Begley Public School Based Learning (SBL)

GECDSB School Based Learning Sessions (SBL)

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Thursday January 12th, 2017

Thanks for inviting me to learn with you on your school based learning day! The group was energetic and excited to learn about meaningful manipulative use, spatial reasoning, concreteness fading and how they all fit with topics like fractions.

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

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:

Tools and Representations

We discussed the importance of tools and representations to help students see mathematics from different perspectives. These quotes help us better understand some of the other important reasons tools and representations are so important:

Tools and Representations Quote - Kilpatrick

 Tools and Representations - representations are critical to understanding

K-12 Process Expectations: Representing

We very briefly discussed the 7 Process Expectations in mathematics that are embedded throughout our K-12 Mathematics Curriculum and looked in particular at the expectations for Representing:

K-12 Process Expectations

Task: The Sandwich Problem

With manipulatives on the table (square tiles, relational rods, cubes, pattern blocks and fake money) we attempted to find concrete and/or visual representations that could help us solve and justify the following task:

The Sandwich Problem

Original task was shared at a Ministry SIM Session. Here’s the slide deck.

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!

Wednesday January 25th, 2017

Great learning with you all again today. Please find some resources below:

Learn More About the Progression of Fractions:

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Other Resources Related to this Session:

Paying Attention to Fractions

Paying Attention to Fractions


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Looking forward to working with you again in the next couple weeks!