Coleman: Fractions Can Be Scary for Kids and Adults. Here’s How to Take the Fear out of Them
Fractions can be scary and intimidating to many adults and students. They seem to have their own set of rules and never make anything easy. Often, we prefer to convert them to decimals so we can put them in a calculator.
Because so many of us struggle with understanding and working with fractions, math instruction frequently resorts to the mindset of “Let’s just learn the steps so we can find the answer and move on.” One example of a set of steps often taught for division with fractions is “keep change flip” (keep the first number the same, change the division sign to multiplication and flip the second fraction). This simply procedural work leads to students who can find the correct answer in the moment but quickly forget the seemingly meaningless series of steps.
I’d like to outline an alternate approach. What if we teach that fractions are just numbers? They happen to be in between the whole numbers we all know and love (1,2 … 10), and they look a little different, but they are just another point on the number line. What if instead of teaching procedural tasks, we teach students to truly make sense of and work with fractions?
Consider the following problem:
Which is larger, 1/3 or 1/4?
Many students incorrectly assume that 1/4 is the greater fraction. After all, 4 is greater than 3, so doesn’t that make 1/4 greater than 1/3?
One approach, usually taught in third grade, is to compare fractions by finding the common denominator. In this case, you must convert both fractions to have a denominator of 12.
First, multiply 1/3 by 4/4 to get 4/12.
Next, multiply 1/4 by 3/3 to get 3/12.
Finally, see that 4/12 (or 1/3) is bigger than 3/12 (or 1/4).
You arrived at the answer, but it took a few computational steps.
Instead, consider an example from daily life.
Think about those giant chocolate chip cookies you see at the bakery. When students are asked whether they’d prefer to share the cookie with three friends or four, they always say, “Three friends!” Their life experience has taught them that when it comes to sharing, fewer people means larger pieces.
Now, let’s create a drawing to visualize the problem. Grab a pencil and paper. Draw a bar and divide it into thirds (1/3 + 1/3 + 1/3).
Draw another bar of the same size and divide it into fourths (1/4 + 1/4 + 1/4 + 1/4).
The units in the top bar are obviously bigger than the units in the bottom one, making it visually clear that 1/3 is greater than 1/4.
Fractions are only scary because, too often, we rush into procedural learning. Many of us never had the opportunity to make sense of the reasoning behind the steps that got us the correct answer.
Many teachers are beginning to understand that when we slow down and teach conceptual understanding of fractions, it allows students to speed up and increases their ability to remember how to work with them. Taking the time to make sense of fractions through concrete objects and representational drawings is what makes sense of the abstract.
Knowing the big idea behind the math allows our students to have their cookie — and eat it, too.
LauraMarie Coleman works with and coaches teachers on professional development for Great Minds. Previously, she was a special education classroom teacher and an instructional coach, working with alternative and special education students and teachers in grades K-8, in Binghamton, New York.