Comments+on+First+Lesson

Bill's additions: What design changes in lesson can help with the flow? What can be done to make ind./ded more explict? What roles does the hook serve in the objectives? Think, pair, share?? Tool for elicit information This is inductive reasoning - we have not tested all polygon. If you had to bet a leg on it beyond shadows of a doubt?? S: in a circle 360 degree T: drawing of a circle with 360 degrees. Le: what do we know aout RP that might ??? sum of the int angles of a regular polygon =(n-2)180 How can we use the info to prove?? Qyestion needs to stop Why not more?? Wait time

Stacy's Comments: Kim's Comments Amelia's Comments Gema's Comments > Stacy: In the classroom, will it be too much time for a student who has never proven something before? It might have been too much for this group but possible not for somebody who has never seen this before > Gema: The goal was to spend time on ind/ded not the proof. I think you would need more time in the class for the proof. Ana's Comments: Add visuals with the words/telling 'add to the questioning.' Tasksheet add comma between "plane, vertex to vertex" Bill's Comments: Tracy: Adam's Comments: Marti's Comments: Gail's Comments; > - more teacher talk, the role of proof in deductive reasoning, colored comments. Suzanna: Ana - write out the goal of the lesson.
 * 1) Should have told the observers to pretend they were students.
 * 2) Between steps 7 and 8, the teacher should interact individually with the group and discuss with them individually.
 * 3) Transitions: uncomfortable using them since it was not discussed with the group
 * 4) We got to hammer out a proof, one or two as a group that we are comfortable with and that have strong conclusions. Something that we can use with the class.
 * 5) Hard to pull info out on the 4b. Induction vs. deduction part.
 * 6) Our proof really depends on the initial conditions.
 * 1) 15 minutes on exploration, 40 minutes on discussion. Students were answering to prompts but not really doing anything. High school students are not going to be able to sit through 40 minutes.
 * 2) Need more discussion they can explore themselves then listening to a teacher prompt.
 * 3) Individual think time was not clear. It should be an explicit think time. Whoever teaches needs to make sure they are very explicit about this aspect.
 * 1) Some of the calculations are large and a waste of time, need them in the classroom.
 * 2) Having some more examples of tiling's to show to them would be useful.
 * 3) Need to build in more opportunities for student engagement.
 * 4) Do we need to build in the term axiom???
 * 5) After they explore we should have them write down their thinking/exploring process and then ask them to do this based off the proof.
 * 1) Spent too much time on proof.-
 * 1) Need to have students more engaged. Can we give students large papers and demonstrate these tilings on the poster.
 * 2) Comma between plane and vertex on the task sheet.
 * 3) Lots of students were bored and drawing things, not paying attention.
 * 1) Stacy was in a position of improvising during the lesson. How can we become more explicit in our questioning?
 * 2) Student contributions in the hook were deductive and inductive reasoning. For example the divisibility by 60. Our lesson can improve by finding some way to record and utilize the mathematical thinking of students. We need to give students a way to separate the deductive vs. inductive components of the lesson.
 * 3) There was no specific mechanisms to monitor or collect student thinking during this part. It put Stacey in a position of improvising.
 * 4) Need a way to make the objectives more explicit.
 * 1) We need to get a way to have students talk more about the inductive thinking process then they did. One implementation is to write things down before the proof.
 * 2) In a room full of geometry students it will be a different ball game. IT may be possible we have one very very strong student is possible but not likely. The teacher needs to feed information to the students. Need to get to that definition.
 * 3) Bill: Need to get the observations on paper up as a tool. She did a lot of improvising.
 * 4) Stacey: comment, did not do step 4a. It is in the lesson plan and might address Bill's comment.
 * 5) To have thoughts percloate up we need to do a) more TPS b) ana's poster idea
 * 1) Do not need a complete proof. Do a low level version of a deductive proof that is more satisfactory
 * 2) Have worksheets that have other tasks to do (since they want to prove) - tasks and questions
 * 3) Evan wanted to play more, did not have time to make observations.
 * 4) Need a summary activity after the observation phase (Lalit Thought: Can we let the kids pick a proof)
 * 1) Do not need a whole proof, can use a piece of a proof. We can use the heptagon or pentagon non-proofs. An inductive vs. deductive argument.
 * 2) Individual think time: If I don't group kids first then they will work individually and you can group them later. Gives each person a chance to get thoughts together.
 * 3) Direct impact: Katie and Sarah, Katie started doing a proof and Sarah stopped her and told her to see if they fit first.
 * 4) Direct Impact: The last phase was the main part drawn attention to during inductive/deductive part.
 * 5) Adam: A lot of people were not really responding because they got confused. (Lalit: I think they were confused about what the proof was)
 * 6) Wording in reflection piece - needs more scripting
 * 1) The value of listening and seeing students work. Marti and Lalit.
 * 2) Look at the board: She did an admirable job of jumping around the board, well organized. One board for conjecture, one for tiling. Not in the lesson plan!!
 * 3) How does that play into the conversation???
 * 4) Tension about whether we want to go to proof!!! Maybe we do not want to do this? The proof does not need to be obvious. "Verify your conjecture"
 * 5) Key questions need to be identified. A set of key questions. How do you know when you were done?(Stacy: When you come to an undisputable conclusion).
 * 6) Need to identify the place for transitions.
 * 7) Automatically roll out of the formula. Once the formula was on the board everybody was very happy. It could become a crucial piece of the lesson they might not know.
 * 8) Can use some more pictures of tilings to set the stage.
 * 9) Tension pts- maybe proof not quite as obvious
 * 1) Acting as a outside observor.
 * 2) Letting students know the lesson is not about polygons, was that decided?
 * 3) Did you think about a plan to bring out some student solutions first? How many students saw the angles off the bat the first time? The two extremes were the oriental lady and the kid. It was not clear how many of the other students knew what she did.
 * 4) Is there a plan for monitoring/utilizing the information at the table??
 * 5) The five sided figure was something that came up from the teacher. Was it planned? Time frame doesn’t mesh.
 * 6) Not enough responses, because kids didn’t have enough time? Would the time you decided already decided as a group? Was it decided about the teacher as she went along? The chart paper was too small. Couldn't see. Can be written on a different paper and glued to the wall (?)