Preschoolers show ability to grasp simple mathematics
By William Harms
Children as young as age 3 exhibit nonverbal math skills, comprehending quantity and performing simple addition and subtraction using groups of objects, according to research by Susan Levine, Professor in Psychology, and Janellen Huttenlocher, the William S. Gray Professor in Psychology.
This ability develops in children at about the same age, regardless of their socioeconomic group, Levine said. Verbal math skills, however, develop at a later age and at a range of ages, depending on a number of factors.
The research also demonstrates that children may bring more mathematical understanding to the classroom as kindergartners than teachers may realize -- including youngsters from disadvantaged backgrounds who may not have the language skills necessary for conventional classroom work in mathematics. Such students are able to comprehend quantity through nonverbal understanding and may be able to learn better if initial instruction is less verbally oriented, Levine said.
"Often when children cannot respond correctly to the verbal mathematics problems that are presented in the classrooms, it is assumed that they lack an understanding of mathematical concepts," Levine and Huttenlocher write in the paper "What Young Children Know About Mathematics," issued by the Early Childhood Initiative at the University of Chicago.
"Our findings show that many children with specific language impairments have well-developed mathematical concepts, but 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 counting on their fingers as a way to do classroom problems. That practice should not be discouraged, Levine said. "One could even argue that if children are performing poorly without using fingers, then they should be encouraged to use this strategy," she said.
To find out when infants and children begin grasping the elemental concepts of mathematics, Huttenlocher and Levine, along with Kelly Mix, a former University graduate student, tested infants, toddlers and preschool children from a variety of backgrounds to determine the age when 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 in number to the number of sounds they heard.
Infants were unable to make the audio-visual matches but could make visual-visual matches. Similarly, 3-year-olds were able to make visual matches between groups of objects that corresponded in number, but could not match visual and auditory sets at above-chance levels. "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 children quickly expand their ability to understand the abstract relationship between numbers and sets as dissimilar as objects and events.
Researchers also tested children's ability to perform nonverbal calculation and found that ability developed 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 reached age 3, most children in the study were able to create a set of objects that matched the number of objects hidden under the box, showing that they understood the elements of computation.
Levine, Huttenlocher and Nancy Jordan, a former post-doc at Chicago and now a professor at the University of Delaware, conducted an additional series of tests with kindergarten students. The children, who came from a range of socio-economic backgrounds, were given verbal and nonverbal calculation tasks. Although the students varied in their ability to perform verbal word problems, the students exhibited essentially the same level of skills in performing 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 quantity. Only later, at about 3 years of age, do children begin to represent numbers exactly.