How Children Learn Math

Children first learn math content and process skills informally. From infancy, they use mathematics in everyday activities and to solve problems. As stated by Vygotsky (1978), “children’s learning begins long before they enter school . . . they have had to deal with operations of division, addition, subtraction, and the determination of size. Consequently, children have their own preschool arithmetic, which only myopic psychologists could ignore” (p. 84). According to Ginsburg, an expert on early childhood mathematics (2006), “despite its immaturity, young children’s mathematics bears some resemblance to research mathematicians’ activity. Both young children and mathematicians ask and think about deep questions, invent solutions, apply mathematics to solve real problems, and play with mathematics. Clearly then, one of our goals should be to encourage and foster young children’s current mathematical activities” (p. 158). Children use math to help make sense of the world. Teachers need to build upon this natural interest, providing children with in-depth opportunities and time to use math materials and ideas (NAEYC/NCTM, 2002).

However, while children intuitively use math to solve problems, according to Piaget, the only way that they can learn social-arbitrary knowledge is from adults or more competent peers. Social-arbitrary knowledge consists of “arbitrary truths agreed upon by convention and rules agreed upon by coordination of points of view” (DeVries & Kohlberg, 1987, p. 21). For example, in math the names of the numbers, signs, and shapes are examples of social-arbitrary knowledge. Teachers must support children’s learning as they use mathematical materials, helping them learn social-arbitrary knowledge.

By the time children begin kindergarten, they have typically learned some social-arbitrary knowledge. For example, more than 90% of children are able to count to 10, recognize shapes, and read numerals. More than half of the children can count beyond ten and 20% can read two-digit numbers (West, Denton, & Germino-Hausken, 2000). However, it is important that they not only are able to count or read numerals, but that they are able to use this knowledge with purpose and meaning.