Several years ago, my fifth graders started telling me about the "butterfly method" they had learned in earlier years of school. They stated it was "much easier" than the way I was making them compare fractions so I figured I'd check into it.
Oh no.
Stay away.
Is it "easy" overall? Yes.
But is that the goal? Does easy translate into truly understanding math in future years? Goodness no.
So why should the butterfly method fly away?
1. I have yet to meet a student using butterfly method who has a conceptual knowledge of WHY 2/7 added with 1/5 could possibly equal 17/35. They just know "this is how you do it."
2. This "trick" doesn't take into consideration many future math lessons. How do you add 3 or 4 fractions together with this method? What will students do once they start having negative and positive numbers? What about denominators like 12 and 24? Are they really going to make a denominator of 288???
3. It doesn't teach a math truth. Truth never changes. Math truths never change. A fraction multiplied with 1 stays the same. A decimal multiplied with 1 stays the same. A whole number multiplied with 1 stays the same. I teach this math truth every time I require my students to find a least common denominator between 7 and 5 and then create equivalent fractions by multiplying each fraction by 1. You multiply by one, you stay the same.
I have my students to write a 1 over the version of 1 they are working with just to cement that idea that a fraction multiplied by 1 stays the same.
Does it take longer to teach this way? Yes.
Would students rather just learn a quick trick? Yes.
But which will benefit them past their year in your classroom and as they process math at higher and higher levels? I think the answer is obvious, but I'll let you decide.
Side Note: This post was not written to make anyone feel ashamed for having taught the butterfly method. I'm sure there have been times in my classroom that I have taught an "easier way" to do something instead of the harder, conceptual way. This is for information purposes only, not to make anyone feel inferior. Teaching math is difficult and I want to praise all teachers who tackle teaching this subject every single day!!!
What are your ways of teaching fractions so that students will understand it at a deep level? Share with me your thoughts; I'd love to read them!