Scene: A classroom
Students are working on pattern recognition
Tell me about this pattern
It looks like a plus sign
Awesome! What else?
Each time it's adding one block to each side
Say more about that
It starts as just a square, but each side of that square has another square on it. In each new picture, another square is added
Cool. What about the next one? What will that look like?
It will be a square in the middle with 4 squares in a line on each side
Do we agree?
Students nod and murmur approvingly
Alright, so what about the 10th step? What will that look like?
It will have 21 squares each way
**smiles cunningly** 21? Step 1 had 1, Step 2 had 2. Tell me how you counted 21
It's makes a plus sign and there are 21 squares going up and down and 21 going back and forth
**looks around to rest of class** Thoughts? This isn't at all how we were examining the pattern. What do you think?
Brief discussion ensues where students ask clarifying questions.
Since day 1, we have been talking about how mathematics is a language. Everyone speaks it to a certain degree, but our goal is to become fluent. Student 3 had an idea that was different from the rest of ours, but she was able to make her thinking understood, turning an answer that, on the surface, was wrong, into a class discussion about perspective. While there are answers that may be incorrect, it's important not to discount results that are different without examining the thinking behind them.
Math is more than calculation. Math is discussion, debate, argument and exploration.
Students climb onto their desks.
Oh Captain, My Captain