Four lightly varnished wooden blocks each containing ten
cylinders vary in size in a regular way. Each cylinder has a
knob to hold it by.
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.
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
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.
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
the four blocks. Also, the circumferences of the holes are all
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
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
places it silently on the table in front of the block. She
cylinder in turn, holding them in this way, placing them silently
front of the block in mixed order. When all the cylinders have
removed, she pauses. She looks at the cylinders carefully,
largest (or smallest) and returns it noiselessly to its place.
replaces the cylinders in order in this way.
At any point of the lesson the child may join in. If he or she
and replacing cylinders, the child can be left to work alone. The
hold the cylinders incorrectly. He or she will make mistakes in
in the holes. The child will probably handle them noisily. The
replace the cylinders in any order he or she likes.
The child must not be interrupted when working, but the next day
should take a block and show him or her the right way to handle
For example: The teacher shows the child her hand, points out her
two fingers and thumb, and demonstrates how she holds the knob
removes a cylinder. She then says to the chid, "Show me your
hand. You have two fingers here and a thumb. Take out this
using those two fingers and thumb." The child will enjoy taking
cylinders and replacing them while the teacher watches. The child
begin to handle the material correctly.
If the child is being noisy, on another day, the teacher can take
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
all. Are you listening?" The teacher demonstrates how to handle
"Now, I will listen to you. You try it." Let the child try.
love this. Their attention is drawn to noise, and they begin to
their hands well and to make a great effort to handle the
quietly. The teacher also shows that the cylinders can be
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
material is self-correcting. If a mistake has been made, there
always be one cylinder that does not fit. Corrections will not
one can teach another to judge size. The child learns through
The child helps him or herself to a block and continues to use it
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
into the classroom until some children are proficient with the
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
the cylinders in the middle of the triangle and then replace them
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
cylinders inside the square and then replace them.
In blocks 1, 2, and 3, the cylinders cannot all be replaced if an
has been made. In Block 4 all can be returned, but some will be
and others too short to fit the holes. Most children can see that
Note: Do not introduce the later stages until children are
proficient with the 4 blocks used singly. The aim is never to get
children to work quickly, but to let them work with apparatus for
long as they will perfect themselves and arrive at abstract
This must be understood as applying to all the apparatus.
This exercise is a sight exercise. A blindfold is never used. It
possible to match the size of the cylinders to the size of the
touch as some holes are too narrow for the fingers to reach the
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
Block 1 and 2: large - small
large- larger- largest
small - smaller- smallest