Unlocking the World of Numbers: A Guide for Kids

Numbers are a huge part of our everyday lives. One of the first lessons we learn as kids is how to count numbers. Introducing numbers and learning to count is something most parents can do with their children in their everyday activities. When children begin kindergarten, their knowledge about numbers helps prepare them for learning math. Building an understanding of the numbers will help kids develop math skills in the future.

The Building Blocks: Introducing Numerals (0-9)

Teaching numbers doesn’t have to be a daunting task. Children are exposed to numbers at the very beginning of their lives, whether that be with pattern recognition or the ability to discern quantity amounts. That being said, children can begin learning their numbers as early as preschool.

The main step is to teach kids how to identify the first ten numerals (0 through 9), teaching them the sounds of numbers in English and also how to write the numbers. This learning process might be a bit difficult but also very rewarding, since kids need to put different skills in practice to differentiate some numbers from others, e.g. number 6 from number 9, which are quite close in appearance, they are not only learning math but developing other important skills as well.

Why Start with 0-9?

Simplicity: There are only ten characters that you need to teach or remediate (0-9). Many of our children have names with more than 10 characters, especially when you consider writing their first and last name. It is much easier to teach ten numbers instead of 26 lowercase letters and 26 uppercase or capital letters. Also, numbers do not come in lowercase and uppercase. They are just one size.
Consistency: So many children struggle with where to start letters or numbers when they are writing. They generally form letters and numbers inconsistently, sometimes starting at the top, the next time starting at the bottom, and the next time maybe starting in the middle. All numbers start at the top. This is easy to remember. With the Handwriting Without Tears approach, we have a song, “Where Do You Start Your Letters.” Well, one of the verses of that song goes, “Where do you start your numbers? At the top!” Yes! The kids really love this song. We have a short version and a longer version that really gets the kids moving as they learn about start, top, and bottom. The song even teaches them how to “shake it in the middle,” which is so much fun for little kids. Please be sure to check it out.
Formation: Consider how numbers are actually formed during the writing process. We refer to this as start and sequence. We now know that all numbers start at the top. But what happens next? To help young children learn to write numbers, we have developed what we call Number Stories for each one. These are clever ways to help our young children remember the correct way to form their numbers.

Multisensory Approaches to Number Formation

At Learning Without Tears, we use the terms Big Line, Little Line, Big Curve, and Little Curve. For our younger children, we build numbers using our Handwriting Without Tears Wood Pieces. As they progress and learn to hold a writing tool, we use small chalkboards and chalk to teach proper number formation. Then we introduce small crayons and Gray Blocks to provide a visual guideline for not only the formation of the number but for size and placement as well. We even have an app for the iPad called Wet-Dry-Try to help teach, practice, and eventually master number formation. This is a great way to incorporate technology and add additional multisensory techniques to enhance learning opportunities for children. Check it out!

Placement and Baseline

The placement of numbers on paper is also something we need to teach and address during our summer number lessons. All numbers are to be correctly placed on a single baseline. With young writers, we use the Slate Chalkboard to provide a strong visual and tactile representation of the baseline. When the children transition into a student workbook, they have a visual of the Gray Block to guide placement. The next step is to place the numbers, starting at the top, onto a single baseline. Eventually, on math papers, the student will not have a line to place numbers on. At this level, they will “see” the line in their minds and place the numbers on it. This takes a while and a great deal of practice for children to be able to do this.

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Making it Real: Connecting Numbers to the World

After this, it becomes easier to start teaching the little ones the amount that each numeral represents. This knowledge is essential for children going to school. As children grow up, it’s very useful to help them learn the concepts of cardinal numbers and ordinal numbers as well. These are also called cardinal numbers. Since they express quantity, they are mainly used when counting in English.

Everyday Activities

Count in everyday activities to make the everyday connection. Adults can mention that we need four forks to set the table and involve kids in getting four forks out of the drawer, or saying “just three more pushes on the swing” and then counting out “one, two, three” - these are both the kinds of everyday interactions that activate statistical learning and help children discover the meaning of the number words.

Notice that everyone uses numbers. Be a number detective. Find numbers and ways to use them, and help your child find them, too. Talk about numbers. Notice amounts. Point out amounts of things in storybook pictures. Count aloud when your child is near. Be a number detective. Count and compare amounts with your child. Use number words to talk about order. “We are third in line. The order of things (grocery store aisles) or the sequence of events (“First, put on your socks. Numbers help us compare, measure, order, add, subtract, and solve problems of all kinds.

Practical Exercises

Teacher will hold up each card or allow the student to touch each card as they count to five.
Game ideas: clap the number, jump the number, put a yellow 3 inch paper circle under each flashcard to show what each number represents and count them, show 2 flashcards and ask the student to point to the correct number requested, have 2 sets of flashcards and match 1-5, play singing videos on an iPad or computer (I love “Five Little Pumpkins“).

Tools for Learning

High contrast simple number books.
Braille stickers to adapt flashcards and place on materials. They are made by American Printing House and qualify for federal quota.
Starfall is a very popular app for students learning numbers.
APH’s hundreds chart has many uses including addition, subtraction, multiplication, and patterns. Use this to count to one hundred over and over again. This helps students understand that numbers go on FOREVER. It is also nice to find a peer who is good at counting and have them help. Make sure you have the child point and look while counting, however be mindful of fatigue and if the student has CVI. If it’s too much, take a break or practice auditorily. Avoid changing flashcards, the look of numbers, fonts, etc., until the student is proficient at recognizing numbers.

Counting Skills: Preschool vs. Kindergarten

Children develop solid foundational counting skills over time, and they look different in preschool than in kindergarten. One day, they may seem confident, and the next day, counting feels inconsistent or confusing.

Preschool

In preschool, the focus is on recognizing small quantities and understanding that numbers represent real things.

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A common example parents may notice at home is during playtime. Before children can count with understanding, they need to recognize that numbers represent actual amounts.
Being able to tell which group has “more” or “less” does not require counting. A preschooler might say, “You have more than me,” even if they cannot explain why.
For example, sliding blocks into a line as they are counted or placing toys into a box one by one helps children stay organized.
As preschoolers become more comfortable counting objects one at a time, they also need to learn that numbers follow a specific order.
To support this skill, it helps to pause after counting and restate the final number.

Kindergarten

At this stage, children are expected to use counting skills more independently and with greater accuracy.

As children enter kindergarten, subitizing continues to play an important role, but it expands beyond small groups like 1 to 5 objects that they can instantly recognize without counting.
In kindergarten, children begin counting larger groups of objects, usually beyond ten, while trying to stay accurate and organized. These behaviors are positive signs that the child is learning strategies to count more accurately.
A kindergartener might say, “That’s my age,” when they see the number five or six written down.
Parents may notice this when a child counts down before jumping or counts backward as they clean up toys.
Parents may notice their child counting off from a number instead of starting at one or using fingers to keep track while solving simple problems.

Common Development

Children begin learning about numbers much earlier than formal counting begins. Around ages three to four, preschoolers typically start developing foundational counting skills, such as recognizing small quantities or attempting to count objects. Yes, this is very common, especially between the ages of three and four. Short, frequent practice works best. Some variation in counting skills is completely normal between ages three and six. In these cases, extra support can be helpful. For some children, extra guidance can make early counting skills feel clearer, more manageable, and more enjoyable.

The Cognitive Perspective: How Children Learn Numbers

Kelly, in your talk you identified four key cognitive processes that help young children learn about math: statistical learning, structure mapping, language, and spatial cognition.

Statistical Learning

The way I understand it, statistical learning is about an ability we all have to detect similarities. That is, in the case of number learning, we eventually come to associate the word “three” with “three-ness” because the word and the cardinal amount are frequently paired. When they are paired again and again, we notice the pairing, and distinguish it from random noise.

Yes, you have it right - frequency is a big part of this learning mechanism. Children need lots of experiences that help them pair quantities and number words. In statistical learning terminology, we like to talk about dense co-occurrences and regularity. Dense co-occurrences means how often and how close together in time experiences are paired. So, if a parent labels a set of 3 items such as three tea cups repeatedly in the same play session, that would be an example of dense co-occurrences. If they label a set of 3 on Tuesday and then do it again on Friday, that would provide co-occurrences, but they would not be dense. Regularity means that the words and experiences are structured in a clear, predictable way. For example, if parents count and label sets every time they comment on number (e.g.

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There are many ways parents and caregivers can help by talking about quantities when there is some way for kids to simultaneously see or experience those words and quantities.

Structure Mapping

Another of the processes you discussed, structure mapping, suggests that when we compare things, we tend to see the similarities and differences between them in greater detail, and the similarities become generalized. For example, when we compare a car and a motorcycle, we might think about four wheels versus two wheels, but we might also think about the idea of transportation.

The thing about number is it’s fairly difficult to “see.” Think about trying to explain to a visitor from space what we mean by “two.” You might point to two mittens, two cookies, and two trees, saying “these are all two.” This is a good approach, but there is so much detail and information in each of these kinds of objects, that it’s hard to focus on the quantity. Because of this difficulty, comparison processes may be particularly important for number learning.

For example, children can get a sense of “two-ness” by comparing object sets. A good way to “see” number by comparing is to demonstrate one-to-one correspondence. For example, when children see three dogs and three dog dishes, they can match the objects one-to-one and see that the sets are equivalent. Another way is to hear the sets labeled with a number word, and then look to see what attribute the label refers to. If multiple sets are called, “two,” they must have something in common-what is it?

One of the things we know about structure mapping is that it works best when the two structures are alignable. A set of dogs and dog dishes is easier to align than a set of airplanes and a set of whales in the ocean, or a set of claps and a set of glasses on the table. Just like statistical learning, this process of structure mapping highlights the importance of adult input for children’s learning.

Symbol Grounding

Number names, counting, and written numerals are all different symbols for quantities that children must link to each other and to the underlying meaning. In your talk, you suggested it is helpful to think of developing early numeracy as a “symbol grounding” task.

The central idea of symbol grounding as it applies to early numeracy is that each child must make connections between the symbols we use to talk about quantity and the underlying meaning of these symbols. That is, the word “five” is itself a symbol, and children must learn to map it to examples of five in the world or to the abstract idea of “fiveness”.

An easy way to think about symbol grounding is to think about how children learn other words, like words for objects. The word, “tree,” for example, is an arbitrary symbol that has no meaning until it’s linked to examples of trees in the world or to the abstract concept of trees. Symbol grounding is what happens when people make these connections between symbol and meaning.

To learn to think mathematically, then, the child is exposed to lots of math-related symbols, and must connect each one to its meaning. It’s for this reason that adult input is so important. Number names, counting, and written numerals are all different symbols for quantities that children must link to each other and to the underlying meaning. Both statistical learning and structure mapping support this grounding process by helping children notice that words and written symbols go together, or that the same quantities are called “three,” are counted, “1-2-3,” and can be labeled by the same written numeral.

In the very early years, we can almost think of “symbol grounding” as “language grounding” instead, since language is the child’s most powerful symbol system, both for learning and for being understood. In terms of advice for parents and caregivers, we can boil this down to: talk with your child about small numbers!

Additional Support

Personalized learning plans: Every child begins with an assessment that helps identify exactly where they are in their math development. A proven method focused on understanding: The Mathnasium Method is built around helping children make sense of math concepts. Trained instructors who work with young learners: Mathnasium tutors are trained to explain math in clear, age-appropriate ways. Whether your child needs help catching up, wants to stay on track, or is ready to move ahead, Mathnasium can support their journey. To get started, schedule a free assessment at Mathnasium of South Westminster or your nearest learning center.

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