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Unformatted text preview: s were meant to repre
sent bowls. Manipulatives are thus not useful or useless in themselves. Their utility
depends on the relationships children can make, through constructive abstraction.
Children's Preference for Drawing. Olivier, Murray, and Human (1991) made
the following statement about children in a constructivist math program they
developed in South Africa: Although informal writing materials as well as counters are always available, it seems
that students seldom use counters to model a problem. Rather, the problem con
text is drawn in greater or lesser detail, and then solved by further drawing in the
actions needed. For example, Leana (grade 1) divides 18 cookies among three
children one at a time [see Figure 2.3], and Conrad (also grade 1) two at a time,
(p. 17) I (CK) have asked many kindergarten and first-grade teachers in many parts
of the United States and Japan to conduct research in their classrooms to test
the validity of Olivier et al.’s statement. I asked them to remind their students
frequently that they (the students) were free to use the counters, paper, pencil,
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This document was uploaded on 03/13/2014.
- Spring '14