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.

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.