Let's Talk Fractions

I recently had a conversation with a family member who was baffled when a friend wanted to know how many quarters were in a basketball game. I initially laughed with her – as many people just understand that there are 4 quarters in a basketball game, because of the emphasis we place on the word “quarters”. I almost dismissed the conversation entirely, until I realized the question may not be as silly as I initially thought. With all the misunderstandings about fractions and fractional language floating around in the world, is it really that implausible for someone to question the use of the word “quarter” in this situation? Maybe not so much.

I believe people struggle with fractions (and mathematics in general) when their foundation is fragmented by partial understandings and/or faulty ideas about what a fraction really is. This isn’t always as obvious in the early grades when students are introduced to fractions, but once the concepts move beyond part-whole relationships and involve multiple representations or even operations with fractions, the cracks begin to show.

Fortunately, this foundation is repairable, if a student is exposed to a solid conceptual understanding of fractions which includes instruction about how fractions are both formally and informally presented in the classroom and in the real world.

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Models are important for fractional understanding. The variety of models and the context in which they are used is key. I have concerns with misusing tools/objects, as in the case of “popsicle stick fractions”, when they are used as a model for fraction notation (i.e. being represented as 2 popsicle sticks placed over a horizontal line and 3 popsicle sticks under the horizontal line).

The popsicle sticks themselves can be a powerful tool for teaching fractions of a set if used in a way that allows students to see fractions as numbers. Placing two popsicle sticks over three popsicle sticks does little to help a student see "two-thirds" as a number, and understand it lies between 0 and 1.

Other tools (manipulatives), such as fraction circles are great, but add in other representations like modeling fractions on number lines, rulers, fraction bars, and real objects – even paper folding – because they work well.

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Carefully evaluate the language use when describing fractions. Do students understand all the “parts” in a whole need to be the same size? What does it mean to “reduce” a fraction – is the fraction really getting smaller? What about “improper fractions” – what makes them improper?

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Twitter: @brea_ratliff

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