2 a child would say that there is no change because

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Unformatted text preview: arguments is identity, which is the understanding that if nothing is added or taken away, nothing changes. For example, on the conservation of number task described in Table 5.2, a child would say that there is no change because no coins had been added or taken away. A second operation or argument is negation or reversibility. Negation is the understanding that for a particular operation or action, there is an action or operation that undoes the effects of the first operation. In the conservation of number task a child would say that if you mentally push the coins back together, you can see nothing has changed. The third operation or argument is compensation, which is a form of decentering. The compensation argument is that changes in one dimension can explain the observed change in another. With 16 the conservation of number task, the one row is longer, but that is because the inter-item spacing is larger. Seriation and classification. Seriation and classification are two additional operations that figure prominently in Piagetian discussions of the stage of concrete operations. (Piaget, 1941; Piaget & Inhelder, 1969). Seriation is the operation that allows children to arrange objects in terms of increasing or decreasing size. Consider this example of seriation. ⇒ Sally, a seven-year-old, is cleaning her room. She has decided to put her stuffed animals on her shelf in order from tallest to shortest. “The big ones are first, then the medium-sized ones, and then the tiny ones.” Classification is the operation that allows us to place objects into categories on the basis of shared characteristics. For instance, our ability to categorize different examples of triangles, squares, and circles correctly would be the result of the classification operation. For the Piagetians, both seriation and classification are important for children’s development of mathematical and scientific logic. The Stage of Formal Operations The stage of formal operations theoretically begins at the end of the concrete operational stage, and it is the final of the four Piagetian stages. Formal operations act on ideas rather than on objects, and there are a number of important 17 differences between formal and concrete operational reasoning (Gruber and Voneche, 1977; Piaget & Inhelder, 1969; Wadsworth, 1996). Hypothetico-deductive reasoning. The first and most important change that marks the advent of formal operational thinking is the ability to reason from hypotheses. Piagetians refer to this type of logic as hypothetico-deductive reasoning. During the stage of formal operations, adolescents become capable of forming theories or hypotheses, and of developing systematic ways to test and/or prove their hypotheses. Mr. Farley makes use of this potential in his high school world history class. ⇒ “Rather than telling my students the reasons for historical events, I start by explaining the event. Students then try to guess at possible causes of events. They then talk about how they would research the causes of this parti...
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