In learning the fundamental theorem of calculus I relied on both deductive and inductive reasoning. I did find it easier to use inductive reasoning more than deductive reasoning, just because it was easier to grasp what is being talked about. I usually learn better by seeing and then doing rather than being thrown a bone and left to fend for myself when being introduced to a new idea. I am able to learn on my own, but I do struggle when things are assumed to be understood and I don’t completely grasp the idea. As a dancer I am able to see what I am supposed to be doing and then I can recreate it myself. I have found over the years in math that once I have seen a certain type of problem I can do them and build upon them, I just need to see a basic example to get myself going. The fundamental theorem of calculus is so fundamental because it shows that every continuous function has an antiderivative, that the process of integration and differentiation are inverses of one another, and that definite integrals can be evaluated directly from the antiderivative of a function. Because this is known then you are able to find the integral of an equation much easier In my mind the fundamental theorem of calculus is still a little fuzzy. At times I completely understand it, but at other times I am completely lost. I know that it really is allowing for the area under a curve to be found, but it still is slightly difficult to grasp.
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This week was the first week back from break and I think that it could basically summarized in the four words, I'm going to die. After not doing much math, besides trying to figure out if I had lead my family on the 27 mile snowshoe trail or the 4 mile snowshoe trail at Tahquamenon Falls, it took a little while to understand what the heck I was supposed to be doing for the chapter four test.
I have learned after this week that it took us almost 6 weeks to get through a chapter and that the chapter reviews are generally much harder than the actual tests. The first 10-15 problems in the assignment were over the oldest material in the chapter and while the chapter does build on itself for the first 4ish sections the last few sections had nothing to do with those problems. The last few sections were what was slightly fresh in my brain, so the last half of the assignment wasn't very difficult. I felt a lot better on the second day back to class but I did still have a few moments where I thought I was going to die because it couldn't handle the types of mathematics it was being asked to do. However by Thursday I understood the majority of topics that were going to be on the test. After that I was okay, but I still slightly felt like I was going to die because I realized that we have no planned days off from school until spring break.. |
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March 2017
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