# Myths and Realities of Early Mathematical Learning

Most parents nowadays know the importance of mathematics knowledge. Many of them, however, are unsure about mathematical learning for their young children. “How early should children start learning about mathematics? What does early mathematical learning entail? Which concepts is it most important to expose young children to? What should I do if my child seems to have more trouble counting than playmates of similar age do?” Responses to such questions are not always clear and consistent. This short article describes commonly held misconceptions or myths and counters them with findings or realities based on the most recent research in the field of early mathematical learning and teaching.

**Myth 1:**

Mathematics is highly abstract in nature. Young children are concrete thinkers, not competent enough to acquire abstract mathematical concepts. They are not ready for math learning.

**Reality 1:**

A large body of literature shows that certain mathematical concepts, such as number and basic geometry, seem to emerge very early in infancy. Young children, regardless of background and culture, develop many everyday mathematical concepts, such as intuitive ideas of more and less, taking away, size, location, and position. Readiness is a relative concept. Whether young children are ready to learn particular concepts or skills depends largely on how supportive the educational as well as the home environment is. The more appropriate supports we provide to young children, the more ready they are to explore and learn. The real question is not whether young children are competent enough to learn mathematics, but how we can work with them properly and effectively.

**Myth 2:**

Early mathematics learning should focus primarily on number concepts, such as magnitudes (more or less), counting words, and enumeration because children hear number words in the everyday environment and acquire them naturally just like learning language.

**Reality 2:**

Number words and related concepts are often the most spontaneous mathematical activities that adults engage in with young children. However, young children are interested and have some degree of competence in many aspects of mathematics, not just numbers. Early mathematics learning should include many other content areas, such as geometry and measurement. Young children can learn many basics in mathematics in developmentally appropriate ways.

**Myth 3:**

Early mathematical learning entails much factual knowledge and rote memory, such as naming numbers, counting up, and recognizing patterns. Such exercises have minimal value to the development of young children’s cognitive abilities.

**Reality 3:**

Early mathematical learning is more than the acquisition of factual knowledge; it not only involves skills, but also important concepts, principles, and strategies that are fundamental to a child’s cognitive development. For example, pattern activities, such as learning to alter three different shapes in a sequential order, foster young children’s logical reasoning and help to develop their abilities to make predictions and abstract rules. In fact, some research studies indicate that the strongest predictors of later achievement are school-entry math, followed by reading and attention skills.

**Myth 4:**

Young children pick up mathematics concepts naturally through play and in their daily living. Direct instruction is unnecessary. In fact, teaching mathematics explicitly through instruction is against the principles of developmentally appropriate education.

**Reality 4:**

Although young children learn a great deal of mathematics knowledge on their own, they learn much more with adult guidance. Children need to play and play is the most natural way for young children to learn. However, play is not enough to ensure that systematic and coherent learning will take place. To promote mathematical thinking and concepts basic to the discipline of mathematics, intentional teaching with well-planned activities is essential. Teaching math to young children requires their active participation. Learning math should be fun, engaging, and challenging.

**Myth 5: **

Mathematics is primarily a non-verbal subject; manipulatives are the primary means young children should use to learn mathematical concepts.

**Reality 5:**

Manipulatives are necessary, but not sufficient to the development of young children’s mathematical knowledge. Equally important for early mathematical learning is adults’ math talk or math-related verbalizations. Examples include “I divided this slice of pizza into two equal parts,” and “I have three cups of different sizes. What should we put in the biggest one?” Research indicates that the more preschool teachers talk about math, the greater is children’s gain in math knowledge. Language input from adults may help young children elaborate and consolidate the math concepts they are developing.

**Myth 6:**

The development of mathematical knowledge in young children follows a straightforward stage progression. Children at a certain age should know certain mathematics concepts and skills.

**Reality 6:**

There is considerable variability in children’s mathematical learning, as in other content areas. Some children pick up one concept quickly, but have trouble with another. A child may look puzzled about a particular mathematical concept one day, but act knowledgeable the next. Sometimes children appear to forget what they have just learned; other times they surprise adults by revealing mastery of mathematical knowledge they did not seem to learn. Individual difference is the rule rather than the exception in children’s learning and development. There are no particular mathematical concepts or skills that young children must learn by a certain age.

Due to an increased interest in early mathematical learning and teaching, we know much more about what is appropriate to help young children develop early mathematical thinking and skills than we did a decade ago. We have learned that early mathematical learning benefits from a rich mathematics environment, which includes at least three components: an assortment of math manipulatives, adults’ math-related verbalizations, and intentional teaching.