With the snow day on Tuesday and a Talent Show on Thursday, I only spent a couple periods on observations. First, I just observed Mr. Gmerek introduce a new concept to his students and go over the latest test. The next period was review for an upcoming test in Mrs. Horne's room. I was just walking around the room, helping the students with their logarithms. I enjoyed it, though it was a struggle at first for me to remember graphing logarithms. The students benefited from my presence, and it was interesting to think on my feet again. Nothing major overall for the week.
I had originally thought that this week would be application of derivatives to geometric polygons and solids, but I had forgotten they actually completed that unit back in December, which I even wrote about at the time. Instead, this week was the introduction of u-substitution, which is essentially a method used to simplify complex integrals. Students really struggle with this, because integrals are basically the inverse of the derivative concept they've been learning all year, and applying substitution (an algebraic concept that students are hesitant to use) to something they are shaky with can be overwhelming. Because of this, the classes spent the entire four-day week on just one section of the chapter, to make sure they are standing on solid ground before they continue in to advanced u-substitution. There was definitely significant improvement; On Monday some of them didn't even understand why we use u-substitution, but by Thursday most of them were simply pointing out to me that their work was right and the textbook answer key had to be wrong. Which it was... this led to an interesting dilemma. In past years, Mr. Gmerek had students scratch out the wrong answers in the book for this unit and replace them with the proper solutions. However, online copies can't be updated like that, and this year more than ever his students are using their phones, tablets, laptops, etc. to access the book questions and keys. Therefore, those who didn't have their physical textbook with them were at a disadvantage. I found this to be a good example of how the evolution of the modern classroom isn't always smooth. It was a quick fix, Mr. Gmerek simply wrote up the question numbers of "wrong solutions" on the board and told the students to check a physical copy of the book for those. Still, it was a major problem during the first couple periods until he realized what was happening. Students were completing and recompleting questions, trying over and over to get the "right" answer that they saw online, but all along they were actually doing just fine. In the end, I think it was a good way for them to get more practice and get used to the method, but I don't think the students necessarily agree with that sentiment... They were a bit frazzled.
I have a friend who is coming back from a weeklong vacation tomorrow, so he was hoping I could catch him up in Calculus this weekend. We'll see how well I can explain the material with no teacher to fall back on; should be a good experience.
It was nice to be back to high school observations after three weeks off. Kindness Week at the elementary went well, but I still know I'd rather be in a high school classroom. This week was a bit rough, because the Calculus students started a new unit right after I left, and they were reviewing for their final test this week. I knew the material, but since I was a bit fuzzy on it I had to really think on my feet as I was going through the concepts with students. On the whole, however, it went well and I definitely know they benefited from my intervention. More and more, I grow to enjoy sketching pictures on the board and explaining the most minute concepts so that the students not only know how to use theorems, but they know WHY they work in each situation. My biggest struggle is convincing the students to write out all their work, draw pictures, don't skip steps, etc. They often just work too fast or give up too soon, so I've been working at trying to get students to take the time so they can get it right the first time. The ones who have responded to my feedback do seem to be improving in their ability to learn on their own.
Additionally, a large portion of the students' review was AP packets, filled with questions from the tests of previous years that have been released. This prepares the students for the complex applications of their knowledge for the actual AP Test. This is another case where Mr. Gmerek and I try to get the students to explain their thoughts and understanding, because we know how they should work in order to get a 5 on the AP Test. They're progressing well and adapting to the AP style, so I think they'll be fine, but I definitely want to push them to "just write more, it won't hurt". They'll begin a new unit next week, which will be the culmination of everything they've learned this year. There will be a lot of struggles with students picturing the concepts as we move in to applying calculus to volumes and surface areas of shapes. I'm excited to see how it goes!