Early Childhood Mathematical Reasoning
Mathematical reasoning, like literacy, builds on informally
acquired knowledge. Between 14 and 16 months, toddlers display
a beginning grasp of ordinality , or order relationships between
quantities—for example, that 3 is more than 2, and 2 is more than 1.
And 2-year-olds often indicate without counting that a set of items
has “lots,” “many,” or “little” in relation to others (Ginsburg, Lee, &
Boyd, 2008 ). By the time children turn 3, most can count rows of
about five objects, although they do not yet know exactly what
the words mean. For example, when asked for one, they give one
item, but when asked for two, three, four, or five, they usually give
a larger, but incorrect, amount. Nevertheless, 2½- to 3½-year-olds
understand that a number word refers to a unique quantity—that
when a number label changes (for example, from five to six), the
number of items should also change (Sarnecka & Gelman, 2004 ).
By age 3½ to 4, most children have mastered the meaning of
numbers up to 10, count correctly, and grasp the vital principle of
cardinality —that the last number in a counting sequence
indicates the quantity of items in a set (Geary, 2006a ). Mastery of
cardinality increases the efficiency of children’s counting. Early
Childhood Mathematical Reasoning.
Around age 4, children use counting to solve arithmetic problems.
At first, their strategies are tied to the order of numbers as
presented; to add 2 + 4, they count on from 2 (Bryant & Nunes,
2002 ). But soon they experiment with other strategies and
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Mathematical Reasoning in Early Childhood
Mathematical Reasoning in Early Childhood
Mathematical reasoning, like literacy, is based on knowledge that has been acquired informally. Toddlers demonstrate an early understanding of ordinality, or the order relationships between quantities, between the ages of 14 and 16 months, for example, that 3 is greater than 2, and 2 is greater than 1.
And, without counting, 2-year-olds frequently indicate that a set of items has “lots,” “many,” or “little” in comparison to others (Ginsburg, Lee, & Boyd, 2008). By the age of three, most children can count rows of about five objects, though they do not yet understand what the words mean. When asked for one item, for example, they usually give one item, but when asked for two, three, four, or five, they usually give a larger, but incorrect, amount. Nevertheless,
