LEND A HAND.

[This department is conducted by MRS. E. E. OLCOTT.]

"Look up and not down

Look forward and not back
Look out and not in;

Lend a hand."

SUGGESTIONS IN MULTIPLICATION.

Most teachers who attempt multiplication very early in their number work with first primary pupils are forcibly reminded of the old rhyme "Multiplication is vexation."

The pupil readily sees that two sticks and two sticks are four sticks, and from objects is led to the abstract, 2 and 2 are 4. In response to the request, "Show me how many twos in four," he takes pleasure in separating the sticks into groups and in saying, "There are two twos in four." But when the attempt is made to make him distinguish between the processes and write, “2 and 2 are 4; 2 times 2 are 4; and 4 divided by 2 is 2." the fact that

"Multiplication is vexation,
Division is as bad"

Then

becomes unpleasantly conspicuous. The truth is that the knowledge that 2 and 2 are 4, enables him to solve any problems dealing with the relations of 2 and 4 that may be given him. Take these three kinds of problems: (1) Kate has two dolls and May has two. How many dolls have both?

(2) Two boys each have two tops. How many tops

are there?

(3) I have four birds. If I put two birds in cach cage, how many cages shall I need?

In each case the pupil gives the answer and if asked,

"How do you know that?" he will probably say, "Because 2 and 2 are 4." Even in such a problem as, John had four apples and ate two; how many apples were left? the pupil is not unlikely to think of that same "2 and 2" and that if he takes one of the twos away the other will remain.

Since this is the case, why strive to impress the difference upon the child? Isn't this a sensible rule, "Do not drill and drudge to force upon the pupil those things which, in due time, will come to him pleasantly and naturally?" Too often our work is like climbing a ladder or a long stairway, instead of like ascending a hill whose upward slope is so gradual that we are reminded of our elevation only by looking down upon the valley from which we started.

Let us presume that your class has been dealing, in a general way, with numbers to 10 inclusive without any stress being laid upon the process involved. You feel that the class may, with profit, deal consciously with concrete and then abstract multiplication. The number 12 lends itself so readily to the work that it is well to introduce it at once. You may say, "Who can bring me a dozen pegs?" Then, "How many pegs make a dozen?" When the class have learned that twelve pegs make a dozėn, ask "How many twos make twelve?" Being curious to discover, the pupils eagerly separate the pegs into twos and announce, "6 twos are 12." "Take away one of the twos," you say, and tell me how many twos are left." "5 twos" the class reply. "Five twos are how many pegs?" comes next. Promptly they answer, "5 twos are 10 pegs." In this manner, taking away two each time, they find that 4 twos are 8, 3 twos are 6, and finally that 1 two is 2. Now reversing the order, ask for the story about "1 two." When some

pupil has said "1 two is 2", then request, "Show me with pegs what the next story will be?" All the class arrange pegs into 2 twos, then one child tells the story, "2 twos are 4." Proceeding in this way, they

reach 6 twos are 12.

Then suggest, "suppose we begin again, and show the stories with pegs, and tell them with our lips and then write them." So the written table materializes. "Now erase what you have written and try to write it again by yourselves; the pegs will show you the answers," you say. For the sake of the weaker members of the class, it may be well to leave the following on the blackboard:

1 two is
2 twos are

3 twos are

4 twos are

5 twos are
6 twos are

Those who can write the table easily will not care to look at it, while those who need help can refer to it. There has been no drudgery in this to the pupils, instead they enjoyed the variety. It will take but little stimulating to lead them to commit it to memory. You may even tell them that it is the multiplication table-the long name adds importance to the process in their eyes. Follow this with concrete problems, as, (1) Four boys have how many thumbs? When the answer has been given, let four boys come before the class and hold up their thumbs to prove that eight is correct. (2) Two boxes at two pennies apiece cost how much? Draw a picture to show the cost. Thereupon they draw two squares for boxes and place two rings for pennies under each box, thus:

This impresses the three twos upon their minds. the same way develop the following tables:

In

class is familiar with this form of the table, say: "There is a shorter way to write these. Here is a sign which is called times. If I write 2x 4-8, it means to take 4 two times. That is just the same as 2 fours are 8. Write the table of fours with the sign and read it

And so on.

Gradually substitute the expression "times" until it means as much to the pupils as the other form. If a child hesitates at 3 x 4, aid him with the question, "3 fours are how much?" If that is not sufficient, let him return to the objects and show three fours with pegs. Thus the abstract rests upon the concrete, and multiplication ceases to be vexation, but instead affords pleasant variety in number work.

(5) What will five two-cent stamps cost?

(6) How many feet have three horses?

A LESSON IN LANGUAGE AND GENEROSITY.

Nothing is truer than that the best part of a teacher's work can not be measured and recorded in reports. The spirit of her teaching and the subtle, moulding influence

which, whether she will or not, each teacher exerts in a greater or less degree upon her school, these can not be imprisoned in statistics. To use this moulding influence consciously and skillfully is an attainment which earnest conscientious teachers greatly desire. Illustrations often aid those who are seeking this skill. So a language lesson with a double purpose is given as a suggestion to thoughtful teachers.

Miss A- had noticed a tendency toward selfishness among certain ones of her pupils. One day the fact was shown clearly by contrast. Bertrand brought an unusually dainty lunch, a part of which was a large bunch of delicious grapes. He displayed the grapes and ate a few, and it seemed to add to their flavor that no one else had anything so nice. Soon after, Tommy came in with a large apple. Apples were rare treats to him. Coming to the teacher with a beaming face he said: "See my big apple. I'll give you a bite at recess!" He did not forget it either, but at recess, came with the apple for her to take the promised bite. Looking at him kindly, she said, "I am not hungry now, and I'd rather see you eat it, Tommy." She spoke with such sincere cordiality that he was perfectly satisfied. During recess she saw Bertrand exchange three grapes for a piece of taffy and noted that he selected the smallest grapes in the bunch. She noticed also that though he had more lunch than he could eat he gave none away, but took the remnants home with him at noon.

So that afternoon she chose a certain story for a language lesson. "Children," she said, "I have a legend to tell you. Who remembers what a legend is?"

"It's a kind of fairy story; it most always isn't true, but it helps us to be good," said one. "Well," said Miss A- "this one is about the woodpecker. Most of the