One contribution of Piagetian theory concerns the developmental stages of children’s cognition.
His work on children’s quantitative development has provided mathematics educators with
crucial insights into how children learn mathematical concepts and ideas. This article describes
stages of cognitive development with an emphasis on their importance to mathematical
development and provides suggestions for planning mathematics instruction. Jean Piaget’s work
on children’s cognitive development, specifically with quantitative concepts, has garnered much
attention within the field of education. Piaget explored children’s cognitive development to study
his primary interest in genetic epistemology. Upon completion of his doctorate, he became
intrigued with the processes by which children achieved their answers; he used conversation as a
means to probe children’s thinking based on experimental procedures used in psychiatric
questioning. Piaget has identified four primary stages of development, sensorimotor,
preoperational, concrete operational, and formal operational. Therefore, this academic piece of
writing will shade more light on how the theory of cognitive development could have influenced
in the stated views on teaching of pre-mathematics to children.
However, in the sensorimotor stage, an infant’s mental and cognitive attributes develop from
birth until the appearance of language. This stage is characterized by the progressive acquisition
of object permanence in which the child becomes able to find objects after they have been
displaced, even if the objects have been taken out of his field of vision. For example, Piaget’s
experiments at this stage include hiding an object under a pillow to see if the baby finds the
object.
An additional characteristic of children at this stage is their ability to link mathematics numbers
to objects, for example, one dog, two cats, three pigs, four hippos. To develop the mathematical
capability of a child in this stage, the child’s ability might be enhanced if he is allowed ample
opportunity to act on the environment in unrestricted ways in order to start building concepts.
Evidence suggests that children at the sensorimotor stage have some understanding of the
concepts of numbers and counting (Fuson, 1988). Educators of children in this stage of
development should lay a solid mathematical foundation by providing activities that incorporate
counting and thus enhance children’s conceptual development of number. For example, teachers
and parents can help children count their fingers, toys, and candies. Questions such as “Who has
more?” or “Are there enough?” could be a part of the daily lives of children as young as two or
1|Page
, three years of age. Another activity that could enhance the mathematical development of
children at this stage connects mathematics and literature. There is a plethora of children’s books
that embed mathematical content. A recommendation would be that these books include pictorial
illustrations. Because children at this stage can link numbers to objects, learners can benefit from
seeing pictures of objects and their respective numbers simultaneously. Along with the
mathematical benefits, children’s books can contribute to the development of their reading skills
and comprehension.
However, the characteristics of preoperational stage include an increase in language ability,
symbolic thought, egocentric perspective, and limited logic. In this second stage, children should
engage with problem-solving tasks that incorporate available materials such as blocks, sand, and
water. While the child is working with a problem, the teacher should elicit conversation from the
child. The verbalization of the child, as well as his actions on the materials, gives a basis that
permits the teacher to infer the mechanisms of the child’s thought processes. There is lack of
logic associated with this stage of development; rational thought makes little appearance. The
child links together unrelated events, sees objects as possessing life, does not understand point-
of-view, and cannot reverse operations. For example, a child at this stage who understands that
adding four to five yields nine cannot yet perform the reverse operation of taking four from nine.
Children’s perceptions in this stage of development are generally restricted to one aspect or
dimension of an object at the expense of the other aspects. For example, Piaget tested the
concept of conservation by pouring the same amount of liquid into two similar containers. When
the liquid from one container is poured into a third, wider container, the level is lower and the
child thinks there is less liquid in the third container. Thus the child is using one dimension,
height, as the basis for his judgment of another dimension, volume. Teaching students in this
stage of development should employ effective questioning about characterizing objects. For
example, in mathematics when learners investigate geometric shapes, a teacher could ask
learners to group the shapes according to similar characteristics. Questions following the
investigation could include, “How did you decide where each object belonged? Are there other
ways to group these together?” Engaging in discussion or interactions with the children may
engender the children’s discovery of the variety of ways to group objects, thus helping the
children think about the quantities in novel ways (Thompson, 1990).
2|Page
His work on children’s quantitative development has provided mathematics educators with
crucial insights into how children learn mathematical concepts and ideas. This article describes
stages of cognitive development with an emphasis on their importance to mathematical
development and provides suggestions for planning mathematics instruction. Jean Piaget’s work
on children’s cognitive development, specifically with quantitative concepts, has garnered much
attention within the field of education. Piaget explored children’s cognitive development to study
his primary interest in genetic epistemology. Upon completion of his doctorate, he became
intrigued with the processes by which children achieved their answers; he used conversation as a
means to probe children’s thinking based on experimental procedures used in psychiatric
questioning. Piaget has identified four primary stages of development, sensorimotor,
preoperational, concrete operational, and formal operational. Therefore, this academic piece of
writing will shade more light on how the theory of cognitive development could have influenced
in the stated views on teaching of pre-mathematics to children.
However, in the sensorimotor stage, an infant’s mental and cognitive attributes develop from
birth until the appearance of language. This stage is characterized by the progressive acquisition
of object permanence in which the child becomes able to find objects after they have been
displaced, even if the objects have been taken out of his field of vision. For example, Piaget’s
experiments at this stage include hiding an object under a pillow to see if the baby finds the
object.
An additional characteristic of children at this stage is their ability to link mathematics numbers
to objects, for example, one dog, two cats, three pigs, four hippos. To develop the mathematical
capability of a child in this stage, the child’s ability might be enhanced if he is allowed ample
opportunity to act on the environment in unrestricted ways in order to start building concepts.
Evidence suggests that children at the sensorimotor stage have some understanding of the
concepts of numbers and counting (Fuson, 1988). Educators of children in this stage of
development should lay a solid mathematical foundation by providing activities that incorporate
counting and thus enhance children’s conceptual development of number. For example, teachers
and parents can help children count their fingers, toys, and candies. Questions such as “Who has
more?” or “Are there enough?” could be a part of the daily lives of children as young as two or
1|Page
, three years of age. Another activity that could enhance the mathematical development of
children at this stage connects mathematics and literature. There is a plethora of children’s books
that embed mathematical content. A recommendation would be that these books include pictorial
illustrations. Because children at this stage can link numbers to objects, learners can benefit from
seeing pictures of objects and their respective numbers simultaneously. Along with the
mathematical benefits, children’s books can contribute to the development of their reading skills
and comprehension.
However, the characteristics of preoperational stage include an increase in language ability,
symbolic thought, egocentric perspective, and limited logic. In this second stage, children should
engage with problem-solving tasks that incorporate available materials such as blocks, sand, and
water. While the child is working with a problem, the teacher should elicit conversation from the
child. The verbalization of the child, as well as his actions on the materials, gives a basis that
permits the teacher to infer the mechanisms of the child’s thought processes. There is lack of
logic associated with this stage of development; rational thought makes little appearance. The
child links together unrelated events, sees objects as possessing life, does not understand point-
of-view, and cannot reverse operations. For example, a child at this stage who understands that
adding four to five yields nine cannot yet perform the reverse operation of taking four from nine.
Children’s perceptions in this stage of development are generally restricted to one aspect or
dimension of an object at the expense of the other aspects. For example, Piaget tested the
concept of conservation by pouring the same amount of liquid into two similar containers. When
the liquid from one container is poured into a third, wider container, the level is lower and the
child thinks there is less liquid in the third container. Thus the child is using one dimension,
height, as the basis for his judgment of another dimension, volume. Teaching students in this
stage of development should employ effective questioning about characterizing objects. For
example, in mathematics when learners investigate geometric shapes, a teacher could ask
learners to group the shapes according to similar characteristics. Questions following the
investigation could include, “How did you decide where each object belonged? Are there other
ways to group these together?” Engaging in discussion or interactions with the children may
engender the children’s discovery of the variety of ways to group objects, thus helping the
children think about the quantities in novel ways (Thompson, 1990).
2|Page
