I spent Sunday trying to combine the best of Mighton’s mathematical understanding with Fosnot’s teaching style in order to develop a way of reinforcing times tables in way that would be engaging, meaningful and memorable. I re-wrote the whole lesson about 8 times. I started with the idea of trying to teach number patterns but a conversation with my husband reinforced that these should arise as personal strategies. We all have different ways thinking through multiples of nine in our head…
Eventually, we visually demonstrated that a multiple of one is any original number that can be split into groups of one and then asked the kids to support or refute the conjectures on the board based on our explanation. Partial agreements about some conjectures lead to conversation about whole numbers. Could one student and one half of a second student be split into groups of one? Why not?
The kids, on their own, debated whether zero and negative numbers should be included in a definition of multiples of one. We looked at whether two non-identical conjectures could mean the same thing and both be completely correct. We modified conjectures to make them true.
I thought we’d breeze through multiples of one. We’d planned on coloring in multiples of one, then multiples of two, then moving on to defining odds and evens before the end of class. We didn’t even get past multiples of one. There is so much material that is so often neglected in “simple” math. What a waste to present kids with a definition and miss the magic of abstract mathematical discussion and debate among nine year olds.
We can’t. They won’t.
I have three things to think about for next time:
- How can I guide a discussion without directing it?
- How do I end a conversation without eliminating further possibilities for exploration within the topic?
- How do I know whether everyone “gets” the conversation? How do I continue to provide opportunity for everyone to contribute?