B.E.R.C.S. is my model for planning teaching, learning and assessment tasks that focus on understanding built on fluency with mathematical reasoning and "basic facts"

I want students to know how to think and reason with what others call "basic facts". And I want to expand the list of basic facts to include basics about relationships between shapes, between measurements, between measurements, shapes and spaces and between NUMBERS. Number properties are foundational to understanding the difference between mental strategies and "traditional algorithms" which often ignore number properties leaving students with no understanding of how we can prove without much work that the answer is correct.  successfully transitioning to algebra. 

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What characterizes my work is visual, spatial models that evolve to connect across content and grades. 

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Dots, blocks, ChunkitZ give way to grids and number lines. Grids develop proportional reasoning as well as double for ways to organize data to arrive at generalizations. 

Number lines evolve into the Cartesian plane. 

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I spatialize ideas so that students can literally see their way to a proof.

Students can cut, fold, tape their way to a proof. 

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As several students have told me, the models make it more interesting and give me time to really think about what I am doing. I can see things in my mind when I read math equations.

"I think the models are making me smarter!"