I was sitting in a class about how to teach math. My instructor pulled out these things called base ten blocks and informed us we were going to learn how to teach subtraction with regrouping.
Mentally, I groaned. All that crossing out, writing numbers above other numbers, and trying to figure out what to do with zeros was not my favorite task in elementary school…and now I was going to have to teach it.
But things did not go as I thought they would. With base ten blocks in front of me, we slowly worked through a subtraction problem. And an enormous light bulb began flashing and dancing around above my head. For the first time in my 20-year-old life, I understand HOW subtraction with regrouping worked, and WHY we were placing ones in front of numbers. It finally made sense to me, and learning the WHY was liberating.
I didn’t realize it then, but that would be the beginning of a deep love for math. Not the type of math I learned in elementary school where I followed a procedure to get a random answer that I didn’t understand. No, this class began to develop something in me I never had. It developed number sense.
What is Number Sense?
Number sense is a person’s ability to understand what numbers are and how to use them. If a person is able to know the value of a number’s digits and make good judgments about them, they have a great start on number sense.
And if they can add, subtract, multiply, and divide fluently and with flexibility (this may not always be in the traditional method), that student has developed number sense.
Unfortunately, many Americans have not developed number sense! In the Mathematics Advisory Panel Final Report 2008, it was reported that 78% of adults do not know how to compute the interest paid on a loan. A surprising 71% can not calculate miles per gallon, and 58% can not calculate a tip.
Math is all around our adult world, and building number sense is important…..and it starts with our kindergarten, first, and second graders. And, sadly, a child may work through a solid homeschool math curriculm and yet still be lacking in strong number sense.
Why We Should Be Building Number Sense In Our Students
I could go on, page after page, about why we should all have number sense, but I’m going to limit is to three simple reasons.
When I go to the gym and my instructor says let’s do squats or planks, I do them. I don’t say, “I won’t use this in my everyday life, so why do them?” I do them because I’m working muscles I need to have a healthy body. No, I’m not going to do planks while I’m running errands, but those planks strengthen muscles I use while running errands or chasing after my kids on the playground.
I’ve read numerous complaints online regarding children having to learn long division or solve certain math problems. They can use a calculator, their phone, or they will never have to do this are the reasons listed as to why a child shouldn’t be forced to perform a certain math skill.
But you see, our mind is a muscle. When we work it, stretch it further than we think it should have to go, struggle through a concept until we succeed at it, it becomes stronger. I watched a video recently on Facebook that talks about how our smartphones are actually making us dumb. Why? because we are letting our smartphones do all the work, and we aren’t using our brains. And we all know what happens when we don’t exercise our muscles!
Building Numbers Sense Strengthens The Ability To Do Mental Math
Yes, I have a smartphone that is always with me. But just because I have one in front of me doesn’t mean I have to use it to solve simple math problems.
When I have number sense, I can multiply 23 x 45 in my head. (And this is something I could have never done before my quest to develop number sense in myself and my students.)
I know that the 2 equals a 20 and the 4 a forty, and 20 x 40 = 800. 20 x 5 is 100 so now I’m at 900. Three times 40 is 120, and now I’m at 1,020. Finally, I add 15 because 3 x 5 =15. So 23 x 45 = 1,035. This was all done in my head because I understand the value of each digit and can flexibly think about these digits. Others with number sense may solve it differently in their heads, but the same would be true for them. They have a deep understanding of the digits and their value.
Number sense is important.
Poor Number Sense Interferes with Learning Algorithms and Verifying If An Answer Is Reasonable
So if I didn’t convince you with the mental math aspect, and you are still thinking I will just use my smartphone, let’s check out this reason.
A calculator is only as smart as the operator.
As children get older and the math gets harder, algorithms are thrown at them constantly. There is a lot to memorize, and steps must be followed exactly. One misstep and the problem is wrong, and sometimes it is noticeably wrong…but only if you have number sense. If you can estimate the answer, or have an understanding the answer should be considerably lower than what you started with, you are going to know if you took a big misstep.
If I’m calculating the tip on my calculator, I have to know that 20% is equal to .2 and that when I multiply a whole number by a decimal it becomes smaller. I can’t divide 54 by .2 and get the tip I need. The knowledge that when I multiply a whole number by a fraction or decimal leads to a whole number that is smaller than what I started with is number sense.
We may have hated those word problems at the end of math pages as we grew up, but let’s face it. As adults, that is the type of math we do every day.
How long will it take to make the 145-mile drive to Atlanta, Georgia? What time will we get there if the traffic is bearable? (A true miracle in Atlanta!) What time should we leave if I need to be there at 3:30 and we might hit heavy traffic?
That is problem-solving that adults need to be able to do, and let’s face it. You can’t work out time on your smartphone.
Here’s another one that we need in our adult lives. There are 9 children in my homeschool group, I have three kids that need to pass out candy to each child, and the assorted bag of candy has 12 servings, and each serving is 3 pieces of candy. Do I need more than one bag?
Number one, why in the world can’t the candy makers not just put the total number of candies in the bag on the front somewhere in big numbers? But let’s face it, I have done this type of math numerous times in a grocery store with four children talking to me! I need to have the number sense so that I know if I need to add, multiply, divide, or subtract. My smartphone is not going to tell me that!
Teaching Number Sense
Now that you know how important number sense is, do you have a looming feeling or wonder how in the world am I going to teach this?
I know how that feels because I felt the same way when I started.
The truth is that you already know how to model this behavior. You are already an expert! Your children watch everything you do so model number sense and give them plenty of opportunities to practice it!
Totally agree. My one daughter get number sense just naturally, while my oldest struggles with it…. but she is getting it.