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Math. It can be a dirty word. People either love it or hate. It is the subject that keeps many people from taking the plunge and diving into homeschooling. Those of us who brave the frozen tundra that is homeschool math have a very narrow view of what it is.
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.
This popular meme makes Common Core seem unnecessarily complicated. Neither of these calculations are complicated. But only one of these shows a deep understanding of decomposing numbers and the relationship between addition and subtraction, an understanding that will prove invaluable in higher level maths and sciences.
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 just two 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 I mean
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 or we could even break those numbers down differently into 5*4 (which is equal 10 + 10) and 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 problem to answer doesn’t really matter. Its 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?
What matters is the ability to follow different paths through the maze.
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 does.
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.
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 (notice I didn’t say love) 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 a correct answer.
However, the Common Core Method is better because it ends up being quicker (for children and adults), requires regrouping only after the numbers are under 20, 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 educational facilitator.
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 effectly within itself, you go from the beginning to the end of solving a problem quicker and easier.