If you have a child in elementary school, you may have looked at their math work and thought, “Wait...what are they doing?”
Maybe you remember learning to line up your numbers, carry the one, borrow from the next place, memorize your multiplication facts, and follow the steps your teacher showed you.
Then your child brings home a math problem and solves it in a way that looks completely unfamiliar.
You may even find yourself saying, “That's not how I learned to do it!”
And you're right.
Math instruction has changed.
Over the next few Saturday posts, I want to talk a little about why some of those changes have happened and what they are really trying to accomplish.
Today, let's start with one of the biggest differences:
Understanding the math instead of simply remembering the steps.
It's More Than Knowing the Algorithm
There is nothing wrong with teaching a procedure or an algorithm. In fact, students eventually need efficient strategies for solving problems.
The difference is in what comes first.
When students understand why something works, they aren't as dependent on memorizing a series of steps. They can think about the numbers, make connections, and choose a strategy that makes sense for the problem in front of them.
For example, if a student knows that 8 + 7 = 15, they might solve it by:
Making a ten: 8 + 2 + 5 = 15
Taking one from the 8 and adding it to the 7: 7 + 1 + 7 = 15
Using a known fact: 8 + 8 = 16, so 8 + 7 is one less
Using objects, a number line, a drawing, or mental math
They are all finding the same answer.
But more importantly, they are thinking about the numbers.
That understanding gives students flexibility.
I Didn't Always Like Math
I'll be honest. I didn't always enjoy math.
As a student, I could do math when I could remember the rules. But as the math became more complicated, there were more rules, more formulas, and more steps to remember.
And eventually, remembering all of it became harder.
Math started to feel like something I just wasn't very good at.
Fast forward to becoming a teacher.
As I began teaching math, I had to understand the why behind what I was teaching. I couldn't just know the answer. I needed to understand what the numbers were doing and why a strategy worked.
And something interesting happened.
I started to get it.
Even now, when I learn a new way of looking at a math concept, there are moments when I think, “Oh! That's why!”
And I like math now.
I actually enjoy teaching math.
That experience has changed the way I look at math instruction.
Understanding Gives Students Options
When a child only knows one procedure, they can become stuck when a problem looks different from what they have practiced.
But when they understand what they are actually trying to find, they have more than one place to go.
They can draw it.
They can build it.
They can break numbers apart.
They can use a known fact.
They can estimate.
They can explain their thinking.
They can try another strategy if the first one doesn't work.
And this is one of the things I really like about teaching math this way. There isn't always just one path to the answer.
A child might see a problem one way, while you see it another way. Another child may use a completely different strategy. That's okay.
In fact, being introduced to different strategies can help children discover which methods make the most sense to them.
The goal isn't for every child to solve a problem exactly the same way.
The goal is for them to understand the mathematics well enough to choose a strategy, explain their thinking, and know whether their answer makes sense.
So What Can Parents Do?
You don't have to be a classroom teacher to support this kind of math learning. And if you homeschool, you have a wonderful opportunity to build this kind of understanding into your everyday math instruction.
When you're introducing a new concept, don't feel like you have to immediately teach your child one specific way to solve it.
Give them opportunities to see it, build it, draw it, talk about it, and solve it in different ways.
You might even show them a couple of strategies and ask:
“Which way makes the most sense to you?”
“Can you explain why?”
“Is there another way you could solve it?”
This doesn't mean you should avoid teaching efficient procedures. Those are important too. But when children understand the concept first, the procedure has something to connect to.
And if your child's method looks completely different from the way you learned it, take a breath before correcting it.
Ask them to explain it to you.
You might be surprised by what they understand.
The E3 Takeaway
There isn't really a “math brain” that some children have and others don't.
Some children may have more confidence with math. Some may need more time, more practice, more concrete experiences, or a different way of seeing a concept.
But all children can develop mathematical understanding.
That's why I believe teaching the why matters.
When children understand what they are doing, they don't have to rely solely on memorizing rules and procedures. They can use what they know in new situations, approach problems in different ways, and become more confident problem-solvers.
And maybe, just maybe, we can help some children who think they are “bad at math” discover what I eventually discovered:
They may not have been bad at math. They may just have needed to understand it.
For homeschool parents especially, this can be a wonderful opportunity. You don't have to recreate the way you were taught math. You can take the time to help your child understand the concept, explore different strategies, and gradually help them develop the methods that work best for them.
That is much more than finding the right answer.
It's learning how to think mathematically.
From the Teacher's Desk
One of my favorite things about teaching math now is watching that lightbulb moment happen.
The moment when a student stops trying to remember what they're supposed to do and starts understanding what the numbers are telling them.
That's the moment I love.
Because when the why starts to make sense, math starts to become something they can use, not just something they have to remember.
And maybe that's one of the reasons I like teaching math so much now.
I finally understand the why, too.
Engage. Empower. Educate.
