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1998 and Spring accept peer ideas addition and subtraction Asian children assessed in English Center for Education Childhood Longitudinal Study children demonstrate children whose mothers children's knowledge children's reading Children's Specific Knowledge cognitive knowledge Department of Education differ by child Early Childhood Longitudinal Education Statistics end of kindergarten ending of words enter school estimates fall of kindergarten Fall to Spring gains children Jerry West Kindergarten Class kindergarten program characteristics kindergarten program type knowledge and skills later school difficulty letter-sound relationship mathematics knowledge mathematics scale scores Methodology and Technical mother's education mothers have less National Center NCES noncognitive knowledge percent of children persist at tasks proficiency race/ethnicity reading and mathematics recognize their letters recognizing words risk for later school type Skills by Child skills differ skills i.e. specific reading spring of kindergarten standard deviation standard errors teachers U.S. Department understand the letter-sound Westat words by sight words in context