### Numbers

Most kindergarten children understand one-to-one correspondence concepts and are beginning to develop an understanding of additive relationships and cardinality. Because of the development of a system of ones and hierarchical inclusion, most children of this age can not only count, but also understand that with each number they say, the quantity increases by one. When a kindergarten child counts “five, six,” he understands that in essence he is adding “one” to “five.” Because of this additive thinking, children can begin to compose and decompose sets of numbers. For example, they understand that three red chips and two blue chips make five chips (compose). They also understand that a group of five chips can be broken down into smaller groups of four and one or three and two (decompose). While this is not the formal addition that we will see in first grade, this additive thinking makes it possible to introduce some simple addition games and activities to the curriculum. Kindergarten children may not be able to handle addition with numerical notation such as “3 + 5,” but they can count the dots on dominos or other items. Children in kindergarten may count all or, if they are a bit more advanced, they may count on. For example, if playing a path game that requires two number cubes to be thrown and the game piece to be moved based upon the resulting number, a child might count all of the dots on both cubes. This is composition of a new number set because the child is combining two smaller sets of numbers to make a larger number, then moving his game piece according to that new number. Another strategy is for the child to count on from the higher number—he might throw a five and a three and say “five . . .” and then count the dots on the other cube, “six, seven, eight.” This is called counting on. It is still composition of a new set; it is simply a more advanced strategy than counting all (Smith, 1997). Kindergarten teachers can encourage these composition strategies through the use of games. To encourage children to use counting on, teachers can replace one of the cubes that has dots with one that has numerals. Since there are no dots to count, it encourages the child to count on. It is possible that the child will still count to the numeral on his fingers and then count the remaining dots. If this is the case, the child is not ready to advance to counting on. Kindergarten children have sufficient control of their fingers and hand muscles to permit the use of a pencil. In fact, they begin to prefer writing with a pencil rather than a crayon or marker. Their memory level allows them to remember the shapes of numbers and recall them when writing. Number and letter reversals are common in kindergarten children due to factors such as memory or perception. Given their development, this is normal. Children may have no problem aligning numbers on the top-to-bottom axis so they don’t write them upside-down, but coordinating both the top-to-bottom axis and the left-to-right axis may be challenging for children this age.

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