Development of Cognitive Structures Related to Mathematics
As children develop cognitively from pre-lingual and pre-symbolic stages to the use of language and symbols to manipulate concepts, their abilities related to later mathematics learning are also developing. Some of the most critical cognitive abilities for mathematics learning are memory, language skills, and the ability to make mental representations of number and space.
Young children begin using their memory abilities as they interact with the environment and recall those experiences. Infants will respond to familiar faces and music. Children enjoy retelling stories and singing songs over and over again. As they begin noticing environmental print, children begin to understand the role of letters and numbers as abstract representations for familiar things. Names of streets, stores, candy, and numbers on houses and roads begin to take on meaning. Children ask to be taught to write their names and memorize the markings. Some children are so delighted with their new skills that they make markings everywhere—on books, walls, and under furniture.
With formal schooling, memory tasks become more challenging. Children must recall the written character for letters, numbers, and other symbols used in writing and mathematics. They are required to remember math facts and the sequences for performing operations with numbers. In problem solving, children are encouraged to recall a similar problem type or situation. Memory tasks are more successful when children learn through concept understanding rather than by rote memorization. New concepts should be connected to real-life experiences of children so that cognitive structures are formed in long-term memory.
Language development is critically integrated with mathematics development. Children use language to express relationships, assign labels, manipulate concepts, and communicate understandings with others. Language becomes the mediation tool for performing more difficult mathematics tasks, as can be seen in native language comparison studies (see, for example, Miura & Okamoto, 2003). Teachers use carefully selected language to ask questions and explain new concepts.
Children with language delays may have corresponding delays in mathematics development. Cognitive abilities of symbolic thinking, temporal–sequential organization, verbal memory, and rate of language processing are language abilities directly related to mathematics tasks (Jordan, Levine, & Huttenlocher, 1995). Nonverbal mathematics tasks, such as the manipulation of objects without verbal requirements, are generally developed earlier than verbal tasks (story problems) and are less sensitive to socioeconomic differences. Jordan, Levine, and Huttenlocher examined the calculation abilities of young children (kindergarteners and first graders) and found that children with language impairments performed as well as their peers on nonverbal calculations but significantly worse on story problems (presented orally) than the non-impaired group.
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