Over the past week or two, I have reflected on why I blog and what it does for me after I saw a bunch of tweets from Chris Robinson (@absvalteaching) and Kate Nowak (@k8nowak). This leads into my response to Kate’s request to MTBoS…
Protractors are no fun for the students. The lesson SAS – Drawing triangles was great for the students to discover and learn the material. I do believe that learning protractors will pay dividends in the long run. Important to note that students take a long time measuring and labeling triangles. It is a complete investment in time.
So we finished the proof today and I learned that my mechanics in doing proofs from 1985 was a bit rusty and I have to rebuild them up again. I expect my skills to be able to find the solution for each and every math problem on the fly. This is not the case; and today proved it. I did quickly transition to another activity “Angles, Angles, Angles” from the upcoming edition of Meaningful Math – Geometry. This was a great transition from the proof to other applications of angles. Students did struggle at first, but then were successful in doing the activity. The only challenge was creating an entry point for students who were not building the bridge between Algebra and Geometry. As I plan going forward, I look forward to mixing proofs, Algebra applications and hands on discovery to give the variety that students need to be successful.
Today, I spent time allowing all of the students use the protractor and try to discover the parallel proof for the angle sum property. None of the students arrived at the proof, and all of them tried. I am not sure if I took the best approach on this. I believe there is some scaffolding to get the students to arrive at line of logic for a proof. I will be continuing the proof on Tuesday with a scaffold of all students trying to find the congruent angles and review the definitions to get to a place where they can possibly see a path to a solution. I am reluctant to hand the proof to them, but will probably scaffold to the position. I do like the productive struggle.
Going into Geometry, I knew there were a bunch of manipulatives necessary, but did not realize the extent. Since I feel like I have to supply most of them, this has been a challenge. I do remember the challenges of using a protractor during the old Math A days. However, students did not have to be proficient in using it. Now, they need to know it to get through all of the different types of proofs and postulates of triangles. I think they will realize it is a necessity to gain the skill to prevent being annoyed with themselves. At least, I hope that is the case. If I remember, I will comment on this later.
Once the students tooled around bit with the protractor measuring angles of a triangle, we set out to prove the angle sum property. This is the first proof that we are doing as a class and all of them are struggling. I had all of them be quiet for 10 minutes studying the materials and then had a bunch of discussions at the table and as a class to get them further. Tomorrow will be a continuation of the journey into the proof.
So I had the chance to roll out the different versions of the proof in the honors class. It went seamlessly. Students finished the class trying to construct their own proof with moderate success. In my other class, they were trying to relearn how to use a protractor. One period was not enough, I will continue with the lesson and finish in the next day with a proof about the interior angles of a triangle. I have to remember to build in time for a pair share in some of the discussions. Many of the protocols are falling apart because I am not reinforcing them. It is time to get back to basics.
So I decided to talk with the students about proof. Students are definitely challenged by the concept and this is going to be a long road. To ease the road, I decided to introduce the two column version and flowchart version of the vertical angles proof. I think that this is the beginning of paving of a long road. The lesson ran a bit long and I decided to spend time on making sure the explanation was sound and did not spend time on a solid formative assessment. I look forward to building on the concept.
I walked into school and learned that I will have to leave early and my last period class was cancelled. In my regular geometry class, I spent the better part of the period trying to teach the nuances of proof. It is now abundantly clear to me that this topic will take a lot of time to learn. I also think my model of the vertical angles theorem will have to be revisited. (I do not think that supplementary angles can be stated as a given. This causes some confusion in the class.)
After the second round of trying, students are finally getting the fact that I mean I will grade by my rubric when they hand in the Problem of the Month. I have done projects for 4 years and this is the first time I am getting student responses that solid. They are trying hard and getting better and better grades.
I believe my due date policy is the difference. Each problem of the month is due on the last day of the month. If a student turns in the project by that day, I will grade in pencil and give them one week to make corrections. I will accept projects up to a week late, but the grade will be in pen and no edits will be allowed.
Out of all of the challenges that I have this year, I am thrilled by my little successes 🙂