Indicate which of the following cases best illustrates concrete operations. Hint: There is more than one example of concrete operational thinking. Circle the appropriate letters, and explain why they are the better answers and why each other answer is not as good.
Katie is asked, "Do you have a brother?'' She says, "Yes.'' Then she is asked, "Does he have a sister?'' She answers, "No.''
Ray says, "A fly is like both insects and birds. It's like birds because it flies, but it's like insects because it has six legs.''
Tim is working on analogies. He declares, "Biking is to pedaling as riding in a car is to stepping on the gas pedal because they both make the vehicle go!''
Bobby states, "I understand how this nickel and these five pennies are the same as this dime.''
Her teacher asks Mary, "How can the scale be brought back into balance?'' Mary replies, "The only way to do that is to remove the weight that made one pan sink lower than the other.''
This is not an example of concrete operational thinking. In this example, Katie fails to understand that sibling relationships are reciprocal. According to Piaget this is a sign of preoperational thinking.
This is an example of concrete operational thinking. In this example, Ray is able to understand that flies have attributes that place them in more than one category (creatures that fly and creatures with six legs). According to Piaget this is a concrete operational skill.
This is not an example of concrete operational thinking. In this example, Tim declares that he understands the equivalence of two abstract relationships. Piaget claims this is a formal operational ability.
This is an example of concrete operational thinking. In this example, Bobby is working with two concrete representations of money and is able to add the values of the nickels and pennies to confirm their equivalence to the dime. The equivalence also implies reversibility. All of these points characterize concrete operational thinking according to Piaget.
This is an example of concrete operational thinking. In this example, Mary shows reversibility. However, she can only think of one solution to the problem and fails to realize that there are several ways to balance a scale. Piaget identifies this as concrete operational thinking.