This story begins with a tweet that I read.

How many cookies do you see? How did you count?#mtbos

h/t @Pierre_Tranche pic.twitter.com/J5xSm78hU2— John Stevens (@Jstevens009) March 22, 2017

This tweet poses a nice engaging situation where addition of fractions would be a very useful tools. But, addition of fractions involves common denominators. And, then I began to remember my students attitudes toward fractions, which can be summed up by the following…

… clearly fractions are so difficult that it requires someone with the reputation of Chuck Norris to be able to deal with them effectively.

Except, they aren’t. Or maybe they are, but they certainly don’t need to be. The logic that says that 2 min + 31 sec doesn’t equal 33 of anything is perfectly understandable to most. It’s the exact same premise as requiring common denominators to complete a fraction addition problem. And THAT is confounding to many. It seems like an arbitrary rule that math teachers invented to trick students.

And the teaching of it carries with it some strong opinions, too. I remember during my undergrad, one of my professors asked this:

One of my classmates changed his major that day. He got so angry that it we would be discussing the possibility that a student could write that equation and could be thinking something mathematically accurate. Dude literally stormed out of class and I never saw him again.

It is possible, by the way:

@hs_math_phys Nope! May describe a situation explicitly (1 of 2 voted in A and 1 of 2 voted in B so 2 out of 4 voted). No silly math here!

— Melinda Waffle (@icmcwaffle) March 22, 2017

About the same time I was reading the IES Practice Guide for teaching Fractions. Are you familiar with the IES Practice Guides for mathematics? The Institute for Educational Studies gathers high quality research studies on educational and catalogs them in the What Works Clearinghouse.

The Practice Guides are documents that synthesize the multiple research studies that exists on a certain subject and operationalize the findings. Recently, I explored the IES Practice Guide for Fraction Instruction K-8.

I’d encourage you to check it out. To summarize, making fractions and conversations about portioning and sharing things a common part of math conversation from the beginning can help take the natural understanding that kids have and build fractions into that context. That will give us a chance to use math talk as a tool for students to need more exact language. My preschool son right now uses “half” extremely loosely at the moment. (I’ve drank “half” my water could really mean anything quantitatively.) In order for him to effectively communicate, he’s going to need to develop a more precise definition of “half”. That will require him adding additional fraction vocab to his toolbox.

As teachers, this gives us a chance to build in some more effective language, clearly defining the fractions as numbers. As such, encouraging a lot of conceptual sense-making about the different operational quirks that are required to effectively compute when fractions are involved. (If fractions aren’t numbers, but instead are just made-up, goofy ways of writing numbers, then the rules for computing them are goofy and made-up, too.)

The practice guide provides some tangible steps to achieve this. I’d encourage you to check it out. Lots of steps forward to take in the area of student comfort and effectiveness with fractions.

The IES Practice Guide for Fraction Instruction K-8 is at least three and a half times as much as is needed – a gourmand’s portion.

I am totally mystified as to the looking at addition of fractions before all else. It is really bizarre. Fractions is ABOUT ratios and proportions.

Who apart from schoolkids needs fractions with randomly chosen denominators.

1/2 + 3/8 is quite enough

Knowing the numbers as quantities and being able to compare them comes first in the elementary sequence. For example, there are 2nd and 3rd grade standards about fractions even before students see division. That these quantities turn out to be the same as the result of division later (5th and 6th) and intimately related to rates and proportion (MS and beyond) are one of the truly wonderful things about the rationals.