We began digging a little deeper into the focusing and funneling question with a lighthearted video:
We came up with these ideas about the different types of questions:
Goal: singular – particular answer
“Leading” because you already know the answer
Investigating background knowledge
Can build confidence for students who struggle to articulate thoughts
Ok when scaffolding
Help students learn what questions to ask themselves in solving
Might be better for English Language learners and L.S.
With word problems the reading levels might not match the math ability
They might be hard for students with processing issues
If a student has background knowledge of a different strategy it might be counterproductive
Goal: Open ended, allowing multiple pathways, check for understanding
Allows for explaining the thinking
Higher level process conversation
Build stamina or frustration
Opens up the time for commenting
The students direct the path with guidance from the teacher
You have to be careful you don’t go too far down the right path
You must listen carefully
It takes more planning and foresight on the teachers part who must have thought about what might happen.
There is a website where you can share and comment on mistakes students have made in math class – http://mathmistakes.org/
Charles began our math discussion by looking at the work of a student on the hourglass problem. There was some good discussion about the work and the process and the accuracy of the mathematical representation.
We ended the day with a pedagogy lesson involving making posters to define proportion, y intercept, x intercept, linear relationship and slope and we did a gallery walk for these posters.
Here is a funny video Bernadette shared about slope:
Homework: Read “Never Say Anything a Kid Can Say.” Record any question, “yea, buts” or comments in your journal.