The Sequence of Exercises Through Which the Child Is Introduced to the Group Operations with the Golden Beads.

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The sequence of exercises through which the child is introduced to the group operations with the Golden Beads Math operations include addition, multiplication, subtraction, and division. All these operations require full understanding of quantities on a concrete level before moving to the abstract level of performing these operations mentally. So the first exercise introduced to the child to prepare him for these operations; is the “Number Rods”. The ten number rods are graduated in length from 4 inches length for the shortest one, to 40 inches length for the longest one. The different four inch sections are alternately colored red and blue and can be counted on each rod. So , each rod consists of distinct countable units, united together to represent a number. This overcomes the difficulty of adding one unit after another in a sum total. “The fact that a group is enlarged through the addition of a unit, and that this increasing must be considered; constitutes the chief obstacle for the children of three and a half to four, in learning how to count.” Maria Montessori, The Discovery of the Child, page 263 Several activities are done with the number rods. All of them are activities of moving and joining. One time the child builds them next to each other starting with the shortest and ending with the longest, and another time, he builds them on top of each other. All this joining and moving is an introduction to arithmetic. Then the “Sand Paper Numerals” are introduced to the child, to teach him their names and how to write them. Later on the child learns to match the card to the corresponding rod, which “forms the basis for a lengthy task which a child can continue by himself. The sums of the rods can be written so that they correspond to the numbers.” Maria Montessori, The Discovery of the Child, page 265 Two other objects are used to help the child begin arithmetic; The “Spindle Box”, and “The Cards and Counters”. ”The Spindle Box” attains three main objectives. It gives a child a concept of numerical groups , and at the same time; it fixes before his eyes the succession of numerals, and finally he is introduced to the “Zero”. In this activity; the child reads a number on the wall of a compartment, and then he groups the corresponding number of spindles in his hand, then he places them in the compartment. “Cards and Counters” accomplish another two objectives. It shows that the child has understood the order of the numbers, and that he recognizes the figures representing the numbers. Moreover; it is by this activity that the child realizes the difference between odd and even numbers. By then; the foundation for counting and arithmetical operations is laid.

Till now, the child is working with numbers not more than ten. “Number Games” are then played to make sure that the child deeply understands the quantities and the written symbols of numbers from 1 to 10, and to make sure that he really understands the concept of “Zero”. When this understanding is shown; the child is introduced to the “Decimal System”. First the child is taught “The Names of The Power of Ten” through the bead material. By the power of ten, we mean the unit, ten, hundred and thousand. For this lesson; the teacher uses one single bead to represent the “Unit”, ten beads wired together in the form of a bar to represent the “ Ten”, ten of the ten bars wired beside each other forming a square of hundred beads to represent the “Hundred”, and finally, ten hundreds wired on top of each others forming a cube of thousand beads to represent the “Thousand”. The teacher introduces these names with a three period name lesson, and to make him understand this on a more concrete level; “The Counting Through” activity is introduced. He would see how repeating a digit 10 times makes it become another digit. He will see hoe ten units make a ten, ten tens make a hundred, and ten hundreds make a thousand. This is...
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