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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)

Thursday, August 11, 2016

Rethinking math instruction: designing lessons for a 21st century math classroom

As a still pretty new classroom teacher about 6 years ago, teaching 3rd grade at the time, I didn't think of myself as a very good math teacher. I noticed very early on that I wasn't really reaching my students. And so I made it my mission to learn more math, to learn how to be a better math teacher, and how to interest my students in math.

I attended all the trainings, started reading all the books, and next thing you know I'm presenting to my colleagues on math instruction.

Now, I find myself a math and technology coach for the K-5 teachers in my district, and I notice that, like myself, many others, even if they want to change the way they teach math, have a hard time getting started.

Modern lesson design
Math is a subject that seems to have been taught just about the same way for the last 100 years or so. Facts, memorization, algorithms, etc. Even when we know it's not working, math is a subject that we teachers seem to struggle to change.

Our students should be learning math via experiences, not flash cards. We are not training our students to
become regurgitaters of facts. We need to teach them how to be creators, how to be critical thinkers, how to be problem solvers.

This week I led a 3-day workshop for my K-5 teachers on shifting mindsets around math instruction. The goals:
  • Empower teachers to design lessons & learning experiences in math
  • Shift instruction from teacher-led to student-centered
  • Move math to inquiry-based
  • Make learning hands-on math
  • Design for 21st century learners
By the end of the our 3-days, I was pumped to see teachers excited about math this year! Teachers used what they learned about hyperdocs; interactive math activities using Google tools; self-directed lessons using PBS LearningMedia storyboards, EdPuzzle, and others; Estimation180; number and fraction talks; Which One Doesn't Belong; among other resources to start designing math experiences for their students. And at the end of day 3, all the 'thank yous' and hugs let me know that this might have been just what some of us needed!

Below is the presentation I used with my teachers. (Some is Eureka Math/ENY specific since that's our current curriculum, but scroll past that for most of the good stuff!) Feel free to modify and use as desired!