The wide range you see in your students’ abilities when they are working individually in their notebooks is a product of their hugely varied acquisition and retention of mathematical knowledge. When students get into their groups and start working on vertical surfaces, the skills they need to be successful are things like communication, perseverance, patience, self-reliance, et cetera. And although these skills will vary throughout the room, the variance is typically not as great as with mathematical knowledge. When students get into their groups and start working on vertical surfaces, the
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