One of the best ways of introducing mathematical concepts to preschoolers is integrating them into their daily activities and interests. This way, children learn first-hand the importance of math in their everyday lives. 

During play time, children become intensely engrossed in whatever activity they're doing. In addition, they are also developing and honing new skills, taking part in problem-solving and learning more about mathematics and critical thinking.

Often, when children are engaged in free play, there are seven categories of mathematics content they're exploring:

1. Counting: When children reach age four, they are often able to count. For instance, they may be trying to keep track of toys, and by counting, they're able to know how many they have. It's common for young children to explore patterns and shapes, as well as compare sizes. 

2. Classifying: In addition to counting, preschool children are also interested in investigating different objects and materials. Through grouping similar items, for instance plastic bugs in a container, they're able to come up with a way of ordering and making sense of the world around them.

3. Exploring magnitude: This involves describing and comparing the size of different objects. For instance, preschool students might make a comment when they don't think something is big enough to cover another object (i.e. whether a newspaper can cover the art table).

4. Enumerating: This involves saying numbers, counting, recognizing a series of objects or reading or writing numbers. 

5. Investigating dynamics: As children are seeking to understand more about different objects, they may put things together or take them apart. For example, they may want to flatten a ball of clay to see what shape it can take.

6. Studying pattern and shape: Gaining familiarity with different patterns and shapes is another important activity preschoolers engage in. Through this activity, children are identifying and creating patterns or shapes, as well as exploring geometric properties. For instance, you might have your class make bead necklaces, using a particular color pattern or one of their own choice. 

7. Exploring spatial relations: During preschool, children gain practice describing or drawing a location or direction.

There are a range of different mathematical concepts that children explore during free play. This goes to show the extent to which everyday activities involve math. Preschool is the time when children are learning pre-mathematics, which lay the foundation for their continued success in school. 

While play does not itself guarantee mathematical development, it does offer a range of possibilities. If teachers follow up by asking children specific questions that reflect on the mathematical ideas, children's understanding of these concepts can be enriched. In particular, you can expand children's mathematical understanding and curiosity by asking questions that require them to clarify or extend their perceptions.

Here are some examples of good classroom activities:

1. Math and Blocks - Building towers: Through block building, children develop a variety of skills, including in math, science and general reasoning. At age one, children begin the elementary step of block building: stacking objects together. When children are three or four-years-old, they're able to assemble vertical or horizontal components to make a building. At four, their skills have advanced even more to the point that they're able to use multiple spatial relations, as well as extend their buildings in multiple directions. They are also developing their estimation skills during this time. For instance, they're learning to estimate how many blocks it takes to cover a surface. These are all skills that they will continue to apply as they progress in school. 

Check out our course on Block Play.

2. Math and Manipulatives:

Manipulatives are another activity that preschool children find engaging and meaningful. Children's play with manipulatives ranges from putting flat blocks together to make pictures, to completing complex puzzles. All of these activities require developmental progression, similar to block building. While combining shapes may initially prove challenging for children, gradually they learn how the individual pieces fit together to make a whole object. Many children may be able to complete simple or more complicated puzzles by age four. For others, it may take more time or be more challenging in general. Make sure to offer encouragement and help to students. 

By providing regular opportunities for children to explore math, both during free play and structured activities, you help introduce them to a variety of useful concepts they'll continue to use for years to come. 

If you are interested in learning more about this subject, please refer to our comprehensive course menu. There you can find a range of courses, including "Ignite Their Minds: Making Math an Integral Part of your Teaching," "Block Play as a Creative Learning Strategy" and "Hands-on Excitement: Manipulatives for Teaching Young Children Math." 

We also offer CDA training and CDA renewal for early care and education professionals seeking the CDA Credential, which is administered and awarded by the Council for Professional Recognition. In 2013, ProSolutions Training became the first online training company to become a formal partner of the Council. Contact us to learn more.