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The teacher’s role
Your role is to present the problem and assist the flow of the adventure.
Assisting the flow of the adventure, in this curriculum, requires you to do as little as possible, but as much as needed, to create the environment in which students have the chance to have an idea.
You can do almost anything except have the idea for them.
The support resources for each problem provide some scaffolding for how to assist the flow of the adventure.
Having and sharing ideas
Kids will have lots of different ideas. Sharing them with the class, even before they’re polished, gives the kids a chance to bounce off each other’s ideas.
But kids also need the chance to think of something on their own. Some ideas will act as spoilers if shared too soon. Experience will teach you which ideas are the ones to share, and when it’s the right time to share them.
Which paths to take
Every problem has many potential paths. The problem pages show only one or two.
Other paths might be worth taking if (a) a kid comes up with the idea, and (b) you feel confident about following it.
Finishing the session
Problems do not need to be “finished” by the end of the session.
Problems can remain unsolved, and questions that arise can remain unanswered, but you may wish to reach some satisfying points before finishing the session.
Example of how a session might be run
- you present the problem
- groups work for a time
- you pick some groups’ ideas for them to share, to act as further stimulus for the others, or to connect to other ideas
- groups work a bit more
- etc.
Some tips:
- Encourage your students to share their half-baked ideas with the class, as they go. This can help another student have an idea.
- Be careful about letting a student share too much. It is easy for them to spoil another student’s thinking.
- Keep your checkpoints in mind, but be prepared to change your plan.
- Aim for BAD arguments, but use your own judgement.
- Try not to force your students along the path you took.
The students’ role
Groups
We suggest that students work in groups of 3, where possible (2 is ok, 4 is probably too many).
Students in a group may want to work by themselves for a period. Sometimes working by yourself is the only way to get things clear in your head.
What the students do
The job of the student group is to do mathematics. They should work together on the problem, have ideas and pursue them, think of questions to ask, and generally try to get to the heart of what is going on.
Students may be called upon to share an idea with the rest of the class.
Written Accounts
As the groups work on each problem, they should keep a written account of their adventure.
This should not be a polished solution, but rather a “live recording” of their adventure. This should include ideas they have, what they try, what fails, what works, etc.
Writing down their thinking as they go is a skill that will take practice. Students should be encouraged to practice this skill during all problem sessions.
These written accounts will help you assess the students, if you choose to.