8. A preschool teacher placed eight red chips in a row and asked a child to put out the same number of blue chips. After the child did this correctly, the teacher spread out the red chips or more blue chips. The child said there were more red chips than blue chips but could not explain why. Which of the following best characterizes the child's understanding of conservation of number?
Answer: B
The child does not recognize equivalent sets after a transformation occurs.
The child's assertion that there are more red chips than blue chips after the transformation indicates a misunderstanding of the concept of conservation of number, specifically in recognizing that the quantity remains the same despite the arrangement.
A) The child does not count correctly and cannot build equivalent sets.
This option is incorrect because the child initially placed the same number of blue chips as there were red chips, demonstrating an ability to count correctly and build equivalent sets before the transformation.
B) The child does not recognize equivalent sets after a transformation occurs.
This is the correct option as the child initially matched the number of chips but failed to recognize that rearranging the chips did not change the total count. The child’s misunderstanding showcases a lack of recognition of the equivalency between the two sets after the transformation.
C) The child recognizes equivalent sets after a transformation but does not provide a justification.
This option is incorrect because the child did not recognize the equivalency after the transformation. Instead, the child mistakenly viewed the red chips as more numerous than the blue chips, indicating a failure to grasp the concept of equivalency.
D) The child recognizes equivalent sets after a transformation and provides a justification.
This option is incorrect as the child does not recognize the equivalent sets after the transformation at all. The lack of justification is irrelevant since the child is not aware that the number of chips remains the same.
Conclusion
The scenario illustrates that the child struggles with understanding the conservation of number, particularly in recognizing that the quantity of items remains constant despite their arrangement. While the child can initially create equivalent sets, the failure to acknowledge this after the transformation reflects a fundamental gap in their cognitive development regarding number conservation. Thus, option B accurately captures this misunderstanding.