Second. Large pieces in graded dimensions:—There are three sets of blocks which come under this head, and it is desirable to have two of each of these sets in every school.
(a) Thickness: this set consists of objects which vary from thick to thin. There are ten quadrilateral prisms, the largest of which has a base of 10 centimetres, the others decreasing by 1 centimetre. The pieces are of equal length, 20 centimetres. These prisms are stained a dark brown. The child mixes them, scattering them over the little carpet, and then puts them in order, placing one against the other according to the graduations of thickness, observing that the length shall correspond exactly. These blocks, taken from the first to the last, form a species of stair, the steps of which grow broader toward the top. The child may begin with the thinnest piece or with the thickest, as suits his pleasure. The control of the exercise is not certain, as it was in the solid cylindrical insets. There, the large cylinders could not enter the small opening, the taller ones would project beyond the top of the block, etc. In this game of the Big Stair, the eye of the child can easily recognise an error, since if he mistakes, the stair is irregular, that is, there will be a high step, behind which, the step which should have ascended, decreases.
(b) Length: Long and Short Objects:—This set consists of ten rods. These are four-sided, each face being 3 centimetres. The first rod is a metre long, and the last a decimetre. The intervening rods decrease, from first to last, 1 decimetre each. Each space of 1 decimetre is painted alternately red or blue. The rods, when placed close to each other, must be so arranged that the colours correspond, forming so many transverse stripes—the whole set when arranged has the appearance of a rectangular triangle made up of organ pipes, which decrease on the side of the hypothenuse.
The child arranges the rods which have first been scattered and mixed. He puts them together according to the graduation of length, and observes the correspondence of colours. This exercise also offers a very evident control of error, for the regularity of the decreasing length of the stairs along the hypothenuse will be altered if the rods are not properly placed.
This most important set of blocks will have its principal application in arithmetic, as we shall see. With it, one may count from one to ten and may construct the addition and other tables, and it may constitute the first steps in the study of the decimal and metric system.
(c) Size: Objects, Larger and Smaller:—This set is made up of ten wooden cubes painted in rose-coloured enamel. The largest cube has a base of 10 centimetres, the smallest, of 1 centimetre, the intervening ones decrease 1 centimetre each. A little green cloth carpet goes with these blocks. This may be of oilcloth or cardboard. The game consists of building the cubes up, one upon another, in the order of their dimensions, constructing a little tower of which the largest cube forms the base and the smallest the apex. The carpet is placed on the floor, and the cubes are scattered upon it. As the tower is built upon the carpet, the child goes through the exercise of kneeling, rising, etc. The control is given by the irregularity of the tower as it decreases toward the apex. A cube misplaced reveals itself, because it breaks the line. The most common error made by the children in playing with these blocks at first, is that of placing the second cube as the base and placing the first cube upon it, thus confusing the two largest blocks. I have noted that the same error was made by deficient children in the repeated trials I made with the tests of De Sanctis. At the question, "Which is the largest?" the child would take, not the largest, but that nearest it in size.
Any of these three sets of blocks may be used by the children in a slightly different game. The pieces may be mixed upon a carpet or table, and then put in order upon another table at some distance. As he carries each piece, the child must walk without letting his attention wander, since he must remember the dimensions of the piece for which he is to look among the mixed blocks.
Copyright, 1912, by Carl R. Byoir
The games played in this way are excellent for children of four or five years; while the simple work of arranging the pieces in order upon the same carpet where they have been mixed is more adapted to the little ones between three and four years of age. The construction of the tower with the pink cubes is very attractive to little ones of less than three years, who knock it down and build it up time after time.