There are many benefits to using math manipulatives to teach students math in grade school. This is especially true during the early childhood years as well. The majority of young children are visual and kinesthetic learners. In other words, toddlers and preschoolers learn best by seeing AND doing.

During the early childhood years, learning “numbers” may seem pretty simple and straightforward. But, helping young children understand numbers is actually pretty complex. This is because parents typically focus on being able to count from 1 to 10, or in other words, rote memorization. Counting from 1 to 10 is a great start – but there are other count principles children need to understand before a child is a proficient counter. Being able to count rationally is the precursor to more formal mathematical concept activities such as addition and subtraction. So how do young children learn how to rationally count?

5 important counting principles preschoolers need to know.

Educational specialists Hirsh-Pasek and Golinkoff (2006) reported that by the age of three, most children learned important counting principles entirely on their own¹. When children are in an unsupervised setting and have a deep interest in an object, it led to the discovery of the concept of numbers using those objects. If this sounds familiar, it’s because they are describing children at play!

Below are five important counting principles preschoolers need to understand. Examples are given to provide you with an idea of how each principle may be applied to your child.

1. One-to-one principle: each number represents one thing only (e.g., when a child counts sheep, the first sheep is #1 and cannot be given another number)
2. Stable order principle: numbers occur in a fixed order (e.g., 1, 2, 3, 4, 5, …)
3. Cardinal principle: the final number counted represents final size of a set (e.g., when a child counts 1, 2, 3, objects, that set has a total of 3 objects.)
4. Abstract principle: anything can be counted – physical and non-physical things. (e.g., if a child wants to count “people” they can include friends, family members, and toys; time can be counted although not seen; etc.)
5. Order-irrelevance principle: you can count anything in any order as long as it is given one count (one-to-one principle) (e.g., when counting family members, you can count outside of age order and you will still be able to get to the final count of family members)

What are manipulatives in math?

Remember when I said young children learn best by seeing and doing? Math manipulatives are physical objects that make great teaching tools for kids of all ages. Manipulatives help students visualize and use a hands-on approach to understand math concepts. It helps make abstract concepts more concrete for children and it enables teachers and parents to assess children’s understanding of concepts.

I think many parents make the mistake of first gravitating towards flashcards for preschoolers when teaching how to count. Flashcards have their place and are a useful tool for teaching number recognition. But, teaching the counting principles listed in the prior section begins with the ability to count objects.

If you’re still not convinced, evidence-based research proves the use of manipulatives in math improves student achievement over time. This research was written in 1989 but also included studies from as early as the 1930s! The use of manipulatives in math is not new. The study also found that students’ attitudes toward mathematics improved when concrete materials were provided with lessons.

What are some examples of math manipulatives?

Examples of math manipulatives can include:

• Counting bears
• Stones or rocks
• Sticks
• Pom poms
• Cheerios
• Blocks
• Lego
• Magnetic tiles
• Math link cubes

How to teach math using manipulatives.

Okay, so you’ve sifted through your junk drawers and found math manipulatives for your child to work with (who knew manipulatives were there all along!). Next, I’ll show you how to teach your child math using manipulatives.

Using bear counters as an example, I’ll show you how to check your child’s understanding of the one-to-one principle (every object gets one count only).

I’ll grab a set of random bears of different sizes and colors. We’ll count them together. Next, I’ll present a set of bears all in green. If the child responds, there’s one bear, I will agree and respond with “yes, all the bears are one color, green! Let’s count how many bears there are in total together. 1, 2, 3, 4, 5!. There are 5 bears total in this group!”.

This exchange seems simple, but so much is going on here. The math manipulatives acted as a baseline form of reference for you and your child. Without it, you may have thought your child did not understand how to count when you asked how many green bears there were. You knew they were able to count bears of different colors. But, with the same colored bears – you knew she was thinking of color instead of the count. You affirmed her observation of all the bears being one color. Next, you modeled that you can also count bears of the same color. Can you identify which principles this interaction covered? Let me know in the comments below!

Tools to use with math manipulatives

Additionally, using learning tools like the “Number Sense” learning mat pictured in the video above provides your child with multiple ways to visualize numbers. For toddlers who have trouble counting with their fingers, have them color in the fingers on the mat. Teach your child the one-to-one principle by placing a counter in one space only using the ten frames strategy. The number line on the learning mat demonstrates the stable order principle and is great for older preschoolers to understand addition and subtraction.