The Cylinders



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

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
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.


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.


2 and 1/2 to 5 years.


The teacher sits beside a child at a table and places the block 1 in
front of him or her. 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 or she begins removing
and replacing cylinders, the child can be left to work alone. The child may
hold the cylinders incorrectly. He or she will make mistakes in putting them
in the holes. The child will probably handle them noisily. The child can
replace the cylinders in any order he or she likes.
The child must not be interrupted when working, but the next day the teacher
should take a block and show him or her 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. The child 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 or her. The teacher 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.


The child helps him or herself to a block and continues to use it as presented
for as long as he or she likes.
The child can use any set 1, 2, or 3 without a further lesson.
The child 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


When the child can do each set well he or she can be shown how to use two sets
together, mixing the cylinders from both and replacing them.


When the child uses two sets well, the teacher can show him or her 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.


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


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.


After the child has developed a concept of dimension and has noticed the differences between the various cylinders, the teacher can use the "Three Period Lesson" to introduce the terminology  listed below for each block.

Block 1 and 2:  large - small
                         large- larger- largest
                         small - smaller- smallest

Block 3:            thick - thin
                         thick - thicker - thickest
                         thin - thinner - thinnest

Block 4:            tall - short                             deep - shallow
                         tall - taller - tallest                 deep - deeper - deepest
                         short - shorter - shortest        shallow - shallower - shallowest


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