Hugh Beaton Public School Professional Learning


GECDSB School Based Learning Sessions (SBL)

Tuesday February 7th, 2017

Thanks for inviting Andrea and I to learn with you on your school based learning day! The group was energetic and excited to learn about meaningful manipulative use, spatial reasoning, the progression of multiplication and concreteness fading!

Here’s a summary of what we explored today:

The GECDSB Mathematics Strategy

GECDSB Math Strategy

Mathematical Proficiencies

The full GECDSB Mathematics Vision is here.

GECDSB Mathematical Proficiencies

Paying Attention to Spatial Reasoning

Paying Attention to Spatial Reasoning Document

Warm-Up: How Do You See the Dots?

We did a quick Dot-Card warm-up asking you to visualize how you saw a series of dots on the screen. We went around the table and it seemed that everyone had a different perspective.

Jo Boaler Dot Card Warm-Up

Here’s some of the ways you might have visualized the dots:

Counting Principles – Counting and Cardinality


Counting Principles - Progression of Counting and Quantity

A Progression of Counting and Quantity As a former secondary math teacher and intermediate math coach, my new role as K-12 math consultant has led to a wealth of knowledge that I wish I had during my years spent in the classroom. My conversations about student learning needs with intermediate and senior math teachers always seems to come down to gaps in student understanding, however rarely wer...


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We then explored the progression of multiplication from arrays and area models to the standard algorithm.

For a full summary, see the post below.

The Progression of Multiplication


Progression of Multiplication - Area Models and Standard Algorithm Featured Image

Arrays and Area Models to The Standard Algorithm Did you know that the words "array" and "area model" appear in the Grade 1-8 Math Curriculum a combined 22 times? Not only do arrays and area models help to support the development of proportional reasoning when we formally introduce multiplication in primary, but they also help us understand how to develop strategies that lead to building numbe...


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Concreteness Fading

We attempted to summarize the use of manipulatives on a continuum called “Concreteness Fading”. While the name suggests that concrete manipulatives fade away over time, it is important to remember that they fade away with one layer of abstraction and then reappear as a new layer is “piled” on.

Applying Concreteness Fading to Progression of Multiplication

Hope you folks found this professional learning experience useful. I’d be delighted to come back and learn alongside you all again sometime soon!

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