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I enjoyed Calculus and feel it should be taught with Story Problems as it is infinitely useful in so many real world situations. Yet it is taught as a stand alone topic devoid of links to commonly encountered problems - such as determing the heat output necessary from a heating system to raise the internal temperature of a building within a desired time span, to counteract a given rate of heat loss from a building during winter time conditions, and which has had it's internal temperature decline during unoccupied hours for energy savings.
It comes down to simple aptitude. A person of good intelligence can always book like crazy to get good grades at math. Yet, to some people it all makes sense right from the start and THEY don't have too study that hard.
My experience? I have son who is a high school math & computer teacher, but when it comes to writing, spelling, sentence structure and the like, he has always struggled.
My youngest daughter went to college and had to take remedial college math classes her freshman year due to a low ACT in math. English and science subjects were never a problem for her, unlike my son. She's now a registered nurse and slam dunked her boards when she took them.
The same household, gene pool, and environment growing up, yet totally different aptitudes.
I love math and think it would be fun to take some math classes after I retire (although I have so many other projects, I probably won't get around to the math).
I had introductory calculus in high school (way back in the late '70s) and 1-2 math classes in college (late '70s/early '80s), then I went to grad school for journalism (no math required), then I went to grad school (different school) for a Ph.D. in a social sciences field. That required at least 2 courses in statistics (I took them in the mid to late '90s) and I did well in both. Probably some of that was because I could see how USEFUL they would be for quantitative studies (although I find qualitative studies more fun to do and read about).
I don't remember much of calculus except that it seemed VERY abstract, and I wished it were more concrete. But I still did OK and "got" most of it.
I think a lot of people get it into the head that they are "just bad at math" and that becomes a self-fulfilling prophecy. I have taught statistics a few times at my college and we just went step by step to solve problems I wrote myself (I would write detailed step-by-step instructions on the handouts, then we would just DO the steps in class with the problems). I will never forget that one of my Research Methods students said to me after I went over the normal distribution (including standard deviations, z-scores, etc.), "No one has ever explained it like this before" -- she totally GOT IT because it's REALLY not that hard to understand. AND it really CAN be enjoyable!
The two leading contributing factors for why math is hard
1. Bad teachers
2. Bad textbooks
I was terrible at math until I got to high school - then was blessed with a teacher that made math 'click'.
After that it was still a struggle, but managed to get lucky in college with calculus because the prof required a really good textbook and he communicated well.
Other courses were hit and miss with linear algebra and advanced calculus; terrible teachers and poorly written textbooks.
I don't think there is any one thing but multiple factors that combine to make math "hard." First, I very much agree with this?
Quote:
Originally Posted by Trekker99
The two leading contributing factors for why math is hard 1. Bad teachers
2. Bad textbooks
I was terrible at math until I got to high school - then was blessed with a teacher that made math 'click'.
After that it was still a struggle, but managed to get lucky in college with calculus because the prof required a really good textbook and he communicated well.
Other courses were hit and miss with linear algebra and advanced calculus; terrible teachers and poorly written textbooks.
My observations, from my own school years and raising my kids, is many elementary and middle school teachers dislike math themselves, even the ones teaching it. And they pass this fear on to their students. Combine that with they can't teach what they don't understand and you get kids who believe they can't do math by the time they finish elementary. It becomes a self-fulfilling prophecy.
Next, text books are mostly horrible. Everything from errors to terrible explanations to poorly written word problems. It all compounds to make even basic math hard. Some of the explanations and methods used in the textbooks seem intentionally designed to obscure even simply concept. Common core based texts for example. I was completely unable to help my youngest starting in 6th grade because the methods were unintelligible. Even my oldest, who had just been in the same class a couple years before, but with a pre common core text, couldn't decipher it.
Adding to this is the problem that our current education system in general doesn't teach abstract and logical thinking. It's all about regurgitating back the "most correct" (what the heck does "most correct" even mean?) bubble with their #2 pencil than understanding. Even English (excuse me, Language Arts) plays into it.
Higher level math requires a solid foundation AND the ability to think logically about abstract concepts. When none of those underpinnings are there, learning collapses.
Let's not blame the books or the teachers. The fact is that different people have brains wired in different ways. So people learn in different ways, and think in different ways. What's easy for some people is very hard for others. For me, math is in the middle, creative writing impossible. And my background is science - virology to be exact.
When I was in grad school, a first year course was the physical biochemistry of macro-molecules, as mathematical as it sounds. I was part of the majority of the class that just struggled through the equations, memorizing as much as I could to pass the tests. A small part of the class was three people with masters in physics. They were correcting minor errors by the lecturer in real time. It was amazing to me.
I learned later that folks really good in higher math "see things" through equations. (and see earlier images) Others have said higher maths are like non-verbal languages.
So I think the answer is to figure out what level works for you. For some things, I just memorize equations, and focus on how to use them. For other things, with time I get comfortable enough to learn the theory and derive what I need. But for most things, I google!
Note that there's nothing wrong with you if you struggle. Nothing wrong if you "gut" through and forget most of the stuff after the exam. You're just normal.
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