Math educators debate student problem-solving strategies

After a high school math teacher shared a photo of a student using a problem-solving strategy called the “butterfly method,” many educators in the math sphere critiqued similar approaches arguing that these strategies hinder students from gaining deeper understanding of math concepts. 

  • “My 11th graders told me today that one of their previous math teachers taught them to solve proportions using the ‘butterfly method’… Has anyone ever heard that one before?” —High School STEM Teacher in Michigan
    • “It’s one of those crappy methods that teachers use to try to get students to remember how to do things… then two months later they get it confused and don’t know what [they are doing or] why they’re doing it.” —High School Math Educator in Colorado
    • “Yes, and several math curriculums in 5-8th grade have both encouraged and discouraged its use (learn the concept, then the shortcut was the school of thought).” —Middle School ELA Teacher in Montana
    • “I hate it. Students don’t understand proportions conceptually when it’s taught this way.” —Teacher, N/A
    • “It is illimited and not the most reliable. It is often used by teachers in an effort to drill kids for annual testing, help students who struggle. Unfortunately this is just another rote application that stifles thinking, computation, and critical thinking. Concrete, Representational, Abstract  works best for all kids!” —Elementary Educator, N/A
  • “This comment thread though. It goes to show that when we teach tricks, it hinders students’ true understanding of concepts. Why does ‘butterfly’ work? Do teachers even know? Concrete, Representational, Abstract ensures that students don’t get to 11th grade without actual conceptual understanding. Teach concepts, not tricks.” —Elementary Math Instructional Specialist in Texas
    • “Right. And tricks often get misapplied to other situations… The ‘butterfly’ only works on proportions, but kids often use it for addition or multiplication. You’re right on about teaching the ‘why’ something works, even if it’s more complex.” —High School STEM Teacher in Michigan
      • “For sure! The method works because you’re essentially finding a common denominator. But we always skip teaching why the ‘trick’ works or why finding a common denominator is the easiest way to compare fractions. We go straight to the trick bc it helps kids get test answers correct.” —Elementary Math Instructional Specialist in Texas
  • “Broad question — What do you want for students in terms of mathematics? What is your goal as an educator?” —Math Educator in Canada
    • “I want students to love math, understand that they use it in their everyday lives and be confident that they can do it.  I want to help them become competent, confident and curious mathematicians.” —Math Educator in Connecticut
    • “My goal is to build the math identities and agencies of all students and educators and demonstrate that they can do more than they even dreamed possible when using relationships between operations and numbers!” —Elementary Math Consultant in New Hampshire
    • “My goal is to spark curiosity, inspire and make meaningful, positive and lasting math memories!” —Educator in Canada