Thoughts on Mathematics

[Mr. Altitude]

First off, what do you all think of math? I personally like it, but I like it for the logic. I'm terrible at mental calculations, and I hate when the whole class is simply "here's a formula, plug in some numbers."

I hated math until 6th grade when I realized I was actually good at it. The concepts just made sense to me. Ever since, I was in more and more challenging classes.

I think the reason most people (INTPs especially) hate math is because it's taught in a very Te way, in that the important thing is how well you can use the formulas they give you. In later math, knowing the concepts well becomes more and more important, which may be why INTPs often hate math until sometime in college. It's really a shame math isn't taught in a better way. If people learned about the concepts before the boring stuff (operations, counting, etc) then I think they would learn to love it for the logic and/or the practical applications (depending on the individual, of course).

On another topic, do you think math is an objective, universal truth, or do you think it exists only in our minds? I think the latter, because everything math is founded on, like the concept of addition or even the concept of numbers, was invented by us. Only a conscious mind can invent and use operations and numbers, so math can only exist in a conscious mind. My favorite metaphor is that 3 feet = 1 yard no matter where you are in the universe, but that doesn't make it a universal law.

I dunno, I'm just trying to condense my thoughts in writing. I am still interested to hear your thoughts though, those of you who had the patience to read all that.

 

[Shieru]

I personally like it, but I like it for the logic. I'm terrible at mental calculations, and I hate when the whole class is simply "here's a formula, plug in some numbers."

Exactly. i couldn't get into math until recently, when i took a college course which explained it as a language which describes the relationships between things. that seems like a beautiful and exciting idea to me, i have a lot of interest in math now. before that, it was presented as being all about memorizing certain steps to come to a certain value, which seemed utterly ambiguous. the problem wasn't explained as a theoretical system, there was no context, no 'why' to it.

I think the reason most people (INTPs especially) hate math is because it's taught in a very Te way

i've never thought of it in this way, but you may be right. perhaps Te can better operate on compartmentalized logistics - just doing something in order to fulfill an (arbitrary) objective.

On another topic, do you think math is an objective, universal truth, or do you think it exists only in our minds? I think the latter, because everything math is founded on, like the concept of addition or even the concept of numbers, was invented by us. Only a conscious mind can invent and use operations and numbers, so math can only exist in a conscious mind. My favorite metaphor is that 3 feet = 1 yard no matter where you are in the universe, but that doesn't make it a universal law.

i agree with you, math is something - an explanatory device (language) - we've created. the things we describe with math tend to be objectively true, though. equations can describe, sometimes with surprising accuracy, the qualities of objects and the inevitable causalities of systems.

 

[Artsu Tharaz]

I'm interested in it. I study it at university. So far my best subjects have been discrete maths (number theory and combinatorics) but I quite like topics like topology and group theory. I personally am not a fan of the logic side. Real analysis uses a lot of logic (probably more than topology does) so I struggled a bit, because the things I had to prove seemed intuitively obvious but then I would have to phrase that in epsilon/delta language. I like finding a difficult problem that I can get stuck into, although this tends not to happen often. In terms of difficulty, I mean the level of insight needed to solve the problem, rather than number of tools at one's disposal, which may be why I excel in number theory/combinatorics because the things being analysed are very easy to see, unlike say, matrices, where I have struggled to grasp the reasons behind why the formulas work (I've studied linear algebra multiple times, but I've yet to really sit down with the intent of building a deep understanding of the subject).

 

[Rixus]

Maths is a wonderful thing. I believe it's one of the few universal truths that truly exist. I see it as being a fundamental concept that is all around me and explains the world in which I find myself. Something that makes sense in a world that often doesn't. It doesn't matter whether you call it three, trois, drei or tri. There are still 3 of them. The label is irrelevant - the maths behind it will always be true. So I do not believe it is a construct of our minds, but our understanding of the basic truths of our universe that have always existed until we labelled them.

I do agree maths is taught in a very unappealing way for our cognitive styles. I was just discussing this with my son only a couple of days ago. I don't know how this is taught in other countries, but in the UK, our multiplication tables are taught in the most excruciatingly painful method that any spawn of Satan could devise. Children are selected in some prefabricated order to leave their seats and stand at the front of the class. These poor victims must then slowly recited a randomly selected times table in front of their peers in the following droning manner, "one times three is three. Two times three is six. Three times three is nine .... " This was an experience akin to having one's teeth removed.

I had little problem with basic arithmetic, really. I have always been able to solve complex problems, but I have always gotten the occasional simple sums wrong and the only reason for this is that I just didn't read the question properly due to perhaps laziness or boredom. As a result, I was only in the middle ability group during primary school. Come High School and beyond, though, I was promoted to the highest groups and loved maths. For me it was once they started adding letters, crazy symbols and more abstract concepts that could be applied to the world around me that I started to like it.

I frequently argue with people who tell me that once you leave school, you'll never use algebra again. I argue that all maths is algebra and we use it all the time. Just not those specific equations. But everything is manipulation of the variables around us. When I'm so much as selecting how far to drive behind the car in front, I'm mentally calculating the breaking distance between us.

An example - I recently created ultrasonic eyes for a robot I've been building. The concept of the eyes is simple. A speaker fire's a short burst of sound outside the human frequency range. The microphone hear's the echo and measure's the time it took before it heard this echo. Then use simple maths to convert the time difference to distance by calculating the speed of sound (OK, so I used the speed of sound at sea level and I'm not actually at sea level, but nobody's perfect).

 

[sushi]

i can't find the connection between math and reality, at least abstract math and higher mathematics.

 

[Black Rose]

I took the TABE in January and am now taking basics at my community college. On the math section, I am at the 5th grade level. I don't think I was taught math properly in school. We never read the books all the way through. I was more into science and computers than math in school so I never felt I needed to pay attention. It is allot easier to learn now that I am reading the book from the beginning. I learned how to divide fractions and multiply decimals. I never learned that in school. I did learn algebra and geometry but not trig, calculus nor statistics.

Using math to solve real world problems is still mysterious to me. I want to learn things and solve problems but I don't know what problems I want to solve. I don't want a boring job but I can't think of anything. Something with technology.

 

[Pyropyro]

Math is quite handy when I'm doing statistical research and other experimental projects. Excel is a godsend when it comes to working with large amounts of numbers.

 

[ENTP lurker]

Mathematics is a collection of tools in logical realm. Math is not a science but highly usable.

I just finished my math studies and I'm eligible to teach it in high school level. My profession is a chemist (M.Sc). Means that I have done my courses in algebra, linear algebra, stochasics and most of all lots of analysis which is deeper than what we usually define as calculus and combination of those.

Math is not real and it is not supposed to be it only works in pure logic. Everything else is just approximation. 2 apples + 2 apples is roughly 4 apples but 2+2 is always 4 in normally defined base 10 system.

 

[ENTP lurker]

Using math to solve real world problems is still mysterious to me. I want to learn things and solve problems but I don't know what problems I want to solve. I don't want a boring job but I can't think of anything. Something with technology.

If you mean math as describing static structures rather than dynamics (this is largely physics) then I'd take deeper look into discrete math and computer science which is not dealing with infinities and is very logic heavy.
If you want to design dynamically moving pieces then it is physics and engineering with good basis on calculus.

 

[ToddRyler]

Why most of us end up being taught math in a bad way is, imo, actually an easily answered question. It's just that the better people get better jobs and the ones teaching kids usually come lower on the merit list. Now, assuming the system is fair, these people are not exactly the brightest people around.
But earth keeps jogging around the sun

 

[Haim]

Why most of us end up being taught math in a bad way is, imo, actually an easily answered question. It's just that the better people get better jobs and the ones teaching kids usually come lower on the merit list. Now, assuming the system is fair, these people are not exactly the brightest people around.
But earth keeps jogging around the sun

It is not just that, it is systematic.first a teacher is forced the follow the rules of the system, and I don't just mean human rules but the actual state of the system, such as you give tests to check if a teacher does his job.Second most kids and teenagers can not think, even the ones with more processing power potential which are filtered by tests, and then you are limited by that are teaching some kids in nature, you actual need to force them to study or they will be sure to not.
Third, many teachers also are not capable of thinking, since most people can not, also they learned math the non thinking way.Fourth, in order to use math as it meant to be, you need a goal in which math is a good tool, a scenario which is hard to create, for that most of the time you need other skill such as programming,engineering,more than high school level physics,analytics,management.