Fraction Misconception

I am on a mission to help students master conceptual understanding of fractions. This is NOT an easy task. Fractions are so hard for kids whose minds still operate primarily in the concrete.

I’ve been tutoring some struggling mathematicians after school a couple days a week. This last week, we were looking at comparing fractions with different numerators and denominators. I showed the students region models that represented 2/3 and 3/4.

Just about every one of the 10 kids looked at the model and said that 2/3 was greater than 3/4. I was dumbfounded. How could the kids look at these two models, where one was clearly bigger than the other, and say the smaller one was larger?

I tried to get inside the heads of my students. Where was the misconception? Then it hit me. I had been showing numerous examples of unit fractions and pounding into the kids’ heads how 1/4 was smaller than 1/3, 1/10 smaller than 1/5, etc.

I did my best to drive home the point that the larger denominator actually indicated the smaller fraction. Then, we switched to comparing fractions like 3/4 and 2/3. Eureka! The kids were looking at the individual pieces, not the entire shaded region! When I asked which was bigger, they said 2/3 was greater than 3/4 because 1/3 is greater than 1/4!

Lesson learned. When kids seem illogical and out-of-touch, there’s a reason. Our job as educators is to pinpoint these misconceptions and help students make sense of the world around them.

For a really cool visual math resource, check out this fraction model on the NCTM website, Illuminations.

Have you discovered any math misconceptions with your students that you could share?

Tim Bedley

Tim Bedley has been teaching elementary school since 1988. He was recognized as the 2013 Riverside County Teacher of the year. Tim is also the founder of America's number one educational rock band, Rockin' the Standards. He also produces two podcast found on iTunes: The Bedley Bros. and The 5-Minute MishMash. Tim and his brother Scott are co-founders of Global School Play Day, a grassroots movement to promote unstructured play with today's youths.