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Topic Editor: Jeff Bisanz, PhD, University of Alberta, Canada
Basic mathematical knowledge emerges in infancy. At 6 months of age, infants are able to perceive the difference between small sets of elements varying in quantity (2 vs. 3-object sets), and can even distinguish between larger quantities, provided that the ratio between two sets is large enough (ex. 16 vs. 32, but not 8 vs. 12). These preverbal representations become more refined over time, and they form the early, though not sufficient, building blocks of future mathematical learning.
One achievement in numeracy is the acquisition of fact fluency. Fact fluency refers to the knowledge necessary to produce sums and differences in a flexible, timely and accurate manner. In the toddler years, children progressively acquire the requirements for fact fluency, often beginning with intuitive numbers (ex. know the meaning of one, two, three), leading to the ability to recognize that, for example, any set of three elements has a larger count than a set of two elements.
As they get older, children develop more advanced number skills. By age 3, they begin to be proficient in some nonverbal, object-based tasks, such as understanding the process of adding and subtracting, and judging one set as having a larger quantity than a second one. Although preschoolers can match collections of 2, 3, and 4 elements if the objects are of similar size or shape, they still struggle when the objects are highly dissimilar (ex. matching two animal figurines with two black dots). Preschool children are also likely to get easily distracted by superficial features of a set (ex. judging a set of items as having a larger quantity than another equal set because the items are disposed in a longer row). Research is currently under way to determine how knowledge about quantities in infancy is related to preschool numerical competencies and later school achievement.
Although most children can naturally discover mathematical concepts, environment and cultural experiences play a role in advancing children’s knowledge about numbers. For instance, language acquisition allows children to solve verbal problems and develop a number sense (ex., understanding cardinality, the total number of elements in a set). Children who lack early experiences with numbers tend to lag behind their peers. For instance, children from economically disadvantaged families tend to display poor numeracy skills early on, and these deficiencies later translate to mathematical difficulties in school. Performance on numerical problems and the kinds of cognitive strategies children use are likely to vary considerably across children. Even the range of one child’s responses from one trial to the next can be substantial.
Promoting early competencies in numeracy is important because of its relation to children’s mathematical readiness at school entry and beyond. Preschool children who have acquired the ability to count, name numbers, and make distinctions between different quantities tend to perform well on numerical tasks in kindergarten. In addition, children’s good numerical abilities predict later school achievement more strongly than their reading, concentration, and socioemotional skills.
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