Differential calculation abilities in young children from middle- and low-income families.

This study examined the performance of 42 middle- and 42 low-income kindergarten children on arithmetic calculations presented in a nonverbal format as well as in 3 different verbal formats. On the nonverbal task, the child was shown an initial set of disks, which was then hidden with a cover. The set was transformed by adding or removing disks. After the transformation, the child's task was to construct an array of disks that contained the same number of disks as in the final hidden set. A significant interaction between income level and task format was obtained. Although middle-income children performed better than low-income children on each of the verbal calculation tasks, the 2 income groups did not differ in performance on the nonverbal calculation task. The findings suggest that the nonverbal task format is less sensitive to socioeconomic variation than are the verbal task formats. A number of contextual variables can affect a young child's performance on arithmetic tasks, including the amount of verbal understanding required by the task, the nature of the quantitative terminology used in the task, and the availability of object referents (Gelman & Gallistel, 1978; Gelman & Massey 1987). In fact, our work on the development of calculation abilities in young children has shown that children's performance on addition and subtraction problems varies according to the nature of the task (Levine, Jordan, & Huttenlocher, 1992). In this prior study, middle-class children between 4 and 6 years of age were given identical addition and subtraction calculations in three different formats: nonverbal problems, story problems, and number-fact problems. On the nonverbal calculation task, the child was shown a set of physical referents that were then hidden with a box used as a cover. The hidden set was transformed either by adding or subtracting elements through an opening in the side of the box. After the transformation, the child's task was to construct an array with the same number of elements that were in the final set. The child was never allowed to see the entire set that the experimenter had produced. This ensured that an addition or

[1]  G. F. Stout.  Development of child. , 1903 .

[2]  D. Geary,et al.  A componential analysis of an early learning deficit in mathematics. , 1990, Journal of experimental child psychology.

[3]  K. Fuson,et al.  SUBTRACTING BY COUNTING UP: MORE EVIDENCE , 1988 .

[4]  C. Thornton.  Solution strategies: Subtraction number facts , 1990 .

[5]  Geoffrey B. Saxe,et al.  Social processes in early number development. , 1987 .

[6]  R. Siegler.  Hazards of mental chronometry: An example from children's subtraction. , 1989 .

[7]  D. Entwisle,et al.  Beginning school math competence: minority and majority comparisons. , 1989, Child development.

[8]  R. Siegler.  The perils of averaging data over strategies: An example from children's addition. , 1987 .

[9]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[10]  L. Aiken.  VERBAL FACTORS AND MATHEMATICS LEARNING: A REVIEW OF RESEARCH , 1971 .

[11]  Patricia Howlin,et al.  Origins of cognitive skills , 1986 .

[12]  Mary S. Riley,et al.  Development of Children's Problem-Solving Ability in Arithmetic. , 1984 .

[13]  W. Elley,et al.  THE REDUCTION OF SOCIOECONOMIC BIAS IN INTELLIGENCE TESTING , 1963 .

[14]  Thomas Kellaghan.  Relationships between Home Environment and Scholastic Behavior in a Disadvantaged Population. , 1977 .

[15]  Benson Schaeffer,et al.  Number development in young children , 1974 .

[16]  T. P. Carpenter,et al.  Cognitive Development and Children's Solutions to Verbal Arithmetic Problems. , 1982 .

[17]  Nancy C. Jordan,et al.  Development of calculation abilities in young children. , 1992, Journal of experimental child psychology.

[18]  Herbert P. Ginsburg,et al.  Social Class and Racial Influences on Early Mathematical Thinking. , 1981 .

[19]  Thomas P. Carpenter,et al.  Problem Structure and First-Grade Children's Initial Solution Processes for Simple Addition and Subtraction Problems , 1981 .

[20]  V. Mcloyd,et al.  The impact of economic hardship on black families and children: psychological distress, parenting, and socioemotional development. , 1990, Child development.

[21]  H. Walberg,et al.  Differential Mental Abilities and Home Environment: A Canonical Analysis. , 1973 .

[22]  Herbert P. Ginsburg,et al.  The development of mathematical thinking , 1983 .