Which one of the following alternatives best characterizes a central conceptual structure view of children's mathematical development?
a. Children don't acquire a true understanding of the nature of numbers until they learn how to add and subtract.
b. Even in infancy, children's understanding of quantity has a somewhat abstract quality to it.
c. Children acquire a multidimensional understanding of numbers that integrates earlier, separate understandings of quantity, numerals, and counting.
d. Children have a biologically built-in mechanism that enables them to recognize quantity even in infancy; at around puberty, the rise in certain hormones activates new mathematical capabilities in this mechanism.
Question 2
Fourteen-year-old Ruth mistakenly believes that the number 0.349 is larger than the number 0.80. Which one of the following explanations of her error is most likely?
a. Ruth has not yet mastered the part-whole principle.
b. Ruth has acquired few if any metacognitive strategies for learning and remembering mathematics.
c. Ruth is misapplying a principle of whole numbers.
d. Consistent with Piaget's theory of cognitive development, most 14-year-olds are not yet capable of proportional reasoning.
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