[mxdntz]

	Originally Posted by Monte314 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I do a seminar on teaching mathematics. If people are interested, perhaps I could make some of the materials available.

I'm interested
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[Monte314]

	Originally Posted by Jenny Penny To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I think math is a S thing early on when the basics must be learned, as mentioned above. However, math can be extremely creative and theoretical once the mathematician has a little more freedom to apply it in experimental areas (very N).

This is a very insightful comment. Kids are naturally equipped for mastery of bulk material by rote.... that's how we all learned to speak our respective languages. We just don't recognize it as rote learning becuase the "drill" is embedded in all of our personal interactions.

The mechanical basics must be in hand before any real "freedom" is possible. Mathematics seems to be the one area of study where poeple don't understand this.

We don't expect kids to read before they know the alphabet, and we don't expect musicians to play before they know the fingerings for the notes... but we still think that mastery of number facts and problem solving techniques "stifles kids creativity" in mathematics. The result is predictable: a stream of innumerate kids who "hate math" NOT because of excessive drill, but BECAUSE THEY CAN'T DO IT.

It is this intitutionalized teaching disability that is destroying our future technical base.

[Kisai]

I enjoy math. I have gotten an A in every course up to Calculus II (where I got a B - curses!).

I enjoy mathematics as a tool for engineering. I don't really get the mathematics problems posted on these forums where a monkey performs a five minute task a million times during the night. It doesn't seem useful to me, because its not applicable to the real world, and my brain turns off to it. To me, reality is the testing ground for ideas to work.

[JustMel]

	Originally Posted by Monte314 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	It surprises me that so many of us dislike math. I suspect it is because we were not introduced to it in the right way early-on. Does this make sense, or is it really a built-in aversion? I've always felt that innumeracy was less about "learning disability" and more about "teaching disability".

My biggest problem came when it was time for algebra because I couldn't make my brain understand letters and numbers in the same "sentence" in my 8th grade year they made me take algebra 1 and I had a teacher who taught senior college math teaching me and he would only explain things one way so I got frustrated and turned off. Finally my mother took the paper and erased all of the letters and just left blank spaces---I was fine after that. The teacher failed me because I forgot to put the letters back in on the final but the principal made him regrade with my actual grade because he said I had the answers correct even if the teacher didn't agree with how I got there.

I now hold an associate's in accounting and I double majored in Business Management and Religion. (insert joke here)

I'm currently working on an assocaiate's in paralegal. No desire to be a lawyer.

I like numbers when I'm doing taxes and dealing with the IRS for clients because I can bend them to fit where and how I want them to.

[Zeal]

Ah, maths. Up until High School I loved it. I wanted to work in a scientific profession, because it matched my way of thinking.
In High School... oh dear. I had terrible teachers that completely put me off the subject. I passed in maths, but I didn't learn anything about reasoning mathematically, it was all about memorizing formulas. It frustrates me, because I got good grades in other scientific subjects (Chemistry, Physics), but as I gradually hated maths more and more, I just couldn't see myself studying these subjects at University.

I now realize how fascinating the subject is, and just how far you it can take you. In a way, I regret the fact that I'm not studying science (physics, astronomy or maths). I grew up reading astronomy books, everything else just seems, at best, "OK-ish". I'm seriously considering studying maths/physics during my free time though.

[Theonymic]

	Originally Posted by Monte314 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I've always felt that innumeracy was less about "learning disability" and more about "teaching disability".

I agree. I have some experience tutoring my peers in various math courses, and I've had many of them say that I presented the ideas much differently from their professors. I even had a young man named Tadeh tell me "you just taught me more (about Business Calculus) in an hour and a half than my professor did in a month and a half." I suppose it's a result of the mindset I built around math...

...as a young child I'd go to visit my grandparents frequently, but during midday I'd often get quite bored, and when I (at about 10) learned about perfect square numbers (1, 4, 9, etc) I began calculating them and writing them down in order. When I got up to 10000 I sat back and analyzed the patterns that formed and came up with the formula (a+b)^2 = a^2 + 2ab + b^2 on my own. Around the same time I discovered things such as distribution in multiplication, which led to the development of my faculty for mental calculation, and things such as the somewhat-less-useful fact that the digits of anything divisible by 9 will (in decimal, at least) add up to a number divisible by 9.

From that I gained (or at the very least revealed) a tendency to the "do-it-yourself" approach to learning, as I pissed my stepmom off for years on end in never taking notes, but instead just staring at the board and daydreaming as the equations and whatnot were put up, and then, when it came time to do homework, reading through the textbook and figuring it out for myself. In this I not only learned what equations worked in what situations, but, in fact, how the math itself was working. This, I think, is what often leads to poor teaching: failing to really tell the students what is going on.

After trying several other majors I have finally settled on math and plan on at least being a teacher's assistant when in graduate school so that I can gain experience and decide if teaching is really for me.

[Monte314]

	Originally Posted by Theonymic To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	After trying several other majors I have finally settled on math and plan on at least being a teacher's assistant when in graduate school so that I can gain experience and decide if teaching is really for me.

Another thing you might consider: teach as a sideline.

If you get a graduate degree in a technical field, you will find that there are plenty of openings for adjunct instructors at junior colleges, colleges, and universities. You can generally set your own schedule, you don't have any of the full-time faculty administrivia or politics, and you can do as much or as little as you want. It's a terrific "hobby", second income, and retirement occupation.

I have a full-time position as a research scientist, and teach at three schools on the side (evenings, weekends, whatever I want). I love to teach, and I make an extra $30K a year for my "hobby". And, every once in a while, I develop something for class that I can use at work.

Finally, I've gotten first-shot at a lot of top-notch people to hire right out of school. I know their real skills, they know me... it's "win-win".

[Theonymic]

With a BA in math, how long would it take me to get a graduate degree in a technical field such as, say, computer science?

I would also like to mention that I hope to include musicianship as a decent part of my life.

[rokxal]

PHD's take a while, 4.5 years average I suppose.
MS depends on the program you're in as well as thesis requirements. 1-3 years usually.

[Monte314]

	Originally Posted by Theonymic To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	With a BA in math, how long would it take me to get a graduate degree in a technical field such as, say, computer science? I would also like to mention that I hope to include musicianship as a decent part of my life.

I got my MS in 1 year; typical is 2. You can do it part time, one or two courses a term. A standard MS runs 30 to 36 hours, (tern to twelve 3-hour courses) depending upon how you do it.

[Theonymic]

I didn't realize you were simply talking about an MS. I'm already on route for a BS, since I decide to keep my former major, petroleum engineering, as a minor.

[Shawn]

Loved it all, came easy once algebra made sense. Shawn

[Flamethrower]

	Originally Posted by Kisai To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I enjoy mathematics as a tool for engineering. I don't really get the mathematics problems posted on these forums where a monkey performs a five minute task a million times during the night. It doesn't seem useful to me, because its not applicable to the real world, and my brain turns off to it. To me, reality is the testing ground for ideas to work.

I've notice loads of INTJs saying this. Is this a Te approach to doing math? It has to be practical to make sense?

	Originally Posted by Monte314 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	It surprises me that so many of us dislike math. I suspect it is because we were not introduced to it in the right way early-on. Does this make sense, or is it really a built-in aversion? I've always felt that innumeracy was less about "learning disability" and more about "teaching disability".

Interesting comment Monte. I was always terrible at math when I was a kid but I don't think I really am. I think teachers often don't understand math themselves and have no passion for it so they just teach "practical" stuff without really being able to explain it. I have a really abstract understanding of mathematical things. I am not naturally good at practical every day things because I can see way too many possibilities and interesting questions. I love abstract questions and though experiments! So when I was a 5 year old and the teacher was saying 1 + 1 = 2 I was wondering "why in those increments and how do you know 2 follows 1 and not 1.5? What's between 1 and 1.5? Can you keep asking this question forever? Are numbers infinite? Does 0 really exist? How do you prove 1 + 1 = 2?" I remember being sent outside a lot to do my math so I guess teachers didn't like my questions! Probably because they couldn't answer them and didn't think they were important anyway. I think it would be better if teachers understood the basic history of mathematics and some of the philosophical questions that have been asked in the past. Then they wouldn't rubbish young children for wondering about the same thing. They would (hopefully) be more open minded. My first teacher at school, if I asked why 1 + 1 = 2 always answered "because it just does OK! Don't be so stupid" but I discovered later it takes a whole book to prove it. I would love to send that "book" to that teacher and ask who is stupid now (because she was a bitch also!) But children are naturally inquisitive and it's worth wondering what the answers to their questions are. Probably people stop liking math when they are still kids.

[PHS Philip]

Huh? It takes a whole book? Isn't it just the definitions of 1 and 2 because 1 is sort of the base unit of our number system?
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[Flamethrower]

	Originally Posted by PHSphilip To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Huh? It takes a whole book? Isn't it just the definitions of 1 and 2 because 1 is sort of the base unit of our number system? To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

Yeah, I saw some documentary on the history of math and there was some proof for 1 + 1 = 2 done at some point that was MASSIVE. If I can find the link maybe I will put it here.

[Mozzes]

	Originally Posted by Flamethrower To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Yeah, I saw some documentary on the history of math and there was some proof for 1 + 1 = 2 done at some point that was MASSIVE. If I can find the link maybe I will put it here.

It's not that massive and it's not particularly difficult though it does require knowledge of Peano arithmetic.

[Monte314]

	Originally Posted by Flamethrower To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Yeah, I saw some documentary on the history of math and there was some proof for 1 + 1 = 2 done at some point that was MASSIVE. If I can find the link maybe I will put it here.

In the opening decade of the 20th century, Bertrand Russell and Alfred North Whitehead published their Principia Mathematica ("Principles of Mathematics") to resolve formal logical problems that had arisen in the foundations of mathematics.

In this work (which runs multiple volumes) they sought to resolve problems that arise with the set-theoretic substructure of mathematics. They attempted to do this by completely rebuilding mathematics *from scratch* using their "theory of types".

It was on page 362 that they finally arrive at the proof that "1+1=2". Here is a copy of the page:


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Their theory of types was ultimately discredited. It was replaced by something called "ramified types", which didn't work either.

[ssrprotege]

"Principles of Mathematics"? When you mentioned it, I thought it must have been David Hilbert.....

[Monte314]

	Originally Posted by ssrprotege To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	"Principles of Mathematics"? When you mentioned it, I thought it must have been David Hilbert.....

Isaac Newton wrote a book having the same title, which he was encouraged to publish by his friend, Edmund Halley (of comet fame).

I don't recall DH writing anything with this title, but I'm not familiar with the totality of his work (which is very extensive).

[ClaireMD]

	Originally Posted by aparkedcar To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Since the INTJ type is typically, but not always, associated with engineering and scientific professions I was wondering if the vast majority of INTJs excel at math (algebra, calculus, trig, etc). I myself do not (unless we're talking about statistics). Am I a rare exception?

No. I couldn't actually do it well, but I thought it was beautiful, esp. calculus.

[ssrprotege]

	Originally Posted by Monte314 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Isaac Newton wrote a book having the same title, which he was encouraged to publish by his friend, Edmund Halley (of comet fame). I don't recall DH writing anything with this title, but I'm not familiar with the totality of his work (which is very extensive).

Well, I thought of David Hilbert because he wanted to set the principles of mathematics straight by attempting to make mathematics "logically perfect," the effort screwed up by Gödel's two Incompleteness Theorems.

[Mozzes]

	Originally Posted by ssrprotege To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Well, I thought of David Hilbert because he wanted to set the principles of mathematics straight by attempting to make mathematics "logically perfect," the effort screwed up by Gödel's two Incompleteness Theorems.

That is what Hilbert wanted. I suppose Principia could be considered a part of the Hilbert program since it was concerned with foundational consistency proofs. The only detail you muffed was that it was written by Russell and Whitehead.

[Hitorijime]

	Originally Posted by Monte314 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	It surprises me that so many of us dislike math. I suspect it is because we were not introduced to it in the right way early-on. Does this make sense, or is it really a built-in aversion? I've always felt that innumeracy was less about "learning disability" and more about "teaching disability".

I absolutely agree that innumeracy is a teaching disability. And it keeps getting worse.

Fear of math begins at a young age, when the grade school teachers (who never liked math themselves and so pass on that aversion to their students) make it 'easy' for their students by not forcing them to do all that 'hard work' which is necessary if one is ever going to excel in math or science. Almost all of my education major friends at school are terrified of math, and it's really sad to think that they're going to be teaching future generations that math is an evil subject. If you think about it, the younger you are the more impressionable you are, so even though you don't realize it, you're going to take a lot of what your grade school teachers said for granted. I know that I still have a slight fear of math, and if it wasn't for the fact that I was encouraged by my parents to take hard classes, then I probably never would have ended up in engineering. I had a horrible algebra class in eighth grade, and barely learned the subject at all, but I was stubborn and refused to retake the class in high school, picking up what I needed to know through the rest of my classes. I'm still hurting on some basic algebra concepts though, and I still freeze up sometimes, especially when I'm taking a math exam.

At the same time, if, for some reason, engineering doesn't pan out for me, I'm switching to math.

[Monte314]

	Originally Posted by Hitorijime To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I absolutely agree that innumeracy is a teaching disability. And it keeps getting worse. ... Almost all of my education major friends at school are terrified of math, and it's really sad to think that they're going to be teaching future generations that math is an evil subject.

I teach advanced mathematics and computer science courses. I can count on one *finger* the number of education majors I can recall having as students in my 32 years at 4 universities and 2 colleges.

I'd say more, but when I talk about "professional educators" I start frothing, and my keyboard fills up with spit.

[PreyingMantis]

I excelled at maths at school - was always top of the class. I still like statistical analysis because of the patterns it represents and what they mean about how the real world works. However i now can't be bothered with the mechanics of maths because i'm more interested in real principles in the world, having seen how complex and seemingly impossible they are. I would be much more interested in the theory of pure maths now - if i did a course in it or were introduced to it somehow. I think i could be good at it because it is just another way of dealing with abstract principles.

I also see now that the reason so many bright people that i know don't like it is because they never got a motive to learn it. They want to know about real things - not abstract principles. If they could be taught how analogous some mathematical principles are to things in the real world then i think they would like maths more and learn it much better and be as good at it as at other things they like. I suspect that different people learn the same subject in different ways because of different motivations, which are not always provided by teachers in school.