Kids aren’t born knowing what math symbols mean. In preschool they learn to count out loud: “One, two, three, four.” As they get older, they learn to write numerals: 1, 2, 3, 4. But understanding that “4” represents a group of four things? That’s an abstract idea that can be hard for kids to learn.
A math symbol stands for something — whether it’s a quantity, like four, or an arithmetic operation to carry out, like multiplication.
But there’s nothing about the way math symbols look that helps explain what they mean or what you should do with them. In other words, the relationship between the meaning of the symbols and the shapes of the symbols is totally arbitrary.
Kids need to be explicitly taught that “4” means a group of four. They also need to be taught that “4” means the group is larger than a group of three and smaller than a group of five.
What’s so tricky about learning the meaning of math symbols? Part of the answer involves learning how to generalize. Kids need to learn that the symbol “4” can mean four apples, four inches, four days — four of anything.
That’s a big idea. And some kids need more practice or teaching support to understand how symbols are used in math.
Kids develop at different rates. This means they learn math skills at different rates, too. Keep reading to see what trouble understanding math symbols can look like — and when it might be time to talk with your child’s teacher.
What trouble with math symbols can look like
In many schools, young kids start out solving math problems by moving around small objects like buttons or Popsicle sticks. (Teachers might call these objects manipulatives.) Moving them around helps kids think about adding or subtracting quantities.
But as kids get older, they have to solve math problems using only written numbers. Maybe they can easily find the answer to an addition problem by combining two bundles of Popsicle sticks. But show kids the same problem written as an equation like 5 + 4 = _? They may struggle if they’re not sure what each math symbol really means.
Here are some signs that kids might struggle with math symbols and how they represent different quantities:
Keep solving math problems by counting on fingers or using manipulatives long after classmates have switched to pencil and paper
Can remember basic math facts but struggle with more complicated problems that have steps like “Carry the 1”
Aren’t sure if the quantity on the left of the = sign is the same as the quantity on the right
Have trouble comparing fractions and understanding that ¼ is smaller than ½ (even though 4 is bigger than 2).
One thing that’s not a sign that kids are having trouble understanding math symbols: writing numbers backwards. It’s natural for young kids to write 3’s that look like E’s and 2’s that look like 5’s. With time and practice, most kids learn that numbers (and letters) have different meanings depending on which way they’re facing.
What causes trouble with numerical symbols
Learning how to use math symbols can be hard for all kids. Their brains need to form a strong association between math symbols and what they represent. If kids aren’t solid on what these symbols mean, they’ll have a tough time doing things like adding and subtracting.
To help kids understand what numerals and other math symbols mean, many teachers use a three-step approach:
|1. Concrete materials||2. Representational drawings||3. Abstract symbols|
|Start with objects that can be moved around, like seven beads to help kids think about a set of seven.||Make a drawing to represent the quantity, like showing seven squares instead of using seven beads.||Use only symbols, like writing “7” instead of using seven beads or drawing seven squares.|
All kids need time and practice to move through these steps. And some kids struggle more with this than others.
The = sign is another math symbol kids often have trouble understanding. Kids may know that four apples is the same quantity as four oranges. But they may have trouble understanding what it means to have the same quantity on either side of the = sign.
Trouble with the equal sign
Some kids think the = sign means “that is” rather than “equals.” They may be confusing an equation with a series of steps. For example, they may do OK with 3 + 2 = 5 because they read it as “When you add three plus two, that adds up to five.”
But this kind of thinking can lead to problems when the equation is flipped around. Kids may not know how to interpret 5 = 3 + 2. They may try to keep thinking about it as a series of steps: “When you start with five, you end up with three plus two.”
Thinking of an equation as a series of steps may also mean kids don’t understand that the same quantity is represented on each side of the equal sign. (You may hear teachers talk about numerical equivalence.)
Trouble with math operation symbols
There’s another way kids can struggle with math symbols. They may know that operational signs like × and ÷ are telling them to multiply and divide. But they might not be sure what steps are involved.
The symbol tells them which arithmetic operation to use. But it doesn’t tell them all the steps needed for that strategy.
How to help kids understand math symbols
It’s important to tune in to your child’s trouble with math. But also keep in mind that kids develop math skills over time. There can be big differences from child to child. Struggling with a new skill might just mean your child needs more time and practice to learn it.
Explore conversation starters to help you talk with the teacher about your child’s trouble with math. Ask how long ago the class started working on the skill your child is struggling with. Find out how much time the teacher has spent helping kids master this skill. If your child has been struggling for a few months, it may be time to ask for extra help.
You can also ask about how to help with abstract math. For example, if your child has trouble working with fractions, try placing the fractions on a number line. This helps kids see how big each fraction is and compare it to other numbers.
By partnering with your child’s teacher, you’ll work together to find gaps in your child’s understanding. Filling in those gaps can help your child build a strong foundation. And that makes it easier to learn more math skills.