Unformatted text preview: between concrete objects and mathematical sym
bols. According to Piaget (1945/1951), pictures and mathematical symbols have
different sources, and working with pictures is not necessarily a step toward
becoming able to deal with mathematical symbols. Symbols and Signs
Piaget (1945/1951) distinguished between symbols, such as pictures and
tally marks (the lefthand side of Figure 2.1), and signs, such as words and writ
ten numerals (the righthand side). His terminology is confusing at first because
he used the term symbol differently from common parlance.
19 2q Theoretical Foundation Figure 2.1. The representation of "eight* in Piagets theory. In Piaget’s theory, symbols such as pictures bear a resemblance to the ob
jects represented and can be invented by each child. In other words, the source
of symbols is children’s thinking. For example, children can think about “eight"
(the rectangle in Figure 2.1 labeled “The child’s idea of‘eight’”) and draw 8 apples
or 8 people without any instruction....
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This document was uploaded on 03/13/2014.
 Spring '14

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