I have a twin brother who had a very similar start to math as I did; we both absolutely sucked at it at first (referring to math more than just talking about what a fraction is or decimals, so essentially an entry into Algebra). Since then, we have diverged on two different roads that proves to be a perfect example of where attitude and math can lead.
Middle school was about where my school unit began to show different level math classes; there was a lower level math class, a middle level, and an upper level. This is where effort first altered fate, where in our exam that would determine where we land, I tried a little harder than my brother, but we both tested into the same level of math, except he decided he should be in a lower level.
I never thought I was good at math and still don't think I'm great at it, but effort truly made a difference from this point on; even though I was in a higher level math class and of what was probably very literally the same intelligence level as my brother, I excelled in my class, and my brother struggled with the lower class.
This trend continued through high school, where we started off with a clean slate and were placed into the same level of math (Algebra 1). He failed the class by half a point and I passed with a B.
Failing by half a point, I think, is what truly lit a fire in my brother to begin putting a bit more effort into math. Having to retake a class in high school while his twin brother was moving on probably wasn't the greatest feeling, and so he quickly caught himself back up to me through geometry and algebra 2, where he finished just points behind me and receiving an A.
Sadly though, his experience with math for the majority of his years as a student plagued him into calling it quits there; he was no longer required to take math, and so he took a class that simply reviewed the lessons learned from previous years, while I took AP Statistics. Come college, he'd attempt to take statistics and to my surprise, fail, and I'd find myself taking the most math intensive major available at my school.
We're two different people with different interests, but I think that if he had a better experience with math earlier on, where he got into a higher level math class or felt as though he was capable of understanding it from an earlier time, perhaps he'd have a much better time wrestling with math. By all means, he's very capable, and an understanding of upper level math would probably be very helpful to him in his chosen fields of law enforcement and forensic psychology, but the effort doesn't seem to be worth it to him.
Since he's no longer required to take math, this is probably his end point with it, whereas my point is apparently a limit and therefore I seemingly can't surpass it, though I can get pretty close to never encountering math again.
Sunday, February 21, 2016
Tuesday, February 16, 2016
Exploration 3 Continuity
(Answer to question 5)
A point that lies between a series of negative output regions and positive output regions(example, where A<0, and B>0) will point to a limit, or an area of discontinuity if it exists. The negative output regions could be any number approaching the limit/discontinuity from the left, and the positive output regions could be any number approaching the limit/discontinuity from the right.
A point that lies between a series of negative output regions and positive output regions(example, where A<0, and B>0) will point to a limit, or an area of discontinuity if it exists. The negative output regions could be any number approaching the limit/discontinuity from the left, and the positive output regions could be any number approaching the limit/discontinuity from the right.
Saturday, February 13, 2016
SHP and Groupwork
The Sustainable Harvest Project went very well; although we waited until the last possible day to do the project (mostly a result of a lack of time and difficulty in finding time where we were all available) we feel that it was completed successfully and well understood. The first few questions were fairly easy and didn't take long to solve, but the last question proved to be a bit more difficult for us, but nonetheless was completed without much trouble (creating the spreadsheets to find answers was honestly the most time consuming part).
Our success may have been due to our ability to work well together; communication was strong and despite being in a pinch, we got everything done within a few hours (including an hour gym break!). In the future, I hope that we work together again, or at least with similar hard working people. We corrected each other where it was needed, worked hard, and divided work equally. Neither of us had a particular "role" either; with each question, we were typically on the same direction of thought and if there was any issue with the result of a question, we'd all work toward the answer individually to insure its correctness or check each other's work. The write-up was about the only area where we had assigned roles; we each took a section and answered it.
At this point, I think I'm confident enough with discrete time modeling that if given a problem similar to this project, I could work it out. It now comes relatively easy to me, though I would still need to reference my notes when it comes to putting equations into general solution form when dealing with linear or difference equations, though linear difference equations I can do without much difficulty since I've been working with them more recently.
Our success may have been due to our ability to work well together; communication was strong and despite being in a pinch, we got everything done within a few hours (including an hour gym break!). In the future, I hope that we work together again, or at least with similar hard working people. We corrected each other where it was needed, worked hard, and divided work equally. Neither of us had a particular "role" either; with each question, we were typically on the same direction of thought and if there was any issue with the result of a question, we'd all work toward the answer individually to insure its correctness or check each other's work. The write-up was about the only area where we had assigned roles; we each took a section and answered it.
At this point, I think I'm confident enough with discrete time modeling that if given a problem similar to this project, I could work it out. It now comes relatively easy to me, though I would still need to reference my notes when it comes to putting equations into general solution form when dealing with linear or difference equations, though linear difference equations I can do without much difficulty since I've been working with them more recently.
Saturday, February 6, 2016
Reflection 2: Clear and Fuzzy
Thus far, I think I've done fairly well with learning the information in the course. However, my mind does a brilliant job of pushing one thing out while absorbing another, particularly with concepts in classes such as this and Chemistry; as soon as a new concept is learned, it's almost like I have to re-learn the last unless it is incorporated into whatever the current lesson is. My highest point of confidence with each lesson is anytime between when the homework is finished and the next lesson starts; after that, I really start to question whether or not I truly remember how to solve those problems. Thus far, every quiz has been open notes and so remembering hasn't been such a problem, so I wonder how well I'd perform without my notes.
Though it's often difficult and the most frustrating form of learning, I learn the most from homework. I often have to look through the chapter to figure out how to solve whatever is being asked if I can't figure it out, and thankfully some answers are in the back of the book, so I can assure that I am doing things right. Sometimes, the ability to see the answer allows me to work backwards to understand the process of going through the problem (this reminds me of how in Animal Training we discussed that learning how to perform a sequence of things is best done backwards). It definitely takes a huge amount of my time to run through the homework, but thus far it has been very valuable and has asserted why I feel as though I'm doing well. Sometimes, my notes can be supplemental to solving the homework problems, but surprisingly I find that it often isn't as useful as the book; I've yet to have an "a-ha" moment led by my in-class notes when faced with a difficult question, but sometimes it can help me reach that point.
Perhaps the best way I learn is through practice, but when applying new concepts to problems, having a step-by-step instruction/flow chart has always been something I've always found very useful when trying to figure out something new. However, since Calculus isn't always necessarily a "step-by-step" process, it's somewhat difficult to design a technique for learning the concepts in any other way than through practice. Perhaps more guided practice during class would be useful, particularly since there are some problems encountered in the homework that don't get covered in class; some of them have different rules or techniques for solutions that I never realized existed until spending some time trying to find the solution in the book. It'd certainly speed up my process, but it may also be possible that since I'm not learning it on my own it may not stick as well and I may find myself somewhat lost when I have to do things on my own (though I suppose that's what homework would cover).
Though it's often difficult and the most frustrating form of learning, I learn the most from homework. I often have to look through the chapter to figure out how to solve whatever is being asked if I can't figure it out, and thankfully some answers are in the back of the book, so I can assure that I am doing things right. Sometimes, the ability to see the answer allows me to work backwards to understand the process of going through the problem (this reminds me of how in Animal Training we discussed that learning how to perform a sequence of things is best done backwards). It definitely takes a huge amount of my time to run through the homework, but thus far it has been very valuable and has asserted why I feel as though I'm doing well. Sometimes, my notes can be supplemental to solving the homework problems, but surprisingly I find that it often isn't as useful as the book; I've yet to have an "a-ha" moment led by my in-class notes when faced with a difficult question, but sometimes it can help me reach that point.
Perhaps the best way I learn is through practice, but when applying new concepts to problems, having a step-by-step instruction/flow chart has always been something I've always found very useful when trying to figure out something new. However, since Calculus isn't always necessarily a "step-by-step" process, it's somewhat difficult to design a technique for learning the concepts in any other way than through practice. Perhaps more guided practice during class would be useful, particularly since there are some problems encountered in the homework that don't get covered in class; some of them have different rules or techniques for solutions that I never realized existed until spending some time trying to find the solution in the book. It'd certainly speed up my process, but it may also be possible that since I'm not learning it on my own it may not stick as well and I may find myself somewhat lost when I have to do things on my own (though I suppose that's what homework would cover).
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