This week, the Calculus students were working on multiple choice questions, so most of their work involved some sort of special shortcut, as they won't get nearly as much time per question on the MC section of the AP Test. If there wasn't a good shortcut, I would work through deciding how to attack a question and figuring out what strategy is best for each situation. On Thursday, Mr. Gmerek simply went over the toughest questions in front of the class, so I spent the second period in Mrs. Horne's room. The Algebra II students are working on memorizing the Unit Circle, which is of course a very important part of higher-level math. Unit Circle measures are like the times-tables of high school/college mathematics. For the most part, I was verifying correct answers with students and (if they struggled) going over the process of measuring the distances with trigonometry. There was a lot of talk of the different mnemonics that the students use, which was interesting. What I love about Mrs. Horne's method of introduction to Unit Circle is that she doesn't just introduce radians as a unit for rotation; she actually explains where "radian" comes from visually with picpecleaners around a circle. Each pipecleaner is the length of the radius, and just over 6 and a quarter of them make it around the circle. There are 6.28 radians in a full circles, so this really helps demonstrate the complex concept to students in a very simple way. The poster is a permanent fixture in the front of her classroom.
It was great to be back in the classroom again after so much time away! The Calculus students are reviewing for their AP test in May, so I was just jumping around the room, working with them on recent and old topics to help them remember what they'd forgotten. A big part of this process is teaching them how the AP test is set up, so I also gave a lot of advice for how to approach problems when they truly don't understand what it's actually asking or they only know how to do part of a Free Response. I can see the content coming back to the students, and I hope to see some slow and steady process over the next few weeks!
I've been out with the flu since just after the conference, so I'll just talk about EdRising. My group's "Ethical Dilemma" presentation went better than I expected, and the guest speaker on Thursday, Harvey Alston, was phenomenal. His main idea was that people have to have high expectations in order to have high results, and he believes that positivity is the key to success. Through several short demonstrations that involved the audience, he showed us how a speaker we hardly know can change our expectations for ourselves through just a simple change in vocabulary. Relating this to teaching, I think it really shows the impact a teacher has on their students' morale and ability to self-motivate. As a teacher, I will have to communicate high expectations and also positively cheer on my students throughout the year, which is actually an idea my group used in our presentation too.
Friday was great too; I always enjoy a chance to hear Nick Jackson and Danny Ciamarra speak. Not only did I go to one of their breakout sessions, but I also got to hear them give the closing speech for the conference. Nick and Danny talked even more about the teacher-student relationship and how it is the key to everything. Their discussion really delved in to the topics of student home-life and how teachers can step in to make students feel valued. As a teacher, I will always need to be patient and understanding of my students, even when their actions are seemingly destructive and senseless, because there is always a reason, and there is always a way to show that student that somebody cares about them. I took a lot away from this conference, and I intend to implement these beliefs in everything I do throughout my future career.
Reflect on the activities for GKC at Avery. What was your favorite part of the week? What was your challenge? What needs to improve? Comment on at least one person's post.
I feel that this week went so much better than last time... The teachers last time at JW Reason Elementary were very positive and loved GKC, but I think the atmosphere of Kindness Week was only generated when we were in the room. This time, Avery Elementary was all about Kindness Week. The students actually performed the activities on their Kindness Checklists at home and on the playground, and were excited about each day's lesson. My favorite thing about it all was having the same class each day, so that I built a bond with the students. I was able to actually talk to the students about their out-of-school activities and carry conversations across multiple days to build a great relationship. Because of this, the students responded more positively to me this time. My main challenge was figuring out how to put an abstract (but basic) concept in to words that a 6 year old could understand. I think I handled it okay, but it helped to have Emily and Cassie in the room, because they're very good at speaking to elementary students. Overall, if we did it again I would probably just have some prepared phrases that I could always fall back on to use as mottos. At JW, I constantly asked the students, "when's the best time to be kind?" to which they always shouted "Every time!" or "Always!" If I had done that this week, it might have helped to drill the concepts in better. In the end, it was a good week; definitely better than last round at JW. The students at Avery really embraced the ideas and were more creative, showing that this really mattered to them. Two of my second graders started a Kindness Club at recess, where "the only rule is that you have to be kind." Nowhere in this world will you find that kind of purity but an elementary classroom.
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!
It was nice to get back in to things after two weeks off! I spent 3 days observing this week, 3 periods each, so I think I really got in to a sort of groove. The topic was the same all three days; it's just complex application of a couple concepts (related rates and implicit differentiation) the students learned before Winter Break. The students are seeing just how many ways the tricks can be used to solve different problems, and the reason I love this topic is because it actually has a ton of real-world applications in everyday life, not just for obscure calculations. Each period responded to the work differently, but each day the students became more and more comfortable with the subject. I spent a lot of time drawing pictures and actually backpedaling to Geometry to explain old formulas the students needed to start their work. I think it's important to really make sure students understand the old stuff before they jump in to the bigger concepts, or else they'll forget something small later on. Most details just aren't significant when a student uses rote memorization, so I made sure the students understood where their volume, distance and surface area formulas were coming from, as well as connected the formulas from various shapes to strengthen their understanding with some general guidelines. Overall, they were very receptive and I think the students learned a lot this week. I know I did.
This week, the Calculus students were continuing their work on optimization, now looking at the many different scenarios in which it is applicable. Basically, the students tend to struggle with turning the word problems in to the two equations they need to start the whole process. I spent a lot of time drawing pictures and walking through the basic logic of the situations; stuff that is more geometry and arithmetic than Calculus. I enjoyed going over the concepts with students, even had a lengthy discussion with a student about which method to use when deriving fractions and when. It's always interesting to get a closer look at how students think... Overall, a good week of observations.
Optimization was the topic when I observed this week, which is basically about finding the x value that makes the maximum or minimum y value given two equations with one other variable. This makes for 3 total variables with two equations, and since the students know they need 3 equations to do substitution for 3 variables, they're all lost when they start. The key is explaining to them that they can use calculus to eliminate the variable being optimized, and then they can treat most of the work like basic algebraic substitution.
It's interesting to see how the students will create a mental block when something looks extremely complex, and start asking questions about things they learned a month ago. They tend to let a lot of variables overwhelm them, so I have to be patient and make sure to re-explain older concepts when they get confused. However, it's actually pretty entertaining sometimes when I ask a student "...and what does y equal?" and they can't answer me, even though in the typed question itself it is stated that "y=3". Once again, I'm just seeing some of the struggles that math teachers frequently experience. It's good practice, and I'm still enjoying it each week.