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... 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.
I think that ^^^ is a GREAT point. Math NOTATIONS seem like a completely bizarre foreign language to most (including me, BTW, even though I'm generally good at math) -- but once you get past the notations and see what PRACTICAL value the math can have, you are on your way to UNDERSTANDING those equations -- no matter how bizarre they may look.
I was always quite average at math. I preferred algebra to geometry. When I applied myself, I could get good grades, but if I didn't, I'd forget the formulas and not do as well. Regardless, I never had the motivation or natural talent for it the way I did English. Language comes easier for me than math, or art, for that matter. I love words, spelling, grammar, defending a thesis...I was a natural English major, test taker, book-reader, and paper-writer. I tend to think of math and art as very different brain realms, and neither come as naturally to me as language (especially the written form) always has.
I was always quite average at math. I preferred algebra to geometry. When I applied myself, I could get good grades, but if I didn't, I'd forget the formulas and not do as well. Regardless, I never had the motivation or natural talent for it the way I did English. Language comes easier for me than math, or art, for that matter. I love words, spelling, grammar, defending a thesis...I was a natural English major, test taker, book-reader, and paper-writer. I tend to think of math and art as very different brain realms, and neither come as naturally to me as language (especially the written form) always has.
That's interesting, but I've never thought of things like math and English as being "opposites." I mean, I am a very good writer (judging from my papers, presentations, articles, reviews, etc.) and writing comes very naturally to me (i.e. it's truly FUN and relatively easy -- as it sounds like it is for you! ) -- but I am also good at (and enjoy) math. So what you wrote makes sense, but I think you can be very good at both. (If I had to pick one I'm "naturally" better at, it's writing. So maybe that's what you meant?)
As a high school student (and female) I was placed in some higher math classes until my brain would not compute haha.
I too need to see things mentally to understand them and my eventual calling was in visual arts.
Retired from a photography career now I am an abstract painter who self-taught myself carpentry skills and make 3 dimensional polygonal shapes in wood to paint. Heavy on angles and requiring similar visualization. My brain is now able to handle things it could not at a younger age.
The more you go into a math area you have an interest in the more your brain opens up to absorb it.
Perhaps you need to specialize in those math areas you have a proclivity for, not be an all-rounder in other words.
Your talents and interests may parallel that of the earliest mathematicians who somehow used their visualization to conceptualize the most basic math ideas, like point and number, as opposed to painting on cave walls or creating a wheel.
I agree that some math is more intuitive and attractive than other math. Some visualizations arise in the mind easier than others. In my case, I think I like reading and thinking about mathematics more than I like practicing it. This may be related somewhat to possible Attention Deficit Disorder because my mind likes to jump from topic to topic and subject to subject. My affinity is toward more general ideas and abstractions. Focusing on a specific theorem or problem with sustained concentration requires a mental and emotional shift.
Modern mathematics education must somehow confront all this diversity of abilities and talents and interests and find ways to teach "standard" mathematical subject matter to that diverse population. Its no wonder that textbooks and teachers vary in their ability to do that.
Last edited by highplainsrus; 10-17-2020 at 09:05 PM..
That's interesting, but I've never thought of things like math and English as being "opposites." I mean, I am a very good writer (judging from my papers, presentations, articles, reviews, etc.) and writing comes very naturally to me (i.e. it's truly FUN and relatively easy -- as it sounds like it is for you! ) -- but I am also good at (and enjoy) math. So what you wrote makes sense, but I think you can be very good at both. (If I had to pick one I'm "naturally" better at, it's writing. So maybe that's what you meant?)
I actually listed math and art as opposites, not English There are some brains that seem to process many things well, so I've certainly seen people who can excel at all subjects, but most have noticeable strengths and weaknesses in some subjects over others. My husband is good at both math and language, for example, but not so artistic (can't draw/paint or perform/sing any music).
Why is math so hard for many people and how can that be overcome?
The problems as worded are sometimes unclear and puzzling, with non-intuitive solutions. I remember encountering actual errors in the texts that would hang me up until I consulted other texts for clarification.
For some people, there are pathways lacking in the brain, and probably not much can be done to overcome that, especially after a certain age.
Other people fall behind in math for reasons you allude too, poor teaching and horrid textbooks.
I never got past pre-calculus because of a poor high school teacher, which in the long run prevented me from pursuing economics at the PhD level, which is pure math (econometrics).
Nevertheless I use financial mathematics and probability/risk analysis everyday. I have even developed my own spreadsheets with risk-analysis formulas unique for my situation.
As for textbooks, I have been following with my own eyes and hands a grade-school math curriculum sold to schools by a certain company, and also a science program, and the first thing I wonder is where these people learned how to write English.
Horrible, horrible, horrible.
To be sure, this is a significant part of the reason why the US is behind, supposedly, in so-called STEM: lack of common-sense language in teaching basic math and science.
I am skilled at various levels in about nine languages, including three ancient ones, and often for the life of me I cannot understand what the authors of these grade-school math and science textbooks are trying to communicate to these children.
And I am talking about simple counting and addition to start with. Utterly confusing, tantamount to child abuse.
I know even professional attorneys who have difficulty in understanding what these textbooks are trying to convey to their children. Appalling.
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.
Mathematics is intuitive for me. When my 3 children were young, on a drive I explained to them basic Newtonian Physics: displacement, velocity and acceleration. By observing and feeling, they learned what a rate of change (velocity) and a rate of change of velocity (acceleration) feels like. By making math real instead of just numbers, it becomes easy to learn. I used similar examples to explain heat transfer and aerodynamic lift.
I had magnificent teachers in high school and college. If your teacher really knows the topic he can hit it from many angles until you understand it. I briefly considered becoming a teacher but decided that I could make a lot more money and have more fun as a design engineer.
BTW, two of my 3 kids went on to get advanced degrees in engineering. That third kid was like her mother; no matter how hard I tried, I could not get her to understand simple algebra. Today, she is a successful Nurse.
As I opined, either you can do advanced math or you cannot.
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) -- but I am also good at (and enjoy) math. So what you wrote makes sense, but I think you can be very good at both. (If I had to pick one I'm "naturally" better at, it's writing. So maybe that's what you meant?)
