Hi there. Today, I want to talk to you about having a math focus with your child, the importance of the very foundational skills of math. How can you begin to foster that, and how to build those math skills even when you're not sitting down and doing a very structured math activity or a math worksheet, which is what we typically think of as doing math with our kids.
What are the mathematical skills in the foundation phase?
The foundational mathematical skills are counting, manipulating different numbers, and understanding how things relate to one another, and how objects relate to one another in space.
All of these types of foundational skills are critically important before we get to what we usually think of as standard math operations, like addition and subtraction.
That's why we spend so much time in our free homeschool preschool curriculum, Ready for Kindergarten and Beyond, working on counting, number recognition, and, in particular, one-to-one correspondence.
What is an example of one-to-one correspondence in preschool?
One-to-one correspondence means that a child recognizes that a number stands for a certain quantity of things, ideas, or concepts, rather than just being a word in a sequence that you say when you're counting.
In other words, when a child is counting, they usually learn their numbers by memorization, and they're used to counting “1, 2, 3, 4, 5”. If you're not developing the skill of one-to-one correspondence with your child, what often happens is that they believe that counting is just repeating the string of words. Almost like saying a poem or saying they're ABCs. Five is just a word that you say after four and before six.
What you really want to get into their minds is that five is the quantity. Five stands for a certain number of actual things. Those things are pieces of cereal, toy cars, or whether those things are even abstract things like five ideas or five thoughts.
You want them to understand that that number stands for a quantity. That's one-to-one correspondence.
Fortunately, establishing one-to-one correspondence is fairly easy because all it involves is counting a wide variety of real objects with your child. By doing that, instead of just focusing on repeating the sequence of numbers, when you count, your child will naturally absorb what five is.
The importance of noticing your child using math in play
So, in addition to one-to-one correspondence and working on counting a wide variety of things, I encourage you to develop foundational math skills by really noticing how children are using math in their play, pointing this out, and praising them for it. You really want to catch them in the act of using math as they're playing, which they do all the time.
It makes us as parents feel a little bit better that even though we're not sitting down with them and doing a worksheet, our children are actually getting real, concrete math experience in their play and their everyday lives.
It also encourages your child when you can point that out to them and make them see that their mind is really operating on that higher level. It helps them to build confidence, and they're far less likely to hesitate when it comes time to “sit down and do math”. They won't think of it as some very foreign and abstract concept that they're not familiar with. They think of it as something that they already know how to do.
Examples of praising your child using math concepts
You'll see them using math a lot when they're building or working with anything that involves a number of things. Children love to line up objects, and sometimes, they'll put them into a grid.
You simply need to point out what it is that they're doing and say, "Do you know that that's a type of math? When children line up items in a grid, it's a form of multiplication".
They're making sure that there is the same number of objects in each row and lining them up until they either run out of objects or until they have a nice neat little square grid there, and that's a form of multiplication.
You see children doing this a lot with Legos or building blocks. They'll build one tower over here, and they'll have a shorter tower over here, and they will calculate, without even thinking about it, how many more blocks they have to stack up on this tower over here to be the same height as the other one.
And if you're playing with your child, you can even ask them little questions like that out loud: “How many more blocks do we need here to make these towers the same height?” When they answer, you can say: “Wow, did you know that you just did subtraction?” That's a form of subtraction.
But whether or not you know exactly what the child is doing is really beside the point. It's that you're giving meaningful praise by calling it out and noticing that your child is working with numbers anytime they're working with measuring shapes and quantities, comparing one object to another, whether it's the height of something or the amount of something. All of these things are forms of doing math.
And the more that you notice it, the more you learn little tricks to be able to work on math skills through play so that you don't have to pull your child to the table to do a structured lesson.
The importance of repetition in building a math foundation
Repetition is essential in math. That's why we repeat the counting exercises in the curriculum as well. It's why when your child gets to actual learning, actual math facts, addition and subtraction facts, it's important to repeat those.
Memorization of things like math facts was really unpopular in the education world for many years. Now it's starting to come back and have a resurgence because people realize how critical it is once your child gets to the higher grades and starts doing more complex math that they actually have these math facts memorized.
The benefits of playing with 10 units
Especially at the preschool age, playing around with units of 10 can be really, really beneficial. Give them 10 cubes or 10 of anything, and just let them play with those numbers. Let them see what breaking it into two groups of five looks like, and that you can also make a group of three and seven, or that you can make five groups of two.
Letting them play with a unit of 10 is a fantastic way to practice math skills, and it can be easily done through play with 10 of anything.
Developing preschool math vocabulary
Another really great thing to do with preschoolers to work on future math skills and to really lay a solid foundation is to work on vocabulary. Because once they get into addition and subtraction, which we would consider math in kindergarten and first grade, if they don't have a strong understanding of the words that they'll be using there and that math vocabulary, they'll struggle even if they have a good concept of numbers and quantities and things like that.
The more you can work math vocabulary into your everyday life, or notice it and capitalize on it in those moments when it comes up naturally, the better. There are tons of different categories of words that fall into math vocabulary:
- Quantity words. Words like more or less or equal to another.
- Propositions. Propositions are math words, so anything that shows space in relative positions, such as before, after, later, or sooner, falls into this category.
- Vocabulary related to time. What an hour is, what a minute is, what yesterday is, what tomorrow is, days of the week. Any words related to time fall into the category of math words.
- Vocabulary related to money.
- Vocabulary related to measuring. Units of measurement like inches or feet, or longer than and shorter than, heavier, lighter. Anything related to measurement counts as math words.
- Words that show order. First, second, and third. Those are called ordinal counting as opposed to standard counting, which is just 1, 2, and 3. It is helpful for kids to learn.
All of those are fantastic foundational math skills that you can practice with your child just in conversation, no matter where you are. In the bathtub, in the car, in the store, or in the kitchen.
Keeping vocabulary in mind is a wonderful way to work on foundational math skills with your preschooler. It'll go a long, long way to helping them when they get to kindergarten or first grade, and they’re sitting at the table doing more structured math exercises. They will be able to take off and soar because they will have those foundational skills.
As you see, they don't necessarily need to jump into addition or subtraction at the beginning. We need to go even below that to the foundational math skills and really build them up with those first.