how to teach math effectively

How to Teach Math Effectively: The Biggest Mistake You are Making While Teaching Math and How Common Core Fixes It

How to teach math effectively when you don’t feel exactly confident in your own abilities? The number 1 concern when it comes to homeschoolers and math.

But what if I were to tell you everything you think you know about math is wrong? That the homeschool community unfairly maligns Common Core Math? 

That is exactly what I am here to tell you. ​

How to Teach Math Effectively? Start with Understanding

We all know long division, but have you ever heard of short division? Did you realize that not all triangles have angles that add up to 180 degrees? These are 2 of my favorite examples of the depth of math that most of us miss in our educations. 

Most people have begun to see math a strict set of steps from A to B. As homeschoolers, we need to lead the charge that math is so much more than algorithms. Math is like a maze with more that one path to the exit. 

What do I mean?

how to teach math effectively
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We all know the standard form of 2 digit addition that looks like this: 
This is probably the form most people are comfortable with. But we can also break down 14 into “10+4” and 19 into “10+9” and add 10+10+4+9.

We could even break those numbers down differently into 5*4 (which is equal to 10 + 10). Then add that product to 4+9 and get the same answer. 

Does this flexibility scare you? It’s ok if it does. But I promise this flexibility is what makes math beautiful, and it sets the scene for creative problem-solving. 

There are many ways to do this calculation without using the add the ones place, carry the one, add the tens place algorithm we are all used to. 

The same is true of every single math problem. And homeschoolers need to celebrate that beauty. 

Why This Matters

What’s the big deal? The path you take from the problem to answer doesn’t really matter. It’s like asking whether you should wash your dishes in the dishwasher or by hand. You will get the same result either way, but one is easier than the other.

Now, let me ask you this: Which person has the advantage? The one who can wash them both ways or the one who can only use the dishwasher?

Flexibility is Key

Problem solving is an important part of math, and it is hard, y’all. It’s hard because it means we need to recognize patterns, examine problems, and then try different methods to get the final answer. 

As our kids get into higher level maths, they need to real understanding of how numbers work. Memorizing an algorithm doesn’t teach them that.

Working problems multiple ways does. Seeing math as a maze or puzzle where you need to fit patterns and pieces together work. ​

When we get stuck in thinking “There is this one way to do this” our reasoning cannot escape that cage to be more creative in solving problems.

When we work hard to model and come up with different ways to work the same problem, we avoid getting stuck in that cage. We need to explore the maze. 

This ability to think outside of our comfort zone is also extremely important in higher level sciences and maths. 

Getting Outside the Box

How to teach math effectively? Focus on inventive calculation strategies and problem-solving strategies.

Engineers make careers out of solving problems. They must be able to approach situations many different ways and try different approaches to find one that works well.

Einstein is credited with saying “It’s not that I am so smart; I just stick with problems longer.”  Encouraging our kids to approach problem solving creatively is based in teaching them to approach math creatively. And it starts with leaving the idea of algorithms behind. 

Honestly, we as homeschoolers are kind failing our kids if they don’t develop an appreciation for the beauty of math. We have the ability to incorporate games, living books, experiences, puzzles, and anything else you can think of to really make math come alive for our kids.​

This subtraction problem is pretty straight forward. And it does require regrouping, which is fine if you have paper and a pen handy or a calculator. Both methods will lead to the correct answer. 

The “New Way” presents a mental math advantage to this problem.

Benefits of Common Core

However, the Common Core Method is better because it ends up being quicker (for children and adults) and is just plain easier for mental calculations.  

This form of calculation is also is a great example of the power of decomposing in math. Learning how numbers actually work gives you the power to break them down into calculations that are easy for you.

Second, Common Core Math wants to teach our kids to be able to explain math instead of just doing it. While this seems useless, this is an important check on understanding. 

I can just you that I put dishes in the dishwasher and they come out clean.

But if I can tell you that dishes are washed with very hot water and an abrasive detergent in the dishwaher, I stand a much better chance of being able to figure out how to handwash dishes on my own if my dishwasher stops working, right? 

This understanding is the crux of problem-solving in math. If you can’t explain how numbers fit into their respective roles in a math problem, you probably can’t get anywhere.

Again, I believe it was Einstein that said, “If you can’t explain it to a 6 year old, you don’t understand it yourself.”

I don’t know about your homeschool, but in mine, my inability to explain some concepts are definitely where some our problems come from.

I must seek out many other resources to explain it in unique terms so my kids can hear different perspectives. And it is this practice that causes me to learn more about the world around me as I explore my role as an educational facilitator. 

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Third, being able to change how we work problems challenges our brains. This challenge, apart from being just plain fun, also keeps our brains healthy, lowering our risk for mental health problems like memory loss.  

Mathematical puzzles, in particular, encourage our brain hemispheres to communicate with each other, and, even more importantly different regions in you brain to communicate with each other. 

When your brain is able to communicate quickly and effectively within itself, you go from the beginning to the end of solving a problem quicker and easier.


Now, don’t get me wrong. There are a ton of ways to teach math effectively. And Common Core is just one. But we must all move away from looking at math as a series of steps and move more toward teaching our kids how to use inventive calculation and problem-solving methods.

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