Written Number Symbols

Learning to read written number symbols is quite variable and depends considerably on the written symbols in children’s environment and how often these are pointed out and read with a number word so that they can learn the symbol-word pair (Clements and Sarama, 2007; Mix, Huttenlocher, and Levine, 2002). Unlike much of the number core discussed so far, learning these pairs is rote learning with hardly any possibility of finding and using sequential information. Component parts of particular numbers, or an overall impression (e.g., an 8 looks like a snowman) can be identified and discussed using perceptual learning principles (Baroody, 1987; Baroody and Coslick, 1998; Gibson, 1969; Gibson and Levin, 1975). Learning to recognize the numerals is not a hugely difficult task, and 2- and 3-year-olds can often read some numerals; 4-year-olds can learn to read many of the numerals to 10. Kindergarten children with such experiences can then concentrate on reading and understanding the numerals for the teens, and first graders can master the cardinal tens and ones connections in the numerals from 20 to 100 (see discussions at those levels).

Learning to write number symbols (numerals) is a much more difficult task than is reading them and often is not begun until kindergarten. Writing numerals requires children to have an accurate mental image of the symbol, which entails left-right orientation, and a motor plan to translate the mental image into the correct sequence of motor actions to form a numeral (e.g., see details in Baroody, 1987; Baroody and Coslick, 1998; Baroody and Kaufman, 1993). Some numerals are much easier than others. The loops in 6 and 9, the curve and straight line in the 2, and the crossovers in the 8 are difficult but can be mastered by kindergarten children with effort. The easier numerals 1, 3, 4, 5, and 7 can often be mastered earlier. Whenever children do learn to write numerals, learning to write correct and readable numerals is not enough. They must become fluent at writing numerals (i.e., writing numerals must become overlearned) so that writing them as part of a more complex task is not so slow or effortful as to be discouraging when solving several problems. It is common for children at this step and even later to reverse some numerals (such as 3) because the left-right orientation is difficult for them. This will become easier with age and experience.

Coordinating the Components of the Number Core

We discussed above how children coordinate their knowledge of the number word list and 1-to-1 correspondences in time and in space to count groups of objects in space. They also gradually generalize what they can count and extend their accurate counting to larger sets and to sets in various arrangements not in a row (circular, disorganized). However, accuracy for the latter comes quite late, except for small sets (Fuson, 1988). Gener-

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