I want to keep track of how I am learning from my speed demons and katamari in Algebra 1.
I want to be clear about two things. Not all speed demons are alike. And also not all katamari are alike.
Slowly I am finding my way to the most discouraged and shut-down learners. I group and regroup, based on formal and informal assessments. Also based on intuition. The great thing about using PBL and the adapted Exeter problem sets is that together they are giving me a lot better information and opportunities to identify, target, and support my students. Most of what we do in class is problem-solving in groups — interpreting, reasoning, and making sense using group whiteboards and whatever other tools we need.
I notice the need to provide much more intensive support to most discouraged katamari than I had expected. These are the most shut-down of my learners. These are the students who are being quiet to avoid being noticed. In math class, they live in a defensive psychological crouch. I know this posture well. But the only way I can understand it is to join the process and probe. I ask questions: when you are AT such and such, how far away are you?
I am really shocked at how shut down and disassociated these students are from their intuition and their natural intelligence. I wonder how long they have been cultivating this posture of hiding.
I draw a crude map on my paper and point to different positions. When you're here *pointing to the diagram*, are you further or closer to X? *moves pencil closer to destination* What about now? what about now?
By probing, I discovered something amazing — three tables of students didn't really understand what it meant to be AT the destination.
I tried different tactics until finally I asked, when you're IN your kitchen at home, how far away are you from your refrigerator? How many miles away are you? It took a while to convince them that they actually knew they were ZERO miles away.
Once they figured out what the meaning of being AT someplace or crossing the destination was/is, they could begin to build a table. One step after the other. Let's work backwards -- when you're one hour away, how many miles away are you?
This is a lack of basic trust in their own innate natural functioning. A lack of trust in their own intelligence and problem-solving skill. It takes skill to get this going. They have to be prompted/encouraged to start from where they're at — not to hide the fact that they are lost.
These students are good hiders. They know how to hide in plain sight. They are skilled spies. They know how to evade detection. I am more tenacious than most. I do not accept evasion. I probe, I question, I support, and if need be, I help. I help because they are too shut down emotionally to take the risk of humiliation. They are exhausted from not-knowing and from hiding their not-knowing. But not-knowing is the start of knowing. You can't begin to know until you know that you do NOT know.
Not-knowing is an empty space in which knowing can arise.
Katamari don't realize this yet, but they are closer to finding out. Speed demons have no clue about it yet, and they are so far away from discovering it there's not even any point in raising the issue yet. Katamari are so much closer to the truth. I don't mention any of this to any of them. I just keep probing and asking questions and asking what if and how much and how do you know.
At the end of class, one of my speed demons told me she would really like to collaborate (unlike the other speed demons at her table, who are just zooming along and only occasionally conversing). She asked if she could move to Table X, where some very discouraged Ss are. These are the students I was probing the most with. I was thrilled. She was eavesdropping on us when I was working with them. These are the questions she herself likes to ask and think about.
I don't have any conclusions to offer, just these noticings and wonderings.
We are still in the early community-building days, when discovery is young.