The students in Calculus were learning how to relate values of functions to their derivatives, and the derivativesof their derivatives (acceleration), so it was a really rough week for some of them. These concepts are mostly based in one's ability to visualize graphs and interpret data in their head, and calls for complete mastery of previous derivative information. The students can get easily confused by the difference between a decreasing slope and anegative slope. As it's also easy to mix things up as the person explaining the material, I have to be very careful with my wording, and do my best to help paint the picture the students need. It's almost impossible to explain complex calculus without drawing the graphs themselves (though technically this is simple in comparison to what they will do later), so I've been doing a lot of board work and arm waving. Though it's difficult sometimes to really get the right point across, it's extremely satisfying when the students truly understand because it's more obvious in these cases that the visuals were the key. This was yet another good week for practicing explaining complex concepts to students in unambiguous ways, and it's helping me expand my repertoire of strategies for getting the student to finish my thought for me. That's often the best way to know they got it.
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I just spent the two days before Thanksgiving break working with Mr. Gmerek's class on a concept called Mean Value Theorem. It's a fairly complex rule, and being able to understand it involves using just about every other concept the students have used that year. I enjoyed just walking through the various problems with the students, showing them the ways that everything ties together. It's good to still see the light turn on in people's minds. Overall, it was a successful week, though I know they'll have forgotten most of it over the break. Will be interesting to see how quickly they bounce back.
This week, I helped the students in Gmerek's room on Monday to review for their test on Tuesday, then I spent Tuesday observing in Mr. Limbird's AP Physics room. I take doubleblock Physics, so we're about a month ahead of the rest of his AP students. It was interesting to see such a large class (30 students) who all learn differently... some students were helping each other, others relied solely on their notes, and others asked Mr. Limbird and I for help. It was another reminder of how important it is to fully understand all aspects of a subject when trying to teach it, because my little experience with it was barely enough for me to explain complex problems to them. Overall, it went well, but I definitely wasn't as helpful in Limbird's room as I am in Gmerek's.
Thursday was just simply working with Gmerek's and Horne's students on new concepts, which they seemed to understand pretty well. Working with Horne's kids on their Algebra 1 skills was key, as they are learning to classify functions but forgetting their terminology and exponent rules. I'm continuing to see how all the courses lead in to each other as I compare Algebra II to Calculus AB and BC. Very insightful. I also went to a Parent conference for HCSD on Tuesday night with Mr. Wise, director of the ILC, to discuss emerging technology and apps with parents. There was a representative from each school, as well as Doug Maggied from the Board of Education and our Superintendent, John Marschhausen. It was a great chance to see some of the behindthescenes debates that occur to inform the district of issues, and hear how the administration makes their decisions. When it was our turn to speak, most of the people in the room seemed annoyed that we were discussing social media at a school conference, and there was only one question from the audience. However, after we answered that question, there were suddenly two more, and then more, and we ended up discussing social media for over an hour. I really like how the parents' attitudes visibly changed from contempt for the ILC to respect as they realized what it does and how it's leading the future of education. It was a great lesson for all of us to open our minds and learn to change. This week, Gmerek's students have been working on combining all the rules they've learned this year to synthesize complex derivatives. For the most part, I've been individually explaining the ins and outs to them, as well as going over commonly overlooked trivialities. I'm pretty sure that the students are making great progress, but I definitely had trouble this week as they began to head in to methods and rules I hadn't used in a while. My memory was fuzzy, but I was able to still explain things without confusing the students. I tend to make the students explain the problem back to me or tell my why my method works to ensure they understand. As the topics get more and more complex, I find myself having to try two or three methods to explain things to the students, so I'm seeing the advantage of really knowing your topic well before you explain it. This also helps in being able to explain WHY a student was wrong. They often look at their work and understand what the key says, but they don't see why their work got the wrong answer. Being able to not just point out mistakes but EXPLAIN why they're wrong makes students much less likely to repeat them. In general, I'm continuing to learn valuable lessons each week through my observations, despite staying in the same place. From talking to Gmerek and Horne, it sounds like they continue to learn new tricks everyday too, even after years of teaching the same class. I look forward to that as I become a teacher.
This week, I only got to observe once, but I enjoyed it. The students were learning a concept I was a bit fuzzy on, so I had the challenge of reteaching myself something while teaching them. It went pretty well I'd say; the students understood what was going on and began explaining it to each other, but I definitely see the value in filling out student worksheets yourself beforehand. If you have an exact idea of what they're doing, you can just focus on helping them because you know what specifically the questions are asking. Good lesson for the week.
I spent the majority of this week in Calculus again; the students are working with multiple derivative rules that intertwine and it's important to work through problems with them and make sure they understand how and when to apply each rule. Since the unit is started with the most basic problems, students tend to think that most of the rules only apply in certain cases, so they tell themselves they don't need to worry about them for some problems. Really, the problems at the beginning of the unit usually use most of the rules anyway, the difference was just negligible to the problem. I spend a lot of time demonstrating this to the students, often showing how there are just extra "times one" occurrences that don't physically alter the easier equations most of the time. I definitely feel like the classes benefit from my presence, and each week I enjoy observations more and more. I really like hearing a student explain their thought process to me, and trying to pinpoint where things went wrong so that they don't repeat their mistake; the more time I spend doing this, the better I seem to get.
While in Mrs. Horne's room, I really enjoyed working on quadratic functions with the Algebra II students. Whenever they're confused, I like hearing them explain their work to me and basically explain the concepts. It's interesting to see how strong of an understanding some students have, and how weak of a grasp others have. However, I've been able to help students of all math strengths and levels of understanding so far, and it's been a naturally rewarding process. I just really like it when somebody's eyes light up with that "Aha" moment once they get it, and my favorite thing is when they can interrupt and finish my explanation on their own because they just figured everything out. This week, I observed on Monday because Mrs. Horne was out, so I was in her room helping the students for two periods as they continued working with quadratic functions. It was pretty simple, and the substitute was able to just stay at her desk all period while I went around the room assisting students here and there. For the most part, I would have students pull out their old notes and classwork to see if they could figure things out with their own notes; I want them to be able to see what it's like to take useful notes. Most of them were able to use their notes, but if they couldn't, I'd help them and then suggest better ways to point out minor details to themselves in the future.
Tuesday and Thursday were spent in Mr. Gmerek's room; His students have been working with derivatives of trigonometric functions and more advanced derivative rules. I've really enjoyed working through complex concepts with the students and breaking down the complex language of calculus to something they can easily understand. Typically I'll just provide a basic example of something that they already understand, and then see if they can explain it to me and suddenly realize what their problem set is trying to say. That tends to work best; I would definitely say that this has been good practice for me in communicating with students. Mrs. Horne left positive feedback for me, so I guess that means I'm doing pretty well. She asked me on Tuesday how her students were with the concepts from Monday, and she said that based on my general confidence in them she was wiling to give them a small riskfree pop quiz. I think so far my observations have gone well and been beneficial to everyone involved, which is a good feeling to have. On Tuesday, Mr. Gmerek was out, so he had a sub in his room. I stayed in Gmerek's class through 3rd, 4th, and most of 5th Period because the sub had no idea how to help the students with their work. After 4th Period, the substitute actually just sat in Mr. Gmerek's desk for the remainder of the time, only speaking to the students initially to tell them what to work on for the period. Though I didn't teach a specific lesson or necessarily have any control over the classroom, I essentially directed the class that day, giving students the papers they needed throughout the period and assisting them with their work while the substitute was just on the computer. I used the whiteboard a lot more than usual since there was nothing already on there from Mr. Gmerek for the day. I enjoyed working with the students, and when I came back Thursday many of them said that they were lost on Wednesday without me. I've had a lot of them tell me in the past that I should be in their class more often, and that they benefit greatly from my help, but it was nice to actually see the difference for myself.
On Thursday, Mr. Gmerek was back, so I went to Mrs. Horne's room for 4th Period and stayed halfway through fifth to see her Precalculus class. It's a very drastic shift in students between Algebra II and Precalculus; the latter are much more focused and selfsufficient in their learning for the most part. Mrs. Horne also asked me if I could come in Monday because she will be at a wedding, and the students would be more familiar with me than a sub, so I'll be doing Observations that day now too. Overall, it's nice to feel useful and actually play a role in the students' learning during my Secondary Education observations this year. I felt very involved during my elementary observations last year, but my middle school ones were often pure observation without any real work on my part, so I definitely am enjoying myself this year. I am still enjoying my time in Mr. Gmerek's Calculus room, as well as spending time here and there in Mrs. Horne's Algebra 2 class. This week I got pictures of part of a fire drill, so I can add that to my Portfolios. Mrs. Horne's class was working on factoring, which really just involves practice until you get used to the patterns, so I spent a lot of time in Mr. Gmerek's room. His class was learning the heart of calculus concepts, and starting to use derivatives. I enjoyed it a lot, and had some interesting conversations with Gmerek about assessing curriculum and figuring out how to teach a topic. He also confirmed my thoughts on how it's important for a teacher to use handouts and lessons that THEY created because familiarity with the questions is essential to explaining a concept. As I've witnessed myself, if I've just walked in the room and a student asks me for help, it's a lot harder to explain unless I've already seen the specific problem. I need to be able to tell exactly what the students were doing leading up to the question, and what they need to be able to do by the end of the packet. That way, I can minimize confusion and maximize understanding/application of concepts. Overall though, the students seem to benefit from my assistance regardless, so I'm really enjoying myself.
This week, I spent both of my observation days just in Mr. Gmerek's Calculus class again. I've been staying past my standard observation time and continuing to work with his 5th period class during my free period before lunch... This is getting to be a minor problem though, because I enjoy it so much that I'm progressively getting to lunch later each day. On Thursday I was only halfway through eating when I had to head to class. I don't mind though, really I'd just rather observe all day. I'm continuing to see how each period, you get better at explaining to the students and predicting their problems/mistakes. It's really fun to try different methods of explaining each time you talk to someone, so that eventually you figure out just how much information to just tell a student so that they can figure things out on their own without just giving it away. Overall, I plan to continue with the Calculus observations past the end of this quarter, and see where it leads.

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