1. “Show me another way…”

2. 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

3. 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

4. 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?”

5. Grade level tasks: K – Model “3 + 7”, showing the progression from the most concrete to the most abstract. 2 - Add: 236 + 456 3 - Multiply: 3263 x 4 4 - Multiply: 23 x 23 5 - Multiply: 45 x 24 Look for: Concrete / Pictorial / Abstract solutions. “Show me another way…” Different tools don’t always show different strategies

6. “Mathematics” or “Mathematizing”