I got an email asking, why do kids struggle with subtraction facts? She said, “they eventually get addition, multiplication, and even division facts, but students continue to struggle with their subtraction facts.”
I’m Christina Tondevold, The Recovering Traditionalist and I hope you stick around because today, we are going to take a look at How To Make Subtraction Not So Hard, in our quest to build our math minds so we can build the math minds of our kiddos.
Watch the video or read the transcript below:
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Fluency in subtraction compared with addition by Constance Kamii, Barbara A. Lewis, Lynn D. Kirkland
If you Google, “why is subtraction so hard?” you’ll get just under 50 million hits. So, if you’ve ever asked that question, just know you are not alone.
There are three main reasons why subtraction is hard. Instead of just focusing on why it is so hard, let’s take it a little step further about what we can do to help it not be so hard.
#1: We need to de-emphasize subtraction fluency.
Yes, I know that everyone is concerned with getting kids fluent in subtraction facts, but the moment we focus on that end result, we’re missing out on the bigger picture.
And that’s one of the reasons why they struggle. If we are focusing on getting them fluent with facts, we aren’t focusing on helping kids truly understand what subtraction means. The research of Constance Kamii, Barbara Lewis, and Lynn Kirkland found out that kids figure out differences from their knowledge of sums. So if a kid knows the sum of 7 + 3, they are more likely to know 10 – 3.
One of the stances that they take throughout this article is that we jump too quickly to helping kids be fluent with subtraction instead of spending time helping kids really build an understanding of what subtraction means.
If you ask your students, what does it mean to subtract? Like what is 7 – 3? And if all they can give you is the answer 4, they don’t really understand what subtraction means. Kids need to understand that subtraction can be takeaway (young kids first start out thinking of subtraction in that way), but that’s not the only version of what subtraction means.
Subtraction is actually the difference. What’s the difference between 7 and 3? If I’m subtracting 7 – 3, how far is it from the subtrahend, the 3, to the minuend, the 7?? Kids don’t need to know that exact definition (the distance from the subtrahend to minuend), but they need to understand that subtraction is the difference between those two numbers.
So, again tip #1 is to stop stressing about helping your kids get fluent with subtraction. It will come. Spend more of your time helping develop an understanding of what subtraction really means, by giving them situations, contextual situations, like “Sierra has $7. Her little brother has $3. How much more money does Sierra have than her little brother?”
Yes, we can subtract to figure that out, but it’s finding the difference between those amounts. And when they see it as finding the difference, then it helps build a connection to addition. And that’s our #2 recommendation.
#2: Spend more time building addition fluency
Kids are using their knowledge of sums to help them with subtraction. So if they’re not fluent with addition, then it becomes harder for them to become fluent with subtraction. If a kid knows that 3 + 4 gives them seven and they see a situation like “Sierra has $7, her little brother has $3. How much more does Sierra have than her brother?”, they can use their information about addition to help them solve that subtraction problem.
So we need to spend more time building that addition fluency. I’m not just talking about memorization, I’m talking about true fluency. I’ll link to a video about what it really means to be fluent. But just as a quick reminder, fluency really has three pieces. We do need to be accurate, we need to get the correct answer when it comes to knowing our facts. They also need to be efficient, we need to be fast. It shouldn’t take a kid 15 minutes to solve one subtraction problem or one addition problem, whatever it is you’re working on being fluent at.
The third piece is really the missing piece: flexibility. Flexibility is the missing piece to fluency. If students don’t have flexibility, they’re not truly fluent with addition. If they don’t just know it, do they have an alternative way to get there? That’s what really shows whether or not a kid is fluent.
So again, what we learned from Kamii’s article is that we want kids to be able to be fluent with addition because they use that understanding to help them solve subtraction problems. But one other interesting thing that they found was that it doesn’t just help with subtraction, kids also use addition to solve multiplication and division problems. So this is why we see kids who eventually develop fluency with multiplication and division, but they still struggle with fluency with subtraction. That’s because we haven’t spent enough time with tip #3.
#3: Develop the relationship between addition and subtraction
So typically we will build an understanding of addition and we’ll help kids get fluent. Then we’ll move on to helping them get fluent with subtraction, but they’re seen as isolated things. The kids are not seeing the connections between the two.
Now you will always have some kids who will see those connections, but we’re talking about the kids who are struggling with subtraction, and those are the kids who are not seeing those connections. So we really need to emphasize that relationship between addition and subtraction.
So, often subtraction is just done through memorization. If we do it that way, that’s 121 new facts that kids need to memorize. Instead, use what they’ve built around their addition fluency to help them make that connection to how that helps them with understanding subtraction.
If we do those other two tips that we’ve talked about, which is helping kids understand what subtraction really means by de-emphasizing fluency by focus more on building the understanding of subtraction & helping build their fluency with addition, and then we also build the connection between addition and subtraction. Those three things will help our kids be able to really understand what subtraction is, while we are also building their fluency.
So, in short, focus on building fluency with addition, helping them understand what subtraction really means, and then helping them build the connection between addition and subtraction. Those three things will make subtraction be not so hard for your kiddos.
All right, I hope that this video helped you build your math mind, so you can go build the math minds of your students. Have a great day.
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