How important is it that our students understand fractions? According to a study conducted by Carnegie Mellon University, it’s super important.
The research team found that fifth graders’ understanding of fractions and division predicted high school students’ knowledge of algebra and overall math achievement, even after statistically controlling for parents’ education and income and for the children’s own age, gender, I.Q., reading comprehension, working memory, and knowledge of whole number addition, subtraction and multiplication.
In other words, they found that it was the single most reliable predictor of success with higher math. Unfortunately, we don’t always do a good job teaching fractions for understanding. It’s a topic that is often “taught” using tricks and memorized procedures. So how can we do better?
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First and foremost, we have to provide students with lots of concrete and pictorial experiences so they can create mental pictures to draw upon when they encounter a fraction. When a student can visualize both one-eighth and one-fourth, it makes comparing fractions a whole lot easier. When the only image students can conjure up is symbols, they often apply faulty whole-number thinking and decide that one-eighth is greater than one-fourth because eight is greater than four.
Oftentimes, the use of manipulatives drops off in 3rd grade. There are a couple of reasons why that happens.
First, there is the misconception that manipulatives are for younger students. That stems from misunderstanding the concrete, representational, abstract (CRA) sequence of instruction. The use of concrete materials is not based on age at all. Students should have concrete experiences whenever they are introduced to new concepts, regardless of age. When students are introduced to foundational fraction concepts, like equivalent fractions in 3rd grade, the bulk of their instruction should be supported with a variety of fraction models—fraction tiles, number lines, fraction circles, etc. When they begin computing with fractions in 4th and 5th grade, they should again be supported with models. It’s even in the standards!
Another reason that upper elementary teachers often give for not using manipulatives is that they face a time constraint teaching their curriculum before state-mandated testing. I get it. But the argument is actually counterproductive. When we skip manipulatives and other visuals during instruction, we often find that students don’t retain what they’re taught. So then we end up spending precious time remediating skills because we rushed to teach them in the first place. When we slow down and give students the concrete experiences they need, it saves time in the long run.
I promised you a free resource, and here it is! Grab this set of visual fraction cards that students can use for multiple games. One game they can play, for example, is Equivalent Fractions Memory. It’s important to have students verbalize their reasoning when playing games like this. As you can see from the cards, players could recognize that the two fractions are equivalent without even considering what the two fractions are! So we want the expectation to be that the player would say, one-fourth is equivalent to two-eighths. If they play this game enough and state the fractions each time, it would be pretty hard to think that one-eighth is greater than one-fourth.
Check out this post for an exploration of equivalent fractions. There is a link to download the activity.