The Cylinders

MATERIAL:

Four lightly varnished wooden blocks each containing ten cylinders. The

cylinders vary in size in a regular way. Each cylinder has a wooden

knob to hold it by.

Block 1

The cylinders vary in height, length, and width (taking width and

length through the diameter) by 1/2 cm. on each dimension between

any two cylinders in succession. The largest cylinder is the

tallest and thickest.

Block 2

The cylinders vary in height, length and width as in block 1, but

here the tallest cylinder is the thinnest and the shortest is the

thickest.

Block 3

The cylinders are all the same height. They vary by 1/2 cm. in

length and 1/2 cm. in width (measured through the diameter)

between any two in succession.

Block 4

The cylinders vary only in height. They cylinders differ in

height by 1/2 cm. between any two in succession.

 

Blocks 1 and 2 are the easiest, as there are three differences in

dimension.

 

Block 3 comes next with two differences in dimension.

 

Block 4 differs only in height and is by far the most difficult of

the four blocks. Also, the circumferences of the holes are all the

same and, therefore, do not offer a guide.

 

Block 4 should not be brought into the classroom until some

children are really proficient with the first 3 blocks.

PURPOSE:

1) The child learns to judge size by sight.

2) The child reaches an abstract conception of dimension, and

this interest and knowledge enable him to observe the

environment with intelligence.

3) The child develops coordination of movement.

4) The child is given an indirect preparation for writing. The

fingers and thumb, which will later hold the pencil, are being

used to hold the knobs. These digits are also used in the

manipulation of most tools (e.g. spoon, scissors, brush).

Therefore, the hand is being trained for manipulative skill.

5) A preparation for mathematics.

AGE:

2 and 1/2 to 5 years.

PRESENTATION:

The teacher sits beside a child at a table and places the block 1 in

front of him. Holding the knob of the first cylinder with the first two

fingers and thumb of her dominant hand, the teacher removes it and

places it silently on the table in front of the block. She removes each

cylinder in turn, holding them in this way, placing them silently in

front of the block in mixed order. When all the cylinders have been

removed, she pauses. She looks at the cylinders carefully, selects the

largest (or smallest) and returns it noiselessly to its place. She

replaces the cylinders in order in this way.

 

At any point of the lesson the child may join in. If he begins removing

and replacing cylinders, he can be left to work alone. The child may

hold the cylinders incorrectly. He will make mistakes in putting them

in the holes. The child will probably handle them noisily. He can

replace them in any order he likes.

 

He must not be interrupted when working, but the next day the teacher

should take a block and show him the right way to handle the cylinders.

For example: The teacher shows the child her hand, points out her first

two fingers and thumb, and demonstrates how she holds the knob and

removes a cylinder. She then says to the chid, "Show me your

hand. You have two fingers here and a thumb. Take out this cylinder

using those two fingers and thumb." The child will enjoy taking out

cylinders and replacing them while the teacher watches him. He will

begin to handle the material correctly.

 

If the child is being noisy, on another day, the teacher can take a

block and sit beside him. She speaks very softly. "Listen. I can take

the cylinders out and put them on the table without making any noise at

all. Are you listening?" The teacher demonstrates how to handle the

cylinders quietly.

 

"Now, I will listen to you. You try it." Let the child try. Children

love this. Their attention is drawn to noise, and they begin to use

their hands well and to make a great effort to handle the material

quietly. The teacher also shows that the cylinders can be returned

noiselessly to their sockets.

 

If the block has been given at the right age, the child will have

difficulty in replacing cylinders. The teacher must not interfere. The

material is self-correcting. If a mistake has been made, there will

always be one cylinder that does not fit. Corrections will not help. No

one can teach another to judge size. The child learns through repeated activity.

EXERCISE 1:

The child helps himself to a block and continues to use it as presented

for as long as he likes.

 

He can use any set 1, 2, or 3 without a further lesson.

 

He can use set 4 when that is brought into the classroom.

 

Block 4 is by far the most difficult. So, this block is not brought

into the classroom until some children are proficient with the first 3

blocks.

EXERCISE 2:

When the child can do each set well he can be shown how to use two sets

together, mixing the cylinders from both and replacing them.

EXERCISE 3:

When the child uses two sets well, the teacher can show him how to take

any three sets, place them on the table in the form of a triangle, mix

the cylinders in the middle of the triangle and then replace them in

their corresponding sockets.

EXERCISE 4:

Lastly, the child can be shown how to use all four sets together. He is

shown to place them on the table in the form of a square and mix all the

cylinders inside the square and then replace them.

SELF-CORRECTION

In blocks 1, 2, and 3, the cylinders cannot all be replaced if an error

has been made. In Block 4 all can be returned, but some will be too tall

and others too short to fit the holes. Most children can see that this

is incorrect.

 

Note: Do not introduce the later stages until children are really

proficient with the 4 blocks used singly. The aim is never to get the

children to work quickly, but to let them work with apparatus for as

long as they will perfect themselves and arrive at abstract conception.

This must be understood as applying to all the apparatus.

 

This exercise is a sight exercise. A blindfold is never used. It is not

possible to match the size of the cylinders to the size of the holes by

touch as some holes are too narrow for the fingers to reach the bottom.

The cylinders are used on a table - not on the floor.

 

 

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