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
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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This document was uploaded on 03/29/2014 for the course EPS 324 at N. Arizona.
- Spring '08