Unformatted text preview: with only the problem written at the top, they have a chance to
organize their thoughts and decide how to externalize them on paper.
Figure 2.6 is clearly an example of Type-3 representation, except that the
child added qualitative characteristics such as “G” for “gorilla” and “B” for “but
terflies.” (This picture book probably emphasizes the different lands of animals,
and young children are intensely interested in the differences among them.)
Figure 2.7 is a Type-5 representation, and the child drew circles and crossed
them out as he added the numbers.
The great variety of graphic representations suggests why children prefer
to draw rather than to use counters. When they are presented with a word prob
lem and a sheet of paper, they evoke mental images or imageless numerical ideas
and externalize them on paper. For those who made Figures 2.4 and 2.5, the
characteristics of the animals were very important. For those who drew Fig
ures 2.6 and 2.7, these characteristics were irrelevant. When children...
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- Spring '14
- Writing, Numeral system, Table of mathematical symbols, theoretical foundation