Three-, Four-, and Five-Year-Olds’ Thinking and Mathematics

Three-, four-, and five-year-olds’ thinking and reasoning are changing and developing at rapid rates. These changes in cognition allow young children to understand mathematical concepts in new ways. During this period, children are beginning to do the following:

1. Think symbolically.  They are beginning to understand that words such as “Mary” and “Sam” represent a person. Similarly, they are beginning to understand that abstract things such as numbers can represent the quantity of objects (Unglaub, 1997).
2. Understand conservation of number.  Conservation is the ability to understand that materials and objects stay the same regardless of changes in form or arrangement in space. For example, when a child understands that three sticks placed close together are the same number of sticks as three sticks placed far apart, they understand conservation of number. Some three-year-olds can count, by memory. They know how old they are, but do not understand what the numbers represent. Four-year-olds are not capable of understanding conservation. For five-year-olds, conservation of number is developing and is generally solidified by the time children turn six years of age. Conservation is an important ability that allows children to understand more complex concepts in mathematics (Sophian, 1995).
3. Think semilogically.  Children’s thinking and reasoning at this age is called semilogical because their logical reasoning is limited. Three-, four-, and five-year-olds are unable to keep in mind more than one relationship at a time. They have difficulty making comparisons and seeing relationships (White, Alexander, & Daugherty, 1998). In addition, they are unable to use reversible thought processes that would allow them to think with the same logic as an older child or adult.

These cognitive constraints limit the amount of mathematical understanding young children can have. However, experiences and opportunities to learn provide a context for young children to develop the precursors they need for more complex mathematical thinking.