This past week I observed math centers again. This center was themed for geometry. The goal was to have the students use the blocks to re-create the picture on the laminated card. I sat with one of the female students as she did this pattern, seen above. I asked her what she was making, and she said she didn't know. When I asked her why the different blocks fit together, she surprised me by saying "because their sides are the same". I'm not exactly sure how to take her answer. She could either mean that their sides are the same length, therefore the shapes fit together, or she could simply mean that the sides are both flat and not one flat one curved. Either way, she had a rather impressive knowledge of why these puzzles work.
When you say that "The goal was to have the students use the blocks to re-create the picture on the laminated card", you are describing procedurally what the students did. But the key is to think about what the learning objective / big idea for this task is, in terms of the mathematics. As you can see, it is hard to analyze the student work without a clear understanding of how to assess them (e.g., what the conceptual goal of the activity is). That is why identifying the goal is the key first step.
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