, the picture of the landing of the Pilgrims on the shores of Massachusetts will bring to mind the facts which led to their making the journey. It will also suggest circumstances after the landing.

Those stories and facts which the child hears, while looking at the picture, are joined with it in the mind by the law of association, and the operation of the same natural law will tend to recall them whenever the child sees the picture.

A series of large pictures, which all of the class can see while the history lesson is being studied and recited, would help in fixing the facts in the minds of the children. Children who are taught to visualize can form their own pictures and have a wonderful advantage.

Remembering History Dates

This troublesome matter is easily mastered when the child understands the use of the number code as given in the book on Memory. This principle can be applied in every case. As a rule, the century in which the date occurs is not confusing, and the effort can be confined to the particular year. For example, in order to remember the date of the Battle of Bunker Hill, it is only necessary to remember '75, for the year, as every student will know that it was in 1775 and not 1875, or 1675.

A boy twelve years of age learned more history dates in one week after knowing how to use the Number Code than he had learned in weeks before. The knowledge of how to visualize the lesson and how to remember the dates will overcome any prejudice or any difficulty which the child may have with history lessons.

The following are samples of how the Number Code has been applied to remembering history dates:

Landing of the English at Jamestown, 1607. During the first year there was much sickness and the word SICK is '07. The picture of the Jamestown settlers "sick on the beach" will fix the year in mind.

The following dates were in one lesson, and are the word-pictures which a child used in remembering them. Marquette and Joliet explored the Mississippi River in 1673. The word COMB is '73. They were "combing" the river.

LaSalle reached the mouth of the Mississippi River in 1682. He planted the French flag and had a celebration. FUN is '82, they had fun when they planted the flag.

New Orleans was settled by Bienville in 1718. He had a hard time finding a good place for the city, TOUGH (tuf) is '18, they had a tough time.

Washington and the Virginian troops drove the French troops from Fort DuQuesne in 1754. He drove them from their LAIR, '54.

General Braddock was defeated and killed in 1755. He was buried in the woods of Pennsylvania. '55 is LILY, see a lily on his grave.

Some other examples follow: Alaska was purchased in 1867. 18 may be DOVE and '67 CHECK, a picture of a DOVE flying to Russia with the CHECK. Or if you prefer you can use the two words, STOVE-SHACK, or TOUGH-JOKE, it was a tough joke on Russia to sell it for so little.

The Battle of Bunker Hill was June 17th, 1775. This can be remembered by the association SHOOTING KILL. Sh is 6; TING is 17; KILL is '75. 6-17-'75 is the date and it is in the two words SHOOTING KILL, which is easily remembered with Bunker Hill.

The Battle of Bull Run, July 21st, '61. This is 7-21-'61. CAN'T SHOOT (because they ran so fast they couldn't shoot) and the two words CAN'T SHOOT stand for 7-21-'61.

Peary reached the North Pole April 6th, 1909. This can be represented by URGES UP. This is 4-6-'09. He urges his men up to the pole.

Panama Canal was officially opened August 15th, 1914. This is 8-15-'14. VITAL DOOR will represent these numbers. The canal is a VITAL DOOR between the two great oceans.

Examples of the dates of the reigns of the English kings at the end of feudalism. The War of Roses.

Order of Reign. Code Words.

1--Henry IV 1399-1413 Tie--Henry--hear, them pipe--their
doom.

2--Henry V 1413-1422 Snow--Henry--lie, to redeem--true
nun.

3--Henry VI 1422-1461 Home--Henry--show, true
nun to our chateau.

4--Edward IV 1461-1483 Wire--Edward--hear, a deer
shout their fame.

5--Edward V 1483 Wheel--Edward--hail, true
fame.

6--Richard II 1483-1485 Sash--Richard--no, true fame--dare
fail.

Here the Code word TIE stands for I, the first king--Henry hear, for Henry fourth; "them pipe" is 1399; "their doom" is 1413. The whole can easily be visualized into a picture of Henry using the TIE to make an ear trumpet to HEAR THEM PIPE THEIR DOOM. A peculiar idea, perhaps, but it will accomplish the purpose. Use the same plan for other similar lists and make strong picture associations and they will aid you greatly. They can be recalled when the numbers can not.

The following are examples of dates of Greek and Roman History:

Draco codifies Laws of Athens, 621. Joined--He joined the laws.

Peloponnesian War, 431-404. Remote--Razor.

Corinthian War, 395-387. Mabel--Moving.

Alexander King of Macedonia, 336-323. May homage--My name.

Founding of Rome, 753-(?). Column.

Rome supreme in Italy, 264. New Chair.

Sack of Rome by the Gauls, 390. Mobs.

Great Latin War, 340-338. Mars--May move.

Peace between Rome and Carthage, 201. Nice Tie.

Julian Emperors, 27 B. C.-41 A. D. INK Bottle Can--RIDE After Dark.

Claudian and Flavian Emperors, 41-96. Red--Badge.

Good Emperors, 96-180. Push--Thieves.

Invasion of Barbarians, 337-376. May make--My cash.

Charles the Great crowned Emperor of the Romans, 800 Vices.

The History Game

Secure pictures of the principal events in history and paste them on a series of cards. Have nothing on the cards but the picture, no printing, or names. Take three blank cards about 2×3 inches and on the first place the date of the event; on the second the names of the leaders; if a battle, the opposing generals; on the third put the name of the peoples concerned.

For example, first card, a picture of the Battle of Bunker Hill; second card, June 17th, 1775; third card, General Wm. Howe and General Joseph Warren; fourth card, British and American colonists.

A series of such cards should be made covering the events that are being studied at that time. The pictures are shuffled and laid in a draw pile on the table, and the cards are shuffled and dealt to the players. The one to the left of the dealer draws and plays a picture into the middle of the table, and then any cards which he holds which belong with it. The next player has the next opportunity to play, and so on around the group. The player who places the fourth card takes the book and is entitled to draw and play a picture into the center of the table.

Any card which is played in error that does not belong with the event in the picture shall be forfeited to the one who started the play with the picture card. The one getting the most books wins.

The Game of Famous Men

Secure the pictures of a group of 48 or more men of the present and immediate past who are well known in national or international circles. Place the picture on one card, the name on another, on the third, his nationality, and on the fourth, the thing for which he is best known. The last card can contain more than one thing, if you wish.

The game is played like the History Game above, and requires the players to be familiar with the well known men and their deeds, also to be able to call them by name, and to know their nationality.

The same idea can be used by making a game of the famous men of Colonial History; or of the period of the Civil War; or of the great World War just passed. Do you know the face of Gen. Haig, his nationality and principal event of his life? To look up the information for the cards is a good history lesson in itself. Take the ideas of all these games and by using your Productive Imagination make them fit the needs of your study, or the things which you wish most to master.

STUDYING MATHEMATICS

Children learn to count by using objects, in the school room they count the desks, the children, the number of cards, or blocks. The first lessons are object-lessons dealing with objects which can be handled and formed into groups. Digits are symbols which represent objects, 7+3=10, is an abbreviated form for 7 (Apples) and 3 (Apples) are 10 (Apples).

It is easier to teach addition and subtraction by the use of the objects to add and to take away from. The realization of the process comes by seeing the objects and the result of the change. The digits become symbols for the objects that the child has been working with. Counting boards are helpful in teaching children, for they enable you to continue the visual process. All methods of teaching through the visual processes should be continued as long as possible.

The child's interest in the problem will be stimulated if he deals with objects, or things, and not with meaningless groups of figures. The problem 127+323+417= , is a meaningless one and uninteresting, but if you encourage him to think that this is the number of soldiers with which a general is going out to meet an army of two thousand, then he has some interest in finding out how many men the general really has to meet the two thousand with. This makes the problem read thus, in his mind.

127 (soldiers) + 323 (soldiers) + 417 (soldiers) = How large an army?

Figuring a page of problems will be uninteresting, but if you can encourage the child to introduce the imaginary objects, it will increase his interest.

Fractions are usually explained by the division of an apple or some easily divided object. Division, as a process of dividing a group of objects among a smaller group of children, is easily understood and interesting to them. Encourage your child to continue to think of the objects when dealing with fractions.

Visualization Always Aids

All mental processes should take form in pictures. The adding of 4 and 7 should be seen in the mind's eye, if the problem is not written down. A parent tells the story of his difficulty with his son and this simple problem. The child got the idea fixed in his mind that 4 and 7 were 12. The father had told the boy that the answer was 11, and had the child repeat, 4 and 7 are 11, several times. But the original impression was still the stronger, and the next day, when asked by the father, "How many are 4 and 7?" the child's answer was 12. In some way this impression had become a very strong one and was recalled before the weaker one of the correct answer, 11. The idea of visualization was brought to the father's attention during the day by his having attended a lesson in Memory Training given by the author. That evening he called the boy to him and said, "Son, how many are 4 and 7 tonight?" He received the same incorrect answer, 12. Then he took a piece of paper and wrote upon it the figures in exaggerated size, as illustrated on the right. He had the boy look at the problem for a moment and then look away and see it in his mind's eye, then look at the problem again. Thus he placed a visual impression of the correct answer in the child's mind and this became the stronger of the two impressions and was never forgotten. The next morning the father asked the boy the same question, "How many are 4 and 7?" and the answer was promptly given, "Eleven." "Why, I can just see those figures in my mind and I never will forget that."

4
7
--
11

This experience is the natural result of using the stronger sense of sight in preference to the weaker one of hearing. The conscious use of the mind's eye faculty in his arithmetic lessons brought this boy from the bottom of his class up to a reasonable grade in a very short time. Do not overlook the value of visualization. It can be applied with helpful results in any lesson or problem.

The Mental Blackboard

The child can easily learn to visualize his problems in mental arithmetic if he will begin while young. This is especially true if you have used the exercises for visualization given in the First Book. Those on mind's eye counting and the Number and Letter games are especially helpful. Their importance now becomes apparent, and if you have neglected them it will be well to go back and use them now.

Encourage the child to see the figures in exaggerated size on an imaginary blackboard; see large white figures on the blackboard. As soon as the problem is given, let the ear impression become a mind's eye picture, as illustrated. The use of this visual method is gradually being recognized as being valuable, and will in the future come into general use. Give your children the advantage and have them use it now.

7
5
--
12
×2
--
24

Exercises in Manipulation

The mind's eye picture of the figures on the mental blackboard can be enlarged by practice so that the child can visualize problems of some complexity. This ability, of course, will come only after continued practice. Start with simple problems and increase their difficulty as the child progresses. You will be surprised to find how he will be able to retain the figures in his mind and soon will be able to work with them.

Write on the blackboard a column of figures as illustrated below. (A small one in the house is of great value in child training. A yard of blackboard cloth can be purchased and hung on the wall.) Allow the child to look at them for a few seconds and write down the result of his addition. Do not have him write the numbers as in previous exercises, for visualization, but only the total.

Now, add the first two numbers of the first example, subtract the third and add the fourth, then write the total.

In the second example let him add the first two, subtract the third and multiply by the fourth, write the answer.

These exercises of manipulation can be varied in many ways. The length of the columns can be accommodated to the ability of the child.

10
12
9
16
--

15
10
14
7
--

Learning Rules

All rules should be worked out in examples or illustrations and visually impressed upon the child's mind. One visual impression is equal to about twenty repetitions. Many times children get the idea that the problem cannot be worked unless the exact "Rule in the book" is followed. See to it that your children get a broader idea and that they understand the reason for doing a thing. The training in mathematics, that is of most value after school days are over, is, where we understand the reason and have worked out for ourselves the correct result, independent of any set rule for working the problem. When helping the child at home give him practical examples from every day life as well as those in the book.

Fractions

The first step in fractions are often confusing to children, but need not be if they have been taught to be observing and to watch for the little aids which help over the difficult places.

Nominator and Denominator are two confusing terms to many. If you will show the child that most of the fractions that he has to deal with are proper fractions, and that the Nominator, upper number, is smaller than the Denominator, lower number, and that the same relationship exists between the words.

Nominator
De-nominator

The Denominator is the denomination of the fraction, the Numerator is the number of parts. Let the D of Denominator stand for Down and remember that it is Down (lower) part of the fraction.

Many scholars have difficulty in giving the correct answer to the question, What are the three kinds of fractions? The following is all that is needed to fix the answer in mind.

Give the PROPER answer. If you give the IMPROPER you will be MIXED. These capitalized words are the three kinds of fractions.

Think of a fraction as a part of a whole. When the fraction becomes a whole, or more than a whole, it is Improper. It needs to be changed to make it a unit, or a Mixed fraction, a unit and a part.

The Multiplication Tables

These are a problem which every one has to work with and because the use of them requires speed to be most valuable there must be a certain amount of repetition in learning them.

The Multiplication Game

The aim is to teach children their multiplication tables by visual repetition and at the same time to introduce the game spirit, thus to increase the interest and to prolong the period of effort without fatigue.

The child can work with these cards himself and thus by self instruction can learn this most difficult lesson of Arithmetic, and without any possibility of error, accuracy is insured.

The equipment consists of a series of eleven pieces of cardboard about 2×6 inches on which are printed in large black numbers the tables without the answers.

A series of ten odd shaped cards is then made and the digits printed on them in bright red. The following are the suggested shapes for the ten digit cards.

(Digit cards should not exceed one and one half inches in height.)

The digit cards which are the correct answer to the table printed on the larger cards are then laid in the correct position and the shapes marked out. With a sharp knife cut out the shapes a trifle larger than the marked size of the digit card. The result is a card as illustrated, with the table and two holes of irregular shape into which the digit cards with the correct answer in bright red will fit. No other card but the correct one can be put into this opening, there is never any danger of the child seeing a wrong answer to the table.

The only cards which can be fitted into this table are the two and the cipher making the correct answer 20. This card with the black 4×5= and the bright red answer 20 will make a strong impression upon the brain of the child, and by use of the strongest sense, that of sight. At the same time he can repeat the table audibly and gain the added advantage of the ear impression.

Give the child only one set at a time so that he learns one table thoroughly. When he has learned it, mix the cards and place them one at a time in front of the child and see how many correct answers he can give without fitting the cards. In cases where there is hesitation have him fit the digit cards and make sure. See to it that he is accurate and certain.

After one table is well mastered make a similar set of cards for the next table. If you do not wish to take time to cut out the irregular shaped holes for the digit cards, the place can be blackened and the digit cards laid carefully on. The cut outs are far better and well worth the little effort necessary to make them.

For the tables up to 12's you will need the following number of digit cards; with these you will be able to work out any complete table of eleven cards. 10--1's; 8--2's; 6--3's; 6--4's; 10--5's; 4--6's; 4--7's; 5--8's; 4--9's; 16--0's.

After the child has learned two or three of the tables mix the cards, take any six and see how quickly he can fit the correct digit cards into place.

Keep him playing with these cards until he can give the correct answer to any question and give the correct table as a whole. After the tables have been learned you can make many tests of speed and competitive games with several children of the same age or school grade.

The Difficult Tables

There are certain tables which seem harder for some than the others, yet there is often a difference as to which are considered most troublesome. The 2's, 3's, 5's, 10's, and 11's are easy for all of us. The 9's are as easily learned with the aid which follows. This leaves the 4's, 6's, 7's, 8's and 12's, remaining to work on. The combinations that are new in these tables are the following; all other combinations are known from the other tables:

4 × 4 = 16 6 × 6 = 36 7 × 7 = 49* 8 × 8 = 64*
4 × 6 = 24 6 × 7 = 42* 7 × 8 = 56 8 × 12 = 96
4 × 7 = 28* 6 × 8 = 48 7 × 12 = 84 12 × 11 = 132
4 × 8 = 32 6 × 12 = 72 12 × 12 = 144
4 × 12 = 48

The first help in mastering these few necessary combinations is visualization. If you will print them in large figures and the answer in red, each table on a sheet or page by itself so that they can be handled and studied, they will form visual impressions that can be recalled with ease by almost any one. This is especially true of children at the ages when they will be learning these tables.

Repetition seems the most valuable aid, but to be most advantageously applied it should be a combination of visual and auditory repetition. Let the child look at the tables in the large form in which you have made them, while he repeats them.

Use addition and subtraction. In learning the tables there are always some which make a stronger impression and which the child will "never forget." Use these as starting points or bases of operation. For example, 4×5=20, all will recognize this at once. 4×4=16, just four less than twenty, and the subtraction will quickly give the correct answer. Also 4×6=24, or 4 more than the known point of 20. To take advantage of this it will only be necessary at first to learn 4×7=28 in order to master the entire table of 4's. The 4×4, and 4×6, would be figured from 4×5=20, and the 4×8 from the 4×7, and the 4×12, from the known 4×11=44. With these known bases to work from it is only necessary to fix the one starred combination in each table in mind indelibly at the beginning, the others will be easily figured from the known bases and will become fixtures from use.

The Table of 9's

There is a peculiar combination of figures in this table of 9's, which, if once noticed and perceived, will make this one of the easiest of the tables.

9 × 2 = 18 (1 + 8 = 9)

9 × 3 = 27 (2 + 7 = 9)

9 × 4 = 36 (3 + 6 = 9)

9 × 5 = 45 (4 + 5 = 9)

9 × 6 = 54 (5 + 4 = 9)

9 × 7 = 63 (6 + 3 = 9)

9 × 8 = 72 (7 + 2 = 9)

9 × 9 = 81 (8 + 1 = 9)

9 × 10 = 90 (9 + 0 = 9)

9 × 11 = 99 (2 9's)

9 × 12 = 108 (1 + 0 + 8 = 9)

Notice that the two digits of each answer always add up to make 9, and that each first digit of the answer is just one less than the multiple. For example, 9×5=45, the answer will begin with one less than the multiple 5, and the two digits of the answer must add to make 9, therefore it can be nothing but 4 and 5, or 45. This is true in all cases except 9×11 an already known answer, but also only 9's in this answer. This simple idea, when once understood, will master the table of 9's.

Be sure that the children realize that 7×4 in the tables of 7's are the same in value as 4×7, so that the answer to 7×4 becomes familiar with learning the table of 4's. Ask the question both ways 7×4 and 4×7.

The Tables of Weights and Measures

Some of these we learn easily and always retain; some always seem confusing. These can be mastered by the use of the Number Code and the Visual picture combined. Some examples follow:

24 sheets = 1 quire, and 20 quires = one ream. The picture of Two Dozen Squires in a Nice Room, will fix these figures and terms in mind. Two Dozen is 24, Squires is a reminder for Quires. Nice is 20 (2 is N and 0 is C) and room a reminder for Ream.

16-1/2 Feet = 1 Rod, 320 Rods = 1 Mile. Picture a Dish and a Half balanced on a Rod. Dish is your code word for 16 (1 is D and 6 is sh) and the Half Dish makes 16-1/2 Feet on (in) a Rod. Next--Many's the Rod in a Mile. Many's is 320 or the number of rods in a mile.

30-1/4 Sq. Yards = 1 Sq. Rod. Picture--MISTER takes a yard stick and measures off a Sq. Rod. Mister is 3-0-1-4, or 30-1/4.

160 Sq. Rods = 1 Acre. Picture--See a pile of Dishes out in the Acre being broken up by a rod. Dishes is 160 the number of Sq. Rods in an Acre.

640 Acres in a Sq. Mile. Picture--Take the Shears and cut up the mile into squares. Shears is 640, the number of Acres in a Sq. Mile.

792 Inches--1 Link. Picture--792 is Cabin, see the link hanging on the side of the cabin.

4 Rods = 1 Chain. Picture--See 4 Rods wrapped around with a chain. 80 chains = 1 mile. Your Code Word for 80 is Vase; put a chain around it and drag it a mile.

A few picture associations like these will help in fixing the difficult points in mind. Associations which you make yourself will help you most. Be sure to repeat them at intervals; make them permanent.

Pictures for Answers

Familiarity with the Number Code given in the book on Memory, will aid the child in keeping the result of a problem. The numbers of the answer can quickly take the form of an object which can be translated again into the correct numbers. Many children will not be able to hold the visual picture of the digits for any length of time. There is considerable difference in the ability to hold the visual picture of the digit 127. Many children, and adults, will be far more accurate and remember longer if they see a TANK, which is easily translated by the Code into 127, when the answer is wanted.

Learning Rules

The exaggerated example illustrating the rule to be learned, will make its meaning clear and thus make the problem of learning it many times simpler than if it is learned as a group of words, the meaning of which is not always well understood. It is always best to understand the rule first and learn it afterwards. Use the suggestion given for learning verbatim and the exaggerated example as given in the suggestions in spelling. After you understand the rule it will not be difficult to memorize.

Visualizing Geometry

The Theorem in geometry should have the visual process applied to it in the same manner. Make a strong picture of the figure which illustrates it. For example:

=The square on the hypotenuse of a right angle is equal to the sum
of the square on the other two sides.=

To visualize the figure, as illustrated, will aid in fixing this Theorem in mind. Do the same with others. Another example of emphasizing the important lines as in the Theorem:

Two rectangles are to each other as the products of their bases by their altitudes.

In the illustration below the bases and altitudes are emphasized to remind you of the fact that they are the factors to be dealt with. Notice that in the first pages of the Geometry all simple figures are illustrated as explained or defined. Learn to visualize the problem with your book closed, work until you can see it clearly, and you will understand it better.

AIDS IN STUDYING CHEMISTRY

Experiments in Chemistry are its most interesting phase. Let its problems take form in your visual mind and you will add to the enjoyment and also the ease of your understanding.

A teacher of this subject, after appreciating the value and ease of visualization, worked out picture combinations of atoms which helped him greatly. He could see the two atoms of Hydrogen floating through the air and combining with the atom of Oxygen and could see the result of the combination.

Using the Initialing Idea

The ideas which have been given in this and the preceding books can be applied in many ways to the problems of any subject. There is no attempt on the part of the author to work out all applications, but merely to suggest a few possible ones and leave the rest to the student. Each will think of different methods, and those aids which each one works out for himself will be most valuable and most easily recalled.

The Elemental Substances

The six elemental substances of the organic world are: Carbon, Hydrogen, Nitrogen, Oxygen, Phosphorus, and Sulphur, which can be easily remembered by the following: The Organic World--Can Have No Other Principal Story.

The initials of each of the words following "World" stand for one of the elements.

Chemical Formulae

Remembering of chemical formulae can be simplified very greatly by reducing the formulae to an idea using the initialing plan; for example, the formula for Wood Alcohol is CH3OH. This formula in itself has no meaning, and is difficult to carry in mind. By using the initials you can easily make some ideas which will represent this formula and help you to remember it, as for example: CAT HAD ham ON HAND. In this formula the C of Cat stands for Carbon, the H of Had for Hydrogen; Ham being a Code Word for 3 is indicative of 3 atoms of Hydrogen, and the O. H. is represented by the O and H of On Hand.

The formula for Glycerine is C3H5(OH)3, and can be remembered by the following idea: COME HEEL O HAM. In this example notice that the first letter of the word initials the substance and the last letter the number of atoms by the number code. As COME: C for Carbon, and M for 3. HEEL: H for Hydrogen, and L for 5. O for Oxygen. HAM: H for Hydrogen, and M for radicle 3 times. Use whichever method suits you best.

The formula for Carbolic Acid, C6H5OH, or CASH HAUL O, HAY. The formula for Benzine, C6H6, or CASH HASH.

Hardness of Substances

It is often valuable to know the degree of hardness of different substances, and these can easily be remembered by the following list. In degree of relative hardness the list is as follows, the hardest coming first.

Diamond
Corundum
Topaz
Quartz
Iridium
Apatite
Bell Metal
Boric Acid
Rock Salt
Kaolin

Take Kaolin as a basis. The number opposite each substance in the following list indicates its comparative degree of hardness in relation to Kaolin:

1 Kaolin TIE See tie on Kaolin

2 Rock Salt SNOW Poured over Rock Salt

3 Boric Acid HOME Built of Boric Acid

4 Bell Metal WIRE Swinging a Bell

5 Apatite WHEEL With a big appetite for running

6 Iridium SASH Irritating the wearer

7 Quartz EGG Quartz taken from an Egg

8 Topaz IVY To pass the Ivy

9 Corundum WHIP Made Cora run

10 Diamond TOES Set with Diamonds

In the list you have ten substances. Kaolin, the base, is 1, Rock Salt is 2, which indicates that Rock Salt is twice as hard as Kaolin. Iridium is 6, and six times as hard as Kaolin. Diamond is 10, which means that it is ten times as hard as Kaolin.

Learning this list by picturing reminders with the word of the Code list will enable you to easily recall these ten substances and the degree of hardness compared with Kaolin.

Atomic Weight Table

Some students of Chemistry have learned the entire list of elements and their atomic weights. The following are a few examples of how the list can be arranged and learned. It will be excellent practice for you to use this method and make a list of your own.

Element Code No. Reminder Wt. Code Word

1 Carbon TIE Carbine 12.005 Tin Sizzle
2 Hydrogen SNOW Hydrant 1.008 The Saucy Foe
3 Nitrogen HOME Night 14.01 Deer Sat
4 Oxygen WIRE Ox 16.0 Dash
5 Sulphur WHEEL Sulphur 32.06 Money Sash
6 Phosphorus SASH Fuss for us 31.04 Mad Sir
7 Sodium EGG Soda 23.0 Nome
8 Potassium IVY Pot 39.1 Mop It
9 Calcium WHIP Calsomine 40.07 Horse Sack
10 Iron TOES I Run 55.84 Lily Fire
11 Arsenic DOT Arson 74.96 Gray Page
12 Gold TOWN Gold 197.2 Dipping In

Learning Foreign Vocabularies

The principle of using a reminder can be applied with advantage in learning a foreign language. The majority may learn foreign words more easily and permanently by the Reminder Link. In this case the reminder is the connecting link between the English word and the foreign word. Those who usually learn foreign words only by laborious repetition will find a saving of time in learning by the reminder link.

Spanish words:

English Link Spanish

cold freeze frio
drink beer beber
written inscribed escrito
sing cantata cantar
full complete completo
sweet delicious dulce
window ventilate ventana
keep guard guardar
sell vend vender

Latin Vocabularies

Latin is the base from which most modern languages are derived, and you will find in English a very large proportion of the words taken directly from the Latin source. This makes the learning of Latin Vocabularies simpler than any other.

In a great many cases the word is a direct derivative and needs no reminder or intermediate step; for example, the Latin word ANIMAL is the same as in English, although pronounced differently; or Latin: ORNAMENTUM, and the English ORNAMENT. Be resourceful, draw upon your imagination. Note the following suggestions:

English Reminder Latin

boyish Puerile puer
crown coronation corona
free liberate liber
land terrace terra
dog canine canis
think cogitate cogito
mind mental mentis (gen.)
running current curro
pleasing gratifying gratus
soldiers militia milites (pl.)
teaching doctrine doceo
more majority maior
unending perpetual perpetus
shortness brevity brevis
time temporary tempora (pl.)
faith fidelity fides

German Vocabularies become very much less difficult if you search for an intermediate step or reminder:

English Link German

fork gobble gabel
coffee-pot coffee-can kaffekanne
amusing comical komisch
ancient old timer alterthuemlich
easy light leicht
meat flesh fleisch
writing scribed schreiben
gloves hand shoe handschuh
quilt bed cover betdecke
walking going gehen
stove oven ofen
flowers blooms blumen

Studying Music

The visual memory is the best memory for music. Many of the better musicians who learn music readily and remember it well have the visual memory. They can see the page, the bar, and the notes in the mind's eye. This ability can be developed in the child by the use of the exercises for visualization given in the first book. When the child begins to study music give part of the time to practice of visualizing and memorizing music.

First, teach him to visualize a perfect clef. Draw imperfect ones on paper or slate and have the child tell what is the matter with them. Draw different notes and have him become thoroughly familiar with them by reproducing them. Have him draw the whole, half, quarter, and eighth notes, etc.

Teach the child the division of time by grouping the notes with reference to beats. Write a line of notes and have him divide them into groups of whole note value. Then indicate a certain time to be followed and have him divide other rows of notes into bars in accordance with the time indicated.

Teach the child the different rests by the same visual process. Have him write bars of music using the different rests and completing the bar of given time by filling in with the proper notes. Teach the use of sharps and flats and the difference in signatures by the same visual process. Let all practice be simple in the beginning and increase in complexity as he grows older.

Teach the child to combine the use of the eye and ear in musical practice. Have him transfer ear impressions to visual ones by seeing the notes on a staff as he hears the tone. Write a few bars of a familiar tune and have the child tell what it is.

Another application of the visual memory is to look carefully at the staff, then close the eyes and see it in the mind's eye, then look back and correct and improve the picture. Another plan is to see the staff exaggerated in size, covering the entire wall of the room. This exaggerated picture can be colored according to the above suggestions.

It will be helpful to take the piece which is to be memorized, and after fixing the picture of it in mind write it upon a blank staff. Keep improving this written copy of music, writing only that part of the score which is seen clearly. These methods will help to improve the visual ability to carry a picture of the page; and continuous practice with them will help in improving the ability to memorize in this way.

Be systematic in all your efforts. It is best first to memorize the words, then the air, then the technical part. A thorough understanding of the composition and its general plan will be of assistance.

In learning songs apply the principles given in the second book, and learn the words thoroughly. This will enable you to devote all of your time and attention to the technical part of the music. When you do not know the words thoroughly your attention is divided between learning the technical part of the music and recalling the words. Better master one thing at a time and do that well.

Speaking in Public

When you have trained your child's memory and created in his mind a feeling of confidence that he can remember what he wishes to say, there will be very little embarrassment connected with speaking in public.

Teach the child to use the Hitching Post idea in all matters of public speaking.

This subject was covered in Book Two and the following sample outline of the points of a talk "Hitched" to the Code Words will be helpful.

A patriotic speech made after the Declaration of War with Germany.

1 (Tie)--Volunteering for Service.

Young men are taking off their ties and waving them in the air
rushing into the Enlisting Office.

2 (Snow)--Great Need of Shipbuilders.

A partly built ship covered with snow which men are shoveling away
so others can go on with the work.

3 (Home)--Public Speakers for Propaganda.

Speakers going from home to home calling out to people and
addressing them.

4 (Wire)--Conservation of Food.

Boxes of food being wound around with wire so that they cannot be
wasted.

5 (Wheel)--Stopping Criticism of Government.

Setting a lot of men gagged and bound upon a large wheel.

6 (Sash)--Increasing Production.

Factory boss offering a wide, red, white and blue sash to the
worker who makes the greatest increase in production.

7 (Egg)--Lend Your Savings.

Putting your savings in a large Egg and taking out Liberty Bonds.

Be original and make an effort. You will soon learn that these simple pictures will recall the points of the talk in the order in which you have arranged them. The hint is all the mind needs, if it gets the right start you will be able to say what you wish.

Review Your Studies

An excellent method of mental development is to make a practice of recalling the occurrences of the day each evening. This is especially important for students. Time should be taken to sit quietly and review the facts and ideas of the day's lessons. Here is an excellent opportunity to urge your mind to think them over for yourself. There can be little growth of knowledge without independent thinking.

Review as much in detail as possible all of today's lessons before starting on the new. One reason you do not remember more of what you see, read, or hear, is that you do not review it. Reviewing carefully will very largely increase your stock of knowledge. It is not unreasonable to expect that some of the facts or experiences of the day's work and lessons will later become as important and valuable as a business man's papers. He does not hesitate to take time in the middle of the day to file these papers, or even to carry them to the vault. Teach the child to take a few minutes in the evening and review the occurrences of the day and you will be surprised to see his mind begin to take on the retentive power of a vault.

The necessity of repetition will never be eliminated; it may by better methods be reduced to a minimum, but cannot disappear entirely. Some knowledge must be so familiar that it can be used habitually (by the subconscious mind) without the necessity of conscious effort, and this cannot become true without repetition.

Review Improves Observation

Another result which is far from unimportant is the fact that this effort will develop the ability and the inclination to take notice of things as they transpire. Many examples can be given of the extreme value of this exercise, as the experiences of Thurlow Weed. He had the ambition to become a politician, but lacked one necessary requisite--a retentive memory. The above idea was suggested to him by his wife. Mr. Weed practiced by recalling to his wife in the evening all the circumstances and happenings of the day. He was so greatly repaid for this effort that he continued this for many years. Mr. Weed says, "I am indebted to this discipline for a memory of unusual tenacity. I recommend this practice to all men who wish to store up facts and expect to have much to do in influencing men."

A Word to the Student

The greatest lesson of education is thought. The thing you should be striving for and working toward is the ability to think clearly, logically and deeply. One of the greatest aids is the knowledge which is stored in your brain and which you are all able to recall at will.

Your brain is not like sticking plaster, it is like putty; you must make an impression of the things you wish to retain. To make these impressions will always require an effort, no help will ever be devised which will enable you to remember without effort.

The ideas given to you in this book are aids, and you should become able to use them as such. The principles of memory are scientifically accurate and you need to become familiar with them and to use them to add to your success in study and progress.

Do not be like the carpenter who "is too busy to sharpen his tools," or like the drowning man who refused to grasp the rope because he feared it was not strong enough.

Use every idea that proves helpful and apply it in every possible way. There is no intent to give here all of the applications, but merely to give principles and to suggest one or two ways in which they have been used. The applications that are of most value to you are those you make for yourself. The principles will cover every need, if you will be resourceful in their use.

Get Out of the Rut

Make an effort. Insist upon your brain waking up and "getting on the job" and doing its share. The old method of "learning by heart" requires a maximum of time and mental effort.

This visual method requires only a minimum of time and mental effort.

Time is of the utmost value to you. Dr. James tells us that over seventy-five per cent of our Mental power is dormant, asleep. Stir yourself. Put a Maximum of Mental Effort into a Minimum of Time; develop an accurate and retentive memory--a worthy servant to be at all times relied upon--the very foundation of your success. You can work wonders with yourself by intelligent and persistent effort.

The Capacity of the Visual Memory is Unlimited.

Faith is the Atmosphere in which Success lives.

Kill Mental Laziness. It has always been fatal--it is as deadly NOW!

It Can Be Done

Somebody said that it couldn't be done,
But he with a chuckle replied,
That maybe it couldn't, but he would not be one
To say so until he tried.
So he buckled right in with a bit of a grin
On his face; if he worried he hid it,
He started to sing as he tackled the thing
That couldn't be done--and he did it.

Somebody scoffed, "Oh, you'll never do that--
At least, no one ever has done it,"
But he took off his coat and he took off his hat,
And the first thing we knew he'd begun it.
With a bit of a grin and a lift of his chin
Without any doubting or quit it
He started to sing as he tackled the thing
That couldn't be done--and he did it.

There are thousands to tell you it cannot be done,
There are thousands to prophesy failure,
There are thousands to point out, one by one,
The dangers that wait to assail you;
But just buckle in with a bit of a grin,
Take off your coat and go to it;
Just start in to sing as you tackle the thing
That cannot be done--and you'll do it.

--Edgar Guest.

While you are thinking it can't be done--somebody else is doing it.

CHAPTER TWO

In this last chapter will be given applications of the memory principles which have been made by students. Some will be helpful to you, others will suggest ideas which you can change and adapt to your own problems.