This week was the first full week spent on derivatives. On Friday we learned what exactly a derivative was. I realized the reason that we did limits as our first section was because to find a derivative of a function you have to find the limit as h approaches 0. We also talked about continuity because when finding if a function is differentiable it has to be continuous.
I also noticed that back in my week 2 blog post the picture that I used was what we had been using all week to find the derivative of a function, and at the time I had no clue what the thing had meant besides the fact that it said “I like pushing things to the limits.” So the things we learned are building on each other which is pretty cool. Besides that we are building upon things we actually learned a lot of new concepts this week in terms of derivatives (which I had only heard we were going to be spending a lot of time on from past calculus student). I had no clue there were different ways to write derivatives, what differentiability was, or that there were rules for differentiation. I am actually not to overwhelmed by all these new things and found it to be pretty easy things to grasp. I kind of scared for what is going to come next week because you said this is the point where students start to hate you, but I am ready to learn more about what you can do with derivatives.
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This week we had an activity where we created three GIFs, the three that I created are these: This week we had an activity where we created three GIFs, the three that I created are these: The first activity helped with the generalization represented in the first GIF by showing that the slope of a secant line will narrow down until you get to the point where the tangent line is. You can generalize the tangent’s slope by finding the slope of the secant lines that slowly get closer to the tangent line. The one thing that my whole table struggled with was not knowing exactly what tangent and secant lines were. We figured out how to do the generalization problem once we knew what they were. When making the first graph the one thing I struggled with doing was keeping the line at one point instead of having it move up and down the graph. I figured it out after talking it over with people. One change that had to be made from the first to second graph was to make the one stationary point a point that also moves. Instead of having the points for the slope be (a, f(a)) and (2,2) they became (a, f(a)) and (b, f(b)) for the slope equation m. I also had to write a separate equation for the line. The analysis of secant lines helps to determine the tangent line of a function by allowing for us to slide the line along the function until it is at the point of tangency and then the slope can be calculated and the equation for the line can be written. This week we finished chapter 2. I did not find the content very difficult to grasp, but the 2.1-2.2 quiz does not reflect that. I make a lot of stupid math mistakes frequently and when I go back to see what I did wrong, I know exactly what I should have done. Limits are one of those units where I should go back to make sure that I didn’t make a mistake. Continuity is not very difficult either. I found it removable and infinite discontinuity were easier to say exactly where it is discontinuous, but jump discontinuity was a little more difficult to grasp in terms of graphs such as the greatest integer function. When the graph is defined at every point on the domain, yet it is discontinuous at every point as well that was kind of confusing at first but after seeing it and then looking at it on a zoomed in scale I understand it better. I know that after this unit things are going to start getting harder, so I am thankful for the fact that we do get to start with an easier unit that forces me to check my work and make me focus on each step individually instead of the big picture. This week was a lot better than last week was in terms of confidence in my math skills. On Monday we had the ability to finish the math packet and then we started to review the answers for the second half of the hour.
Tuesday we finished reviewing the packet and then took our first assessment. I feel really good about how I did on it, I had already learned everything prior to this year though so that may be why. Wednesday we didn’t do anything because there was a meeting for seniors so that was pretty nice. Thursday we did a lab on limits, which I thought was cool just because I’ve never really done an activity like that in math before. It was a good refresher for limits just because we really didn’t do much with limits last year. Friday was the first time I had to take any form of notes since last year. Limits aren’t particularly difficult yet, but we’ll see where I end up at the end of this unit. I really like that we did so many examples and we were able to contribute to how to solve them instead of just being told how to solve them. The first week of my senior year and the first time I did not have homework assigned on the first day of school. I was beyond excited that I was able to go home and relax after the first day of school, but then we got the review packet and I wished i had worked on my math advanced math skills over the summer. I did tutor a little girl over the summer but practicing long division and multiplication facts can really only help so much... After the first day of working on the packet I was struggling just a little to remember just exactly how one does math. I didn’t struggle with basic algebra, problems where graphing was involved, or volume problems, but the problems that were more involved or contained fractions I really had to think back and remember what I have learned in math the past few years. All in all this past week in calc has been like any normal first week of math, trying to get back into the swing of things. I’m really looking forward to starting to continue to build on to the math skills that I already have (even though they may have a few cobwebs on them) and to learn completely new math concepts. At the end of this first week I would say this is how I’m feeling about my math abilities...Hopefully it stays that way!
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March 2017
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