Development is multi-fold in nature: it proceeds in patterns that are predictable enough that psychologists, doctors, and educators can point to broad social, physical, and mental behaviors that are typical of any age group. In addition, as the child grows each of these areas develop and impact each other; none develop in isolation. Development is also unpredictable in that it is very individual, and patterns of growth can be unruly: at times aligning with the child's chronological age, or at other times, not. Parents and teachers know this from experience.
Young children already possess a rich assortment of mathematical cognitive abilities when they enter school. Through play with their toys and everyday family activities, they have spontaneously compared, sorted, arranged, and counted objects, explaining what they did and challenging others' explanations. (When their senses falter, they can always fall back on their fail-safe question, why?). Young children are intensely curious about their environment and interact directly with it. Much of what they know is filtered through their perceptions, which are particular to them and can be very unreliable. Children at this intuitive stage will believe that a quantity changes when the arrangement is changed, even if they have counted several times. What's more, they don't question their belief.
Although we describe each age separately as a way to organize the information, we will describe the cognitive and mathematical development of children ages four, five, and six in broad strokes. There are no sharp divisions from one stage to another, but rather there are overlaps that indicate the transitional nature of growth.
As children's minds continue to develop, their brains go through successive stages of growth, and children become less dependent on perception. The quality of children's thinking changes; they think differently and are puzzled by their earlier belief that the quantity changed when the arrangement changed. Their more logical thinking tells them that no matter the arrangement, the quantity will remain the same.
At Four Years Old
At Five Years Old
At Six Years Old
For even more helpful information about your child's mathematical development, visit DreamBox Learning. There you can find individualized online math games that your children can play and even more in-depth research about your child's mathematical development.
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