March/April 2007
Preschool: Counting words and quantities
are not well linked
• Recite counting words (one to five or one to ten) in sequence
• Count with one-to-one correspondence
• Make global quantity comparisons (more, less; taller, shorter)
Kindergarten: Counting words and quantities become linked
• Know that small numbers mean a little and big numbers mean
a lot
• Know that the next counting word in a sequence means one
more
• Use numbers to compare quantities (two fewer cookies, six
more steps)
• Can use numbers to make quantity determinations without
using objects
First grade: Counting words and quantities
are linked to symbols
• Recognize numerals and associate them with counting words
• Grasp the meaning of operational symbols (+, –, =)
• Form “number sentences” to express quantitative
relationships (7 – 2 = 5)
Second grade: Children can link words
to quantities along two scales (e.g., tens and ones)
• Understand place value
• Tell which two-digit number is bigger
• Mentally solve two-digit addition and subtraction problems
• Solve problems involving hours and minutes, dollars and
cents, weight and distance
Third grade: Children consolidate the
understandings acquired in second grade
• Apply understandings to broader range of concepts
• Understand multiplication as a relationship among two groups
(e.g., three cars with four wheels each)
Source: Adapted from S. Griffin, “The
Development of Math Competence in the Preschool and Early School
Years,” in J.M. Royer, Mathematical Cognition.
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