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Think back to your days as an elementary math student. You probably remember learning the times tables or how to plot points on a graph, but what do you remember about fractions? If you’re drawing a blank, you’re not alone.

Failing to gain a conceptual understanding of fractions has become a common experience for American math students.

Although you likely do not remember, you spent an extensive amount of time studying fractions in elementary school. Under traditional methods, you were taught how to perform a series of steps without any exploration into the reasons behind them.

You learned the rules, but not the concepts.

For example, many teachers share the "keep-change-flip" method for dividing fractions. This strategy involves keeping the first fraction, changing the sign to multiplication, and then flipping the numerator and denominator of the second fraction.

And this approach will work every time. If you memorize the rule, you can produce correct answers at will.

But consider that there are several more unique rules for equivalent fractions, converting mixed numbers, simplifying, multiplying, and decimals. While these rules are useful and effective for the purpose of computation, the only way to master them is through robotic repetition and rote memorization.

The problem here is that learning is an active process and we want our students thinking, not working on autopilot.

Relying on shortcuts like "Keep-Change-Flip" prevent students from reaching concrete understanding.

Many teachers compound the issue by resorting to tricks and shortcuts (like keep-change-flip) to make learning fractions easier.  Math experts say that relying on these tricks allows students to skip the conceptual thinking that we need to encourage in order for meaningful learning to occur.

Shortcuts do not encourage critical thinking, which is why it’s no surprise that many students develop a “what is the point of this?” attitude that turns them away from learning math at a young age.

Seeing is Learning

Using legos as physical representations of fractional values is a great way for students to develop meaningful and lasting mathematical understanding.

So what can teachers do differently? The answer is using hands-on materials and visual models that allow students to explore the underlying concepts. These tools allow students to make an abstract concept, like fractions, more concrete.

Learning, after all, is meant to be an experience, not a passive event.

Progressive math standards place a strong focus on exploratory activities that give students opportunities to develop a base understanding of a concept. These activities are often multi-sensory and incorporate hands-on materials and visual aides.

For example, activities with Legos provide a fun and engaging opportunity for students to develop context. They help students to visualize how the numbers involved with fractions actually relate to each other. You can learn more about how to use Legos to build math concepts here.

But not all exploratory activities have to be hands-on. The use of visual models like shapes, grids, and charts are also effective tools for transferring a student’s understanding from abstract to concrete. The idea is to make learning more exploratory, multi-sensory, and engaging. We want students to get the right answer, but we also want them to be able to justify it, which requires a high level of conceptual understanding.

The following video lesson, presented by yours truly, is an example of how 4th grade students can use visual fraction models to demonstrate conceptual understanding:

When students can grasp the concepts behind fractions, they are better equipped to perform operations on them without relying on a memorized rule.

And while the rules will always have their place in the math classroom, they can no longer stand on their own as an effective teaching method. If we do not give students the opportunity to explore fractions and build conceptual understanding, then the rules become meaningless.

Visual and hands-on experiences with fractions help students to understand where the rules come from. And if they ever forget those rules, then they can access their conceptual understanding and rediscover them on their own.

And besides, what elementary student would not be psyched to play with Legos during math class!?

by Anthony Persico

Anthony is the content crafter and head educator for MashUp Math. You can often find me happily developing animated math lessons to share on my YouTube channel. Or spending way too much time at the gym or playing on my phone.