Day 2, Reflection, and Plan for Day 3

What I did for my second day with kiddos:

1. Started with the problem 1/2 + 1/3 (3 minutes of individual time) - I reminded them that making mistakes is ok, but not trying absolutely is not.
2. 3 minutes to partner share (during both independent and sharing I walked around and jotted down all the answers I saw)
3. I wrote all the answers on the board, then called the whole class's attention back to the front. I told them that I was noticing a number of different answers, and asked them what they thought about that. 
4. A few students basically made comments that they were unsure about their own answers and thought maybe there were mistakes. I happened to overhear one really great conversation during the partner sharing where one girl told her partner that she got 2/5 but that didn't make sense because that was too small - she mentioned cooking and how the cups work. I asked her to share her insight. The class agreed, so I asked if we could use this same logic to eliminate any other answers definitively. We were able to narrow it down some more :) - Someone also noticed that one of the answers was way too big (by similar logic), so we decided that couldn't be it either. 
5. A student asked to defend the answer 5/6 (this happened in every class - someone was just DYING to say how to do it! LOL). I had the student explain step by step, pausing and asking for clarification, asking for agreement, and calling on other students to restate reasoning. This took a long time, but there were some really nice moments where students started to realize how fractions work. Even my higher kids who totally knew exactly what to do in the procedure struggled to explain clearly why we need a common denominator and why we don't add denominators (the answer EVERY single one of them gave me the first time was basically, "because your answer isn't right that way"). 
6. I had prepared two more problems: 3/4 + 1/2 and 1 1/3 - 5/6. One of my classes wanted to do the "harder" problem, so they jumped right over the middle problem. They had done well in the explanations, and the idea of least common denominator had already come up through the conversation. The other classes did the middle problem. There was not enough time to finish a third problem today. 
7. Again, I had the students write what they learned today. I also told them that they could instead tell me what the most significant/helpful thing we did today was for them personally. 

Reflection:

     Many students said that this discussion was helpful for them, and my higher kids were some of the ones who said that they enjoyed the discussion (so they aren't bored out of their minds by talking about something that they basically already understand themselves). I have decided that it might be better to actually have them just discuss "How do you add and subtract fractions?" and come to consensus around that, and if they don't hit all of my key points that I think are the most important, I could just disagree and pose a problem that their "solution" doesn't fully address. This is my plan for my next class session on Monday (even though we have already talked about it).

First Day of School

Well... I've decided that my focus for the year will be to "Teach Through Structured Problem Solving." I want to focus on how I structure and facilitate discussion specifically, and I've been thinking about how to best document both my plan for my lessons, as well as my reflections on them.

Although I am sort of nervous about having my completely new-to-me and unpolished ideas available for any old person to see, I figure there aren't too many people looking anyway, and this is the easiest way for me to keep track without creating some new way of organizing things for myself. Besides... my lackluster attempts at keeping a blog going otherwise have obviously been unsuccessful to this point :)

So anyway - Today was the first day of school with students. I decided to intro the whole focus on discussion by focusing on the question, "Why are students required to learn math in school?"

Some background: I teach 8th Grade Math in little K-8 country school in the Central Valley of California. I get 80 minutes with my students, but we only have 4 days per week. Oh... and it was crazy today because there were no schedules/rosters yet... but that's another story!

ANYwhoo... Here's what I did:

1. Students set up paper with name, date, topic, and wrote the question
2. 3 minutes of independent time to write their thoughts and opinions (I walked around and read answers)
3. 3 minutes of partner share time to discuss ideas
4. Introduce discussion rules:
1. One Discussion (meaning no side conversations)
2. One Facilitator (I told them that students can be facilitators too, but during that time, I can't also be in that role)
3. One-hundred percent consensus (whatever our "solution" was, we had to all agree with that completely - INCLUDING me)
5. Asked a student to start conversation (one I had chosen because their answer was a "good starting point" - honestly, today I purposely chose kids who I know don't get a lot of "air time" speaking because they wouldn't normally volunteer)
6. Asked questions, "What do you think? Do you agree? Do you have something to change/add?" Basically on repeat
7. We kept track of the discussion on the whiteboard
8. All classes came up with something along the lines of "Math is in practically everything and it helps you in your future both in life and for your job" 
9. I told them that I agree so far, but I disagree that it's complete. I asked them to guess what I might think they should add.
10. It was REALLY funny that two different classes said that I want them to learn math because if it wasn't required in school I'd be out of a job! LOL. I told them that I wasn't that selfish - my reason was for their benefit more than mine! But it still cracked me up. 
11. My reason - It teaches thinking. Thinking that is different than what you are required to do in most other subjects, but that is necessary for really being successful in life, especially when presented with new problems. Basically - the application part of the "you use it in real life." 
12. They agreed - yay consensus!
13. Then I asked them if they wanted to have to write down all of the different points from the board (we bullet pointed ideas as we went and checked to see if everyone agreed - most classes had 4-6 sentences of bullet points). They said they would rather not, so I asked them if they could be more concise. 
14. Partner talk about how we could take all our main ideas and write it in only ONE sentence. 
15. Share out - then lots of editing until we reached consensus. 
16. Most classes came up with something along the lines of, "Math teaches us important ways of thinking that help us solve problems in our every day lives and builds a foundation for all the things to come in our future" 
17. I talked about WHY I am making them do all this discussion instead of just telling them what to do:
1. I want them to THINK
2. I want them to be able to COMMUNICATE their thinking so others can understand them
18. I had them answer the following "Connection" questions:
1. What do you hope to do/learn this year in math?
2. What did you learn today?

Reflection:

• Overall, lots of good discussion. My homeroom class is 20 students, but 5 of them are on IEPs with math goals that are not in the range of my standards. So far, all of them participated and were able to do ok... We'll see how that goes when we get into DOING math instead of just talking, but one of them was SO CUTE! He seriously wrote so much (and I just found out he really struggles with reading at all) and at the bottom where I asked what did you learn today, he wrote down almost all of my messages about making mistakes being ok, that trying is the most important, that everyone can learn, and he had little smiley faces all over with exclamation points. I was planning on giving papers back tomorrow to add to their notebooks, but I kinda want to keep that one because it just makes me smile! :)
• Students were really unsure about taking over as facilitator. I basically stayed in that role, but I'd like to find ways to get students more comfortable so they can take over for me sometimes! I'm sure part of it is just me not really knowing how to get out of their way, too, though. 
• Timing was actually really good! I was able to do all my administrative junk (even with the schedule fiasco), and still finish the discussion with time for students do finish their reflection portion at the end. If I don't have admin junk next year on the same day, I should consider adding something else in because this activity alone will NOT fill 80 minutes (maybe 50 minutes or so?)
• I need to get better about keeping track of who speaks, so I can make sure to ask for opinions specifically from those who don't tend to volunteer as much. I need to think about some structure that will help me do this without making my life more complicated... maybe initials on the board next to what each one says? Worried that might take up too much "real estate" on the board though...
• I like it so far. I'm feeling excited about the possibilities, but nervous about everything I'm doing being so new to me. I guess that makes me human! :)