“Show me another way…”

Why is it important? Research heavily supports C-P-A Provides built-in differentiation Creates flexibility of thought Thinking can be generalized to novel situations

Abstract understanding is the last to develop: algorithms The deepest understanding comes when students can demonstrate understanding in at least different ways C-P-A

C-P-A Progression “Do not confuse easy with foundational ” Visual images (pictorial) cannot come without fluent understanding of the concrete Students cannot do abstract without being able to visualize the problem first “Can you see it?”

Grade level tasks: K – Model “3 + 7”, showing the progression from the most concrete to the most abstract. 2 - Add: Multiply: 3263 x Multiply: 23 x Multiply: 45 x 24 Look for: Concrete / Pictorial / Abstract solutions. “Show me another way…” Different tools don’t always show different strategies

“Mathematics” or “Mathematizing”