June 8, 1998
For immediate release
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William Harms
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University of Chicago Study Shows Children Begin Learning Mathematics at Age 3
Regardless of their backgrounds, children as young as 3 have the ability to recognize numbers, and add and subtract, according to research by Susan Levine and Janellen Huttenlocher, both Professors of Psychology at the University of Chicago.
The ability develops in children from a wide range of social economic groups at about the same age. However, this mathematical ability can be greatly increased with parental and other adult encouragement, Levine said.
The research also demonstrates that many students bring more mathematical understanding to the classroom as kindergartners than many teachers probably realize. Those students include youngsters from disadvantaged backgrounds who do not have the language skills necessary to do conventional classroom work in mathematics. Those students comprehend quantity through a nonverbal understanding of number of objects and may be able to learn better if the instruction is initially less verbally oreinted, Levine said.
"Often when children cannot respond correctly to the verbal mathematics problems that are frequently presented in the classrooms, it is assumed that they lack an understanding of mathematical concepts," Levine and Huttenlocher write in a new paper, "What Young Children Know about Mathematics," issued by the Early Childhood Initiative at the University of Chicago.
"Our findings show that children with specific language impairments have well-developed mathematical concepts, but may lack the knowledge of the conventional verbal symbols of arithmetic and general verbal comprehension skills that are very important to solve mathematical word problems."
Children with limited mathematics vocabularies sometimes resort to using their fingers to count as a way to do classroom problems. That practice should not be discouraged, Levine said. "One could even argue that if they are performing poorly without using fingers, then they sould be encouraged to use this strategy," she said.
To find out when infants and children begin grasping the elemental concepts of mathematics, researchers Kelly Mix, a former graduate student, Huttenlocher and Levine tested infants, toddlers and preschool children from a variety of backgrounds to see at what age they began to recognize the connection between repeated sounds and similar numbers of objects before them.
The researchers made a series of sounds and then observed whether infants looked longer at a set of objects that corresponded to the number of sounds they heard than to a set containing a different number of objects.
Infants were unable to make the audio-visual matches but could make visual-visual matches. Similarly, three-year-olds were able to make visual matches between groups of objects and sets that correpsonded in number, but only made the same number of audio-visual matches they would have made had they been guessing. "In contrast, 4-year-olds performed significantly above chance in both conditions, indicating that the ability to detect audio-visual numerical correspondences develops during this age period," Levine said. The time between ages 3 and 4 was found to be a crucial development stage for mathematics, as youngsters quickly expand their ability to understand the abstract relationship between numbers and sets as dissimilar as objects and events.
Researchers also tested youngsters' ability to perform nonverbal calculation and found that ability developing between ages 2 and a half and 3. To test that skill, they hid a set of objects under a box, and then modified the hidden set by adding a second set or removing some while the child watched the transaction. The child was then asked to form a set of objects that corresponded to the number under the box. By the time they reach age 3, most youngsters in the study were able to select the same number of objects as existed under the box, showing that they understood the elements of computation.
Levine, Huttenlocher, Nancy Jordan, a former post doctoral researcher and now a professor at the University of Delaware, conducted an additional series of tests among Chicago public school kindergarten students. The children, who came from a range of economic backgrounds, were given four tests to determine their verbal and nonverbal calculation skills. Although the students differed in their ability to do verbal word problems, the students had essentially the same level of skills in doing nonverbal calculation tasks.
Levine and Huttenlocher's research establishes with more certainty the period in a child's development when numerical knowledge emerges. Some studies have suggested that abstract numerical knowledge develops in infancy, but Levine and Huttenlocher find that babies only have an approximate understanding of numbers. Only later, at about 3 years of age, can children represent number exactly.
Levine and Huttenclocher researchers with the Early Childhood Initiative at the University of Chicago, an innovative program to study early childhood development and policy. It is funded through a two-year, $875,000 grant from the Robert R. McCormick Tribune Foundation.
The program takes an unusual multidisciplinary approach to studying early childhood learning. It promises to bring new insights to understanding the ways children develop language, learn about mathematics and acquire other many other skills and concepts.
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