Math Without Tricks: Making Sense of the Division of Fractions
The "Keep-Change-Flip" (KCF) method is a common math trick used to teach students how to divide fractions. The instructions are simple: keep the first number, change the division sign to multiplication, and flip the second fraction. This method works and provides the correct answer, but there is a significant downside.
If our only focus is on getting the answer, KCF can seem very appealing. However, students often end up with no clue how they arrived at that answer or if it even makes sense. Additionally, tricks without meaning are frequently applied incorrectly in later problems, leading to confusion and errors.
I am a strong advocate of helping students understand that math makes sense. In this blog post, I'll show you a way to approach fraction division that gets students thinking critically and making sense of their answers.
Watch this 10-minute video for a whole new approach to dividing fractions (without KCF)!
Why We Should Avoid Math Tricks
When I say trick, I mean when students use a method, but they don't know why it works. They get the answer, but they're not sure why. This is different than a strategy. A strategy is when students are using reasoning and sense-making to get to a solution.
Why do we teach tricks? I think most teachers want their students to understand all the math concepts, but we feel like we are short on time. However, we have to remember quickly learning something usually means we quickly forget it. When we're learning, our brain is making connections, synapses are firing. Our brain is growing as we think and problem solve and figure things out. When students are thinking and working through difficult problems, their brains are growing. Deep learning is happening as their brain makes these different connections. However, when we learn something very quickly or we memorize it without a lot of thought, that connection is not very strong, and we usually forget it pretty soon.
Have you ever seen students apply a math trick incorrectly? I know I have. It's usually because they didn't learn the math concept behind the trick, so they apply it at the wrong time. They've also gotten in the habit of not questioning if their answer makes sense. When students rely on math tricks, they see no need to make sense of the math.
So I have a challenge for you, and it's a difficult one. No more math tricks! Can we as teachers challenge ourselves and students to always make sense of the math? Students may discover a shortcut for themselves, but we keep the focus on the sense making. If they can make sense of the shortcut, if they understand it and can explain it, then they can use it.
How do we get away from teaching tricks in math? If tricks ignore sense-making, let's go in the opposite direction and start with something that makes sense. Start with context. Start with things that make sense to students and build from there.
Would you like a printable version of this fraction division activity? Sign up to have it sent to your inbox!
