1. Start with an equation and write an equivalent equation.
2. Fold back the original question so it cannot be seen. Rotate the new equation. 3. Repeat 2x 4. The fourth (last) person needs to unfold the sheet and check if the last equation is actually equivalent to the original.
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I'm still working on this but here's what I have so far. Each student assesses their group (for a group project- but possibly for just working together.) Then I typed their assessments (with some review of if everything was appropriate). Then I will share their peer assessments with them so that they can improve. Still thinking about how to frame this. Next time I think I'll do the group assessment through a google form to simplify process.
I had just spent 30 minutes on an activity today touting the joys and benefits of working in groups and responding to each other think. So I set them on their book work in groups, hoping for the best.
Within 15 minutes, a student - Jori- says to me, "He's not helping me and I find him very rude! I can't work like this." I walked over to Jori's table and see she is pointing at Don, a generally mild mannered student. Jori: He's being rude! I can't stand when people are mean for no reason. Me: Let me hear your perspective. What happened in your eyes? Jori: I asked him for help on a problem and he wouldn't help me. He said, "I'm not going to give you the answer" and looked away. Me: Okay, I hear your perspective. I'd also like to hear Don's- it might not be the same. Don: I thought she was just asking for the answer. I would help her understand but not just give an answer. Me: Sounds like we have a miscom-- Jori: That's not what I was saying! I wasn't even asking for the answer! I just wanted help understanding it. Me: okay, so I hear you- Do you see Don's perspective? Jori: I wasn't asking for the answer! (Jori appears she will cry at any moment now) Me: Don, do you understand that Jori was not asking for just an answer. Don: (disgruntled) I'm sorry that I hurt your feelings. I didn't mean to sound like that. Me: It looks like Jori has a great contribution to the group by asking a question, and Don, it looks like you might have some progress. Let's talk this out. I watched them ask and explain the question before I walked away. I checked in with them 10 minutes later and they were conversing through the problem set as if nothing had happened. This is my SECOND piece of evidence (in my book) that has shown me that conflict resolution has better effects that splitting groups that don't work well together initially. *Names changed I had the wonderful opportunity to think during winter break, think hard about what I wanted to do in the classroom differently. I've recently been meeting more regularly with a mentor (the resident principal at my school) who has given me a lot of helpful and thoughtful ideas for change. I also chatted with Kyle, a dear friend from my masters program, who gave me insight into his own classroom. With these people in my life combined, I made some interesting changes after winter break. 1. No paper. (kind of). Kyle told me he didn't give out worksheets. Instead he has kids continually working on white boards. So I tried it. I put up three questions to help students find distance between two points and a 30 minute timer. I never gave them the distance formula and instead asked them to apply the Pythagorean theorem. Students were generally engaged, able to show their work better to peers, and I was able to evaluate their work easier. I was able to pinpoint misconceptions quickly and some common errors. Afterward, I had students present the problems to the rest of the class. 2. BEFORE I just handed students boards and markers, I wrote on the board two sections: Questions I will answer & Questions I WONT answer. (This idea came through my mentor who came from another teacher Bill who may have gotten it somewhere else but that's as far as my trail leads). Questions I'll answer Questions I won't answer Does our reasoning make sense? Is this right? Here's what we've got so far, but we're not Where do I start? sure where to go next I don't understand why this is the answer I don't get it. Then we had a short (3 min) discussion about why I wouldn't answer the questions on the right. This helped them understand where I was coming from and gave them some rationale. Providing prompts also gave them tools to ask better questions and to see the kinds of thinking I valued. 3. Take-Aways. This was another suggestion by my mentor. I usually end class by letting the time run out. Oh okay! well, see you next time. This hasn't really been the best way to end class. Instead, at the last 10 minutes, we took out our notebooks and we wrote down the two main takeaways (about distance between two points and finding a midpoint). I was listening for students who had figured these out during class and asked them to share them at the end of class. I would write word for word what the student said. Afterward I would circle portions or add blanks to show that our takeaway wasn't complete. I asked students from the class to make our sentence more specific or more complete. Then I had them make a small drawing next to it that represented the sentence. It was a quick way for me to check student understanding (at least conceptually). A lot to learn, but it was... really an enjoyable class experience for me. Different ways students found the distance between two points. On the bottom right is an example of a common misconceptions students have. They see two points and automatically think they should plug it into the slope formula. On the top left, students use -18 and then square it (but keep it negative). This is a common mistake that they make.
"I had seven students in my group. Were there 6 in yours?" This Friday, this quote came out of the lips of NOT a teacher but a student in my class. He was one of my assigned group leaders for a differentiated activity that we were doing in class. He was asking this to another group leader in my class and both of them saw their groups as their own students.
I've never been more proud. I know that in a lot of classes, the struggling students get the majority of attention by the teacher while excelling students sit quietly working on their problems until they're done. Neither group really feels a part of any kind of classroom community. just bodies in a room. Unless... they're talking to each other. Having students continually work together and push each other to help each other has been helpful on days when I simply can't be 6 places at once. And I don't need to be! Sometimes, I had groups of 7 students in one group (usually a logistical and management nightmare) working very hard for most of the period because they had a group leader to guide them through their work. They felt like they could help each other and get help if they needed to. It helped that the task was differentiated to their needs and that they were able to choose which assignment best fit where they were. It helped that students were used to working together and listening to each other. As much as possible, I take a step away from the groups so that they don't even notice me. It's so they recognize their own expertise and forces conversation with each other. So, how do I assess progress on individual students if I'm mostly steering away from groups? Toward the end, I call each group leader one by one outside in the hallway and ask for a (literally) 1 minute assessment of where each of their members are. I get qualitative info like which students are working really hard, which ones are just copying. I also get info like which ones are struggling and which ones are doing well. They are also specific about the types of problems they have difficulty with. This is probably better data than I could have gathered myself. This is only one day, but I'm going to need to continue thinking about how to keep this kind of rigor and intensity in my class more often One of my colleagues showed me a worksheet with a very simple idea and profound effects: "lifelines"... basically agreeing to provide up to two hints when they are struggling most. For me, these lifelines are represented as smiley faces. See below. I'm going to give students a group challenge (a math task that students will struggle with but are within their capabilities). I usually provide hints (thanks to Complex Instruction Consortium's ideas) but this time, I decided to go with lifelines. My colleague told me that students are suddenly very protective of their lifelines. I believe it. I'm hoping this works. Will update once the activity is complete. UPDATE: I tried this in my most challenging class. WOW what a change! First the group challenge was more appropriate to their level but they really did NOT want hints to be taken away. Students were suddenly talking to each other, helping each other, checking answers. They hated the idea of me marking up one of their smileys. Small change, genius results.
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