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Monday, August 29, 2016

The Big Picture-- Understanding the Fractions Progressions in Grades K-5

In 2012, a Carnegie Mellon research team found that a student's mastery of fractions is a direct predictor of how well that student will do in algebra when he/she reaches high school.

Fractions fun in grade 3
I first heard this news two spring semesters ago, during a Eureka Math training that I was attending, as I was preparing to move into my current role as the elementary math/tech coach for my district. The trainers were explaining the progression of instruction in their curriculum to the group, talking about the build from basic number sense, to fractions understanding, and into algebra, when they mentioned that a student's understanding of fractions can directly predict their understanding of algebra down the line.

This absolutely blew my mind! Aside from knowing that yes, it is important for students to know how to perform operations with fractions, I had not fully considered the connection between fractions concepts and the more complex math that students would encounter in high school.

Part of this, I realized, was due to my surface level understanding of math upon leaving college. I'd done fine in math, up until about Trig and Calculus in high school (and the one college Calculus class that I was forced to take in order to graduate, and barely passed), and for the most part thought of myself as an okay math student. But I was well aware of the holes in my math learning, and I definitely had not learned math in terms of the patterns and many connections across concepts that mathematics is actually made up of. And so, as an elementary math teacher, I felt fairly inept at teaching math well, and have spent numerous hours since my first year teaching, learning more math and learning how to be a better math teacher.

Analyzing math progressions
And that brings me back to the importance of fractions. Knowing that a student's understanding of fractions would act as the infrastructure to support their algebra comprehension, I decided to make fractions instruction a focus of my work as a math coach.

One way that I hope to help teachers and parents better support students' work with fractions is to help them understand the bigger picture. We need to know where our students are coming from, and where they are going, in order to best support their learning while they are in our class. And so I've begun to work with teachers and parents on studying the math progressions documents and actually doing the math while learning more about the connections made across grade level spans. In my last math training, teachers studied the Numbers & Operations in Base Ten progressions for their grade level and then created posters that we analyzed for connections and patterns across the grade levels.

My most recent project (below)-- a visual representation of the fractions progressions from Kinder through 5th grade. I'll be sharing this document with teachers in my next math training this month as well as during an episode of my webinar series, the "Math/Tech Minute", to hopefully help teachers develop a better understanding of fractions concepts and the connections between the skills taught across the grade levels. Feedback and suggestions for improvement are welcomed!

(Click to view full size presentation in Piktochart; visit this folder for copy of infographic blocks)

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