Silent_Rebel
Active Member
Are any other INTPs bad at math? I really only have a big problem with fractions, but I am in algebra right now so that is pretty much 60% of the numbers that we deal with.
I've noticed that most schools teach math in a very Si-Te way, and enforce this style or learning, and it seems effective....for most people, most people not being global or intuitive learners. Every math teacher I had expected the students to learn by doing a mass of practice problems, which were all basically the same. This is a big problem for someone who absolutely hates repetitive routine. Thus, even though I could understood the concepts, lack of interest and doing any kind of work resulted in poor grades in this subject.
The other issue is that some teachers expect that problems are solved using the exact procedures they've thought you.
My natural approach to math problems is intuitively trying to "sniff out" a solution, approximating and trying out different variations, which would usually leave me brainstorming and scribbling calculations on the margins of the exam sheet paper, not making it till the end of class with any definite solutions.
Is "global learning" essentially learning through the big picture?
- "Sequential learners tend to gain understanding in linear steps, with each step following logically from the previous one. Global learners tend to learn in large jumps, absorbing material almost randomly without seeing connections, and then suddenly 'getting it.'"
- "Sequential learners tend to follow logical stepwise paths in finding solutions; global learners may be able to solve complex problems quickly or put things together in novel ways once they have grasped the big picture, but they may have difficulty explaining how they did it."
Yes.
Although most web resources portray global learners as right brained NFs, and sequential learners as left brained STs, I don't think it's always the case. In my opinion, the difference between sequential and global learning is more of an intuitive/sensing one.
Fukyo said:I've noticed that most schools teach math in a very Si-Te way, and enforce this style or learning, and it seems effective....for most people, most people not being global or intuitive learners. Every math teacher I had expected the students to learn by doing a mass of practice problems, which were all basically the same. This is a big problem for someone who absolutely hates repetitive routine. Thus, even though I could understand the concepts, lack of interest and doing any kind of work resulted in poor grades in this subject.
This. I managed to make it up to Calculus before finally giving up. I had a number of teachers in elementary school who publicly ridiculed students for wrong answers. I was simply bodily afraid of a few others. I was too scared to ask questions in class.
Mathematician speaking.
I freaking love math. It makes me feel like a magician or something. From just a small number of rules I can imply just about anything, whether it be horribly abstract or concrete and applicable to daily life. I've come to realize though that I learn mathematics in a very strange way. Rather than memorizing the steps and formulas needed to solve the problems, I learned instead how to break the problems up into the simplest component pieces possible and derive my solution from there given the rules that I have memorized.
For instance, I took my linear algebra final today. One of the questions was something like this (note, this question is made up on the fly for the sake of showing an example):
Let S = {(1 1 -2 3 0 5), (0 1 0 2 0 3), (0 0 0 1 0 2), (0 0 0 0 0 0)}
In matrix form:
| 1 0 -2 0 -1 5|
| 0 1 3 0 8 3|
| 0 0 0 1 -7 2|
| 0 0 0 0 0 0|
Find the orthogonal component of S.
Well, my brain starts dissecting this immediately
1) I need to find all vectors x such that x is 90 degrees to a vector of S.
2) This means that the scalar product of S and x must equal zero
3) ie, Sx=0
4) However, we know that the nullspace of a set of functions is defined as the set of vectors x such that the matrix, A, multiplied with x equals zero. Ax=0
5) So I must find the nullspace of S
6) Well crap. How big is the nullspace?
7) Well, by the rank-nullity theorem, we know that the rank of a matrix added to the nullity of a matrix equals the number of elements in a vector of the matrix, and since S is in reduced row echelon form, our free variables have leading ones, meaning that S has a rank of 3.
8) So this means that our nullspace is 5-3 = 2. 2 elements in N(S)
And then from here I'll use simple substitution to find N(S) and so on and so forth.
Most people don't learn this way though. If a person can't use a method over and over again to solve a problem, they just seem to be stumped by it.
*looks at what he just did* I'm a nerd....
Oh, I do hate English and history though. 1942 and 1492 should not be that big of a difference
Heh. Currently though, I'm into C++ programming so you're not alone in the nerd aspect.
Mathematician speaking.
I freaking love math. It makes me feel like a magician or something. From just a small number of rules I can imply just about anything, whether it be horribly abstract or concrete and applicable to daily life. I've come to realize though that I learn mathematics in a very strange way. Rather than memorizing the steps and formulas needed to solve the problems, I learned instead how to break the problems up into the simplest component pieces possible and derive my solution from there given the rules that I have memorized.
Thought this was normal for mathematician!
Math major speaking here BTW.
I think the same thing.EPIC HIGH FIVE!
In my experiences though, most people freak when they see a problem that is unfamiliar rather than trying to work it out little by little. I mean, it's not like you can't reverse your work to check the answer...
I think the same thing.
I mean, just because the triangle is a bit weird doesn't mean you can't use Pythagorean theorem. I don't get people.
What branch of math are you specialized in? I'm personally hoping to go into some type of geometry. Or toplogy. Algebraic, Differential, Symplectic, Geometric Group Theory, or something else.EPIC HIGH FIVE!
In my experiences though, most people freak when they see a problem that is unfamiliar rather than trying to work it out little by little. I mean, it's not like you can't reverse your work to check the answer...
Well, if it doesn't have a right angle you can't. Then you use the law of sines. Or the law of cosines.
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
I enjoy logic puzzles via numbers, sudoku, those little newspaper quizzes and straightforward maths, but, I can never-ever remember the god damn formulae!
Actually, my current plan is to go into the field of computer animation or cryptology. I'd probably be a pure mathematician otherwise. I don't know what I'd specialize in, though. I like all math too much. I think Theory of Artificial Intelligence would be interesting as well.What branch of math are you specialized in? I'm personally hoping to go into some type of geometry. Or toplogy. Algebraic, Differential, Symplectic, Geometric Group Theory, or something else.
Maths is like a puzzle except it can be very cute. You don't like puzzles? Maybe we hate all the rules to learn but puzzles are artificial -- made by man. There is something about describing the natural world -- can't put my finger on it --Can't stand maths. I understand a lot of what they talk about but I'm just not that interested in it. I'd rather be doing subjects like English than maths.
Maths is like a puzzle except it can be very cute. You don't like puzzles? Maybe we hate all the rules to learn but puzzles are artificial -- made by man. There is something about describing the natural world -- can't put my finger on it --
English is like puzzles -- made by man. English has no rules. Maths is forever.
No one said it's easy. Math and English are are difficult or as easy as life itself.I don't get it...
No one said it's easy. Math and English are are difficult or as easy as life itself.
Take the counting numbers: one, two, three, four, five, and so on. Can you find ANYTHING interesting about those numbers?
For example, one is the start or the unity. Two is a pair.
Okay. Now what is the first number in that list you find uninteresting?
I think you should put x into an equation and solve for x.Well suppose that x is the first number that I find uninteresting. I could say that x is interesting BECAUSE it is the first uninteresting number. Does that mean there are no uninteresting numbers?
This is the Interesting Number Paradox. Though I still don't get what your point is...
My point ? That math is interesting.
Physics is the new maths. Example:unhinged said:I would think that most INTPs would like Mathematics. Its all about making coming up with ideas, making patterns and connections. Unfortunately the way mathematics is taught has reduced it to a bunch of rules and formula...
Also, assume that the balloon is a sphere.If it takes ten minutes to blow up a balloon to 13 cm in diameter, how much longer will it take to inflate the balloon to 39 cm in diameter? Assume that the pressure that the balloon exerts on the air inside is proportional to the surface area of the balloon, that you blow a constant number of molecules of air per unit time into the balloon regardless of the pressure, and that the balloon retains he same shape as it is being inflated.
It will take __________ more minutes to inflate from 13 cm to 39 cm
If it takes ten minutes to blow up a balloon to 13 cm in diameter, how much longer will it take to inflate the balloon to 39 cm in diameter? Assume that the pressure that the balloon exerts on the air inside is proportional to the surface area of the balloon, that you blow a constant number of molecules of air per unit time into the balloon regardless of the pressure, and that the balloon retains he same shape as it is being inflated.
It will take __________ more minutes to inflate from 13 cm to 39 cm
I would dispute 14 being boring. 1 fortnight = 14 days exactly.Physics is the new maths. Example:
Also, assume that the balloon is a sphere.
I suppose, paradoxes notwithstanding, I'd consider 14 to be the first boring number. It's not prime, it's not relevant to counting by tens or dozens, it's neither lucky nor unlucky, not a square or cube. To it's credit, though, it is preceded and followed by some awesome numbers. 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.... then another boring one.
True, perhaps we'll have to keep looking. 15's smack between 10 and 20, 16's a square, 17's prime, 18's a dozen and a half, 19's Steve Yzerman's number, 20's two tens, 21's just cool, 22's double numbers, 23's prime, 24's a case of beer, 25's obvious.I would dispute 14 being boring. 1 fortnight = 14 days exactly.
26 is interesting because it is exactly in between a square and a cube. It may be the only number like that but I haven't tried a proof.
But why do you think the others are interesting?
That's very good. 21 is also age for legally voting in some U.S. states. We've got 26, 27 is a perfect cube. What's next in our search for the 1st uninteresting number?True, perhaps we'll have to keep looking. 15's smack between 10 and 20, 16's a square, 17's prime, 18's a dozen and a half, 19's Steve Yzerman's number, 20's two tens, 21's just cool, 22's double numbers, 23's prime, 24's a case of beer, 25's obvious.