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flaymond
November 18th, 2014, 02:45 PM
Mathematics being the most important thing to learn in the world we living by now. But, it has been the most hated subject in the world to learn by majorities of the teenagers and younger. Many people including me :( don't like to learn it because the difficulties to get success on some topics. Do you know anyway to make the 'hatefullness' of teenagers to Maths wiped away? Any tips to share? Also, any 'powerful' motivation quotes or words that you can share with us to increase kids motivation to learn Maths?



* I love programming, but I like to learn Maths more and more. I actually don't love to learn it, but with programming, I can wiped the 'lazy' and 'duh' feels.... ( the reason is I found the power and beauty of it in programming works)

thatguruguy
November 18th, 2014, 05:50 PM
Hi. Long time listener, first time caller.

No matter how much my son tries, he can't sing particularly well. My daughter, however, is pretty good at it. She is much more musically inclined, and always has been. Her brain is wired differently from his.

Math was always easy for me to learn (at least through calculus and linear algebra). It's even easier for my oldest sister, who is an actuary.

I guess my point is, don't assume that something that is difficult for you is universally difficult. Different people have different aptitudes.

Matthew_Harrop
November 18th, 2014, 06:56 PM
I'm not particularly sharp at mathematics, however I (try) to deconstruct what i am attempting to learn into small steps (The smaller the better) Learning each step carefully and understanding its use is key, as is taking copious notes. Try looking at some of the MIT free lectures and course materials (http://ocw.mit.edu/courses/find-by-topic/) and reading/watching the stuff on there. Watch/read and rewatch/reread all the stuff on there till you fully understand what you're looking at.
Also, keep up the momentum! Momentum is key. Don't miss evening/weekends of learning, that is a killer.
Don't worry about the length of time it takes you to get to the party, but rather embrace the fact that your on the road there at all :)

This makes learning a bit long winded, but i fully understand the thing i am attempting to learn then. Its the only way I can do it.

Remember, the length of time it will take you to learn something is fixed, so the faster you get started, the faster you get it done!

coldraven
November 18th, 2014, 06:59 PM
Learning something is all about how interesting your teacher can make it. I was never a genius at Maths but at college I had good teachers and even learned how to calculate quantum mechanics.
I cannot remember any of it now :lolflag:

user1397
November 18th, 2014, 07:49 PM
I agree with thatguruguy on the fact that different people have different aptitudes, and also matthew_harrop and coldraven make good points on how to learn. I will say I've always asked myself that same question interprog, about how we can make learning maths (and indeed other difficult subjects) more interesting to students. It's hard to explain to a student why it is important to know how to calculate derivatives day in and day out...and honestly, there are few practical uses for it (I know some people here might object to this statement, but what I mean is for most practical applications, job, and careers, no one "needs" higher math like calculus). If anything, for most people it is a way to open up their mind and teach them how to solve complex problems, and this can lead to higher brain function and increased synapse connections (or so some believe).

I was always generally good at math, but I never really enjoyed it. I never sat down looking at math homework and went "yay! I'd rather do this than anything else right now!" If only we could find a way to harness that feeling for students then the world might be a better place :)

lisati
November 18th, 2014, 08:05 PM
IMO a connection with real life can sometimes be of help.

For engineering and physics work, knowing at least the basics of topics like calculus could conceivably have an application, but, to be honest, I haven't used it since studying it 40 years ago.

When helping Mrs Lisati with the shopping, basic numeracy, and possibly a hint of algebra, helps me more with figuring out how best to stretch the budget to get the best possible value for money than any of the "advanced" topics. Knowing that sin^2(x) + cos^2(x) = 1 doesn't really help me that much at the supermarket!

monkeybrain20122
November 18th, 2014, 08:10 PM
Self fulling prophecy. We send these messages to children at a very young age: math is boring, math is hard, math is not cool.. It is also very badly taught in many schools by teachers who don't know the subject very well themselves, for example, the way calculus is taught in most schools and even some universities is horrible in that they replace a conceptually very beautiful subject with mindless number crunching from formulae.

Then there is the utility philosophy that math is a necessary evil for doing other useful things, but math is not just a tool, it is an art form, and it is also one of the highest achievements of human civilisation. Would you ask why learn poetry because you don't need it for work or doing shopping?? (well granted that poetry may not be your cup of tea, it is not mine, but it would be silly to ask what is the use of poetry, it doesn't need justification by utility)

sudodus
November 18th, 2014, 08:17 PM
Hi. Long time listener, first time caller.

No matter how much my son tries, he can't sing particularly well. My daughter, however, is pretty good at it. She is much more musically inclined, and always has been. Her brain is wired differently from his.

Math was always easy for me to learn (at least through calculus and linear algebra). It's even easier for my oldest sister, who is an actuary.

I guess my point is, don't assume that something that is difficult for you is universally difficult. Different people have different aptitudes.

+1

QIII
November 18th, 2014, 08:50 PM
As an Applied Mathematician and a developer of calculation intensive software for one of the largest multi-national Actuarial firms in the world, my two cents:

Mathematics is the fundamental language on which our understanding of the entire Universe is built. This even applies to shopping -- what is presented to you and how it is displayed are both the result of mathematical modeling by someone who is interesting in making you buy something, even if it is not what you need or want. Understand that and you will not be taken to the cleaners.

When I was learning Math early on, I was less interested in rote memorization of rules and formulas and more interested in why the rules and formulas were what they were. In High School, that led to straight A's -- and I am far from a genius -- and more than one lecture that ended with "so just do it that way and stop being difficult!". But I understood the "why" and that always served me well when the perfectly formed rule escaped me during a test. A quick review of the "why" in the margin got me going again.

Same thing at the University level. I was fortunate to have two Professors who were also interested in teaching the "why" first and then memorizing the rule second. One of them was a particularly hilarious guy named Chen. Everyone seemed to enjoy his classes.

Since I understood "why" because I sought those answers out, I was well prepared enough that I gained a reputation for falling asleep in class, waking up only long enough to ace quizzes and tests. The entire Math Department had a running joke something to the effect that maybe everyone should sleep in class to improve their grades.

Dr. Chen had me teach one of his undergrad courses for credit one term. He would proctor by sitting in the back of the class and fall asleep (or feign it, as it turns out) almost immediately. At the end of the term, he brought me in for my evaluation and told me he was getting a "B".

I coughed. "How can you give me a B? You don't know what I was doing because you always fell asleep in my class!"

His expression didn't flinch. "Ah. You fall asleep in my class all the time."

"But I get As!"

He smiled wryly. "OK. A it is, then!"

So, here's my take: Mathematics is taught wrong, particularly here in the States. Rote memorization preceeds understanding the concepts. It may be several terms down the road before one suddenly encounters the answer to the "why" in a higher level course.

The "why" should be taught first, which not only aids the memorization of the formula or process but serves well in the case where one does not immediately remember the rule. It also make the process much more interesting and fun.

When my kids were in school I helped them by teaching them why the rules they were asked to memorize were what they were. I taught them to take a breather in tests and make margin notes to re-derive the rule if they forgot it in the heat of the moment. They both got excellent grades in Math classes.

(The same process, by the way, helped them learn when we were working on cars. Instead of "Part A gets bolted to part B and then gets slid into part C", I taught them to understand how and why something like an engine works. The assembly process then became relatively trivial. Learning how the engine and all of its various parts work together was a lot more fun for them than just memorizing the steps in disassembly and reassembly of the water pump.)

To this day there are formulas I don't bother to remember or fill my head with. I take 30 seconds to derive the formula from my understanding of the underlying concepts. That is,
I understand the MATH and don't bother remembering the particular steps in order (except, of course, if it something I use often enough that I can't help but remember!) Math is not a series of formulas. Those are only the convention we use to express concepts.

If a student is having trouble remembering what all the formulas in Trigonometry are, for instance, teach them to use the Unit Circle to conceptualize them. They'll not have to remember the specifics of dozens of formulas. They'll understand the Math, not an inscrutable, disjointed series of formulas they will surely conflate and use incorrectly.

All of the preceeding is to say that I don't think that it is so much that Math (to a certain point -- it is certainly true that each person has their own aptitudes and strengths) is hard to learn as that it is not taught correctly.

Just one professional Mathematician's opinion.

user1397
November 18th, 2014, 11:18 PM
As an Applied Mathematician and a developer of calculation intensive software for one of the largest multi-national Actuarial firms in the world, my two cents:

Mathematics is the fundamental language on which our understanding of the entire Universe is built. This even applies to shopping -- what is presented to you and how it is displayed are both the result of mathematical modeling by someone who is interesting in making you buy something, even if it is not what you need or want. Understand that and you will not be taken to the cleaners.

When I was learning Math early on, I was less interested in rote memorization of rules and formulas and more interested in why the rules and formulas were what they were. In High School, that led to straight A's -- and I am far from a genius -- and more than one lecture that ended with "so just do it that way and stop being difficult!". But I understood the "why" and that always served me well when the perfectly formed rule escaped me during a test. A quick review of the "why" in the margin got me going again.

Same thing at the University level. I was fortunate to have two Professors who were also interested in teaching the "why" first and then memorizing the rule second. One of them was a particularly hilarious guy named Chen. Everyone seemed to enjoy his classes.

Since I understood "why" because I sought those answers out, I was well prepared enough that I gained a reputation for falling asleep in class, waking up only long enough to ace quizzes and tests. The entire Math Department had a running joke something to the effect that maybe everyone should sleep in class to improve their grades.

Dr. Chen had me teach one of his undergrad courses for credit one term. He would proctor by sitting in the back of the class and fall asleep (or feign it, as it turns out) almost immediately. At the end of the term, he brought me in for my evaluation and told me he was getting a "B".

I coughed. "How can you give me a B? You don't know what I was doing because you always fell asleep in my class!"

His expression didn't flinch. "Ah. You fall asleep in my class all the time."

"But I get As!"

He smiled wryly. "OK. A it is, then!"

So, here's my take: Mathematics is taught wrong, particularly here in the States. Rote memorization preceeds understanding the concepts. It may be several terms down the road before one suddenly encounters the answer to the "why" in a higher level course.

The "why" should be taught first, which not only aids the memorization of the formula or process but serves well in the case where one does not immediately remember the rule. It also make the process much more interesting and fun.

When my kids were in school I helped them by teaching them why the rules they were asked to memorize were what they were. I taught them to take a breather in tests and make margin notes to re-derive the rule if they forgot it in the heat of the moment. They both got excellent grades in Math classes.

(The same process, by the way, helped them learn when we were working on cars. Instead of "Part A gets bolted to part B and then gets slid into part C", I taught them to understand how and why something like an engine works. The assembly process then became relatively trivial. Learning how the engine and all of its various parts work together was a lot more fun for them than just memorizing the steps in disassembly and reassembly of the water pump.)

To this day there are formulas I don't bother to remember or fill my head with. I take 30 seconds to derive the formula from my understanding of the underlying concepts. That is,
I understand the MATH and don't bother remembering the particular steps in order (except, of course, if it something I use often enough that I can't help but remember!) Math is not a series of formulas. Those are only the convention we use to express concepts.

If a student is having trouble remembering what all the formulas in Trigonometry are, for instance, teach them to use the Unit Circle to conceptualize them. They'll not have to remember the specifics of dozens of formulas. They'll understand the Math, not an inscrutable, disjointed series of formulas they will surely conflate and use incorrectly.

All of the preceeding is to say that I don't think that it is so much that Math (to a certain point -- it is certainly true that each person has their own aptitudes and strengths) is hard to learn as that it is not taught correctly.

Just one professional Mathematician's opinion.Agreed. The 'why' is probably the key to the whole argument. Good read.

sudodus
November 19th, 2014, 07:30 AM
So, here's my take: Mathematics is taught wrong, particularly here in the States. Rote memorization preceeds understanding the concepts. It may be several terms down the road before one suddenly encounters the answer to the "why" in a higher level course.

The "why" should be taught first, which not only aids the memorization of the formula or process but serves well in the case where one does not immediately remember the rule. It also make the process much more interesting and fun.


Learning physics you can either start from the fundamental theory and make experiments that show how the theory is applied, or make experiments and try to abstract a governing theoretical law (like Einstein) or be shown how such a law can be used to describe the experiment (for the rest of us). Both ways have advantages and disadvantages.

I think it can be similar within math. The conventional way of teaching is 'doing the experiment first - showing how it works' and then (for those interested and talented enough) showing the general law (in this case mathematical theorem). The other alternative is to start with the theorem, the 'why', and it worked well for you QIII, but I don't think it works well for everybody.

Maybe the best method is a mixture of both ways to learn, an iterative process, gradually getting familiar with concepts and using them in more advanced ways. Of course a good teacher can help a lot.

carl4926
November 19th, 2014, 07:51 AM
Learning something is all about how interesting your teacher can make it. I was never a genius at Maths but at college I had good teachers and even learned how to calculate quantum mechanics.
I cannot remember any of it now :lolflag:

Often quoted and truth in it for sure.

Unfortunately, at least here in the UK, school is too focused on league tables. 'Teach the learners how to pass', rather than 'Teach the learners'.
Post school, as in College, you might fare better. Where hopefully, teachers look at individual inclusion by differentiation.

flaymond
November 19th, 2014, 09:09 AM
+1

SagaciousKJB
November 19th, 2014, 10:18 AM
I think it's weird how often I use very complex math, given my totally limited education. See I dropped out of high school and got my GED in the 9th grade, never even learned algebra. But I've gone on to use things as complex as trigonometry for a machining job, statistical analysis routines for use in target shooting ( finding the best ballistic coefficient to plot my projectile's trajectory ), and while I don't ever really understand the mathematics behind what I'm doing, I'm a pretty good programmer.

I've tried to teach myself algebra... I mean I teach myself most other things, why would it be any harder? But I don't know, I guess I'm just one of those people that without having something practical they can apply the theoretical to, they just cannot conceive how those principles can do anything, let alone things that they are interested in.

I think if I offered my opinion it would border too much on political drivel... But I just don't think that the public school systems today do a good job of engaging kids in it. I think Qill has the right idea of the problem, but the issue is the solution is always very poorly executed. I remember teachers trying to make math "cool" by doing things like teaching fractions with slices of pizza, almost pandering to the kids that didn't want to pay attention to pay the least attention. Then the kids that did want to know why, were told "Just do it like this," and then taught a shortcut to pass some standardized test. I guess it's kind of predictable for a high-school dropout to blame the education system, but I'm just saying for a guy who never learned algebra and dropped out in the 9th grade, I sure have learned ( often times teaching myself ) quite a few skills that use complex mathematics.

coldraven
November 19th, 2014, 11:24 AM
The "why" should be taught first, which not only aids the memorization of the formula or process but serves well in the case where one does not immediately remember the rule. It also make the process much more interesting and fun.

QIII is correct. I was taught matrices* when I was about 15 years old.
I learned how to do every sort of manipulation with them but was never told what they were useful for :(
Decades later and I still don't know what they are useful for! :)

* http://en.wikipedia.org/wiki/Matrix_%28mathematics%29

monkeybrain20122
November 19th, 2014, 11:31 AM
It would make a lot more sense to talk about vector spaces and linear transformations before talking about matrices. Geometry always makes more sense :) My background is pure mathematics, we always ask why even if we have no idea how to actually do the computations. :)

Nice post Qill!

coldcritter64
November 19th, 2014, 06:12 PM
....

So spot on gotta give it a, +∞
Excellent read indeed. Cheers. :)

uRock
November 20th, 2014, 01:44 AM
If I can't punch it into my calculator, then I don't bother with it.

mfilacchione
November 20th, 2014, 02:07 AM
I have never personally found Math to be "HARD", yes I have said that is over the years, especially when I was in High School, but I do not think I ever found it hard. If anything I found it boring and that is what made it hard for me to focus on. I honestly could not focus on Math at all, especially in high school. I was always so far behind in my math class's. It usto to puzzle my math teachers, I was always corned with questions like "how are you so good in computers, but your performance in this math class is not good?". Other times I would puzzle some of my science teachers, they would see me working on some kind of project that would involve calculating a speed of a dinosaur from their fossilized foot prints, or working on projects related to existence of black wholes, and ect.

In general when I was in some sort of algebra class or even in grade school learning fractions I never seen any practical application for the information. Even now I rarely use any of it in in everyday life. I do some measurements in fractions at times (for food and building lol). When it comes to algebra or calculus I do not believe I use it all and do not plan to any time soon. Other then that I calculate Hex and Binary numbers, oh and I can give change lol..

echotech2
November 20th, 2014, 11:10 AM
1+1=2, for most values of 1.

coldraven
November 20th, 2014, 11:34 AM
1+1=2, for most values of 1.

Yes but 2+2=5 because some(one) has to be doing the counting. Seriously!

Thee
November 20th, 2014, 12:36 PM
Learning something is all about how interesting your teacher can make it. I was never a genius at Maths but at college I had good teachers and even learned how to calculate quantum mechanics.
I cannot remember any of it now :lolflag:

+1

coldcritter64
November 20th, 2014, 07:42 PM
If I can't punch it into my calculator, then I don't bother with it.

:-k ... wonder how you'd go with imaginary numbers (http://en.wikipedia.org/wiki/Imaginary_number) ... great fun to wrap ya head around :biggrin:

QIII
November 20th, 2014, 07:51 PM
Executive: What's 1 + 1?

Accountant: What do you want it to be?

uRock
November 20th, 2014, 10:10 PM
:-k ... wonder how you'd go with imaginary numbers (http://en.wikipedia.org/wiki/Imaginary_number) ... great fun to wrap ya head around :biggrin:

Lol, I dealt with those in one of my lower level math classes. They were interesting. I did fine in my physics classes, but I didn't bother trying to retain the equations. If I ever need them, I still have the text book.:p

Old_Grey_Wolf
November 20th, 2014, 10:40 PM
Everyone learns differently. I learned mathematics best when it was applied mathematics. I didn't learn it well when it was just theory.

My father was an engineer. I helped him build a house on his lake property when I was 10 to 12 years old. He taught me geometry and trigonometry in the process; however, I didn't know that it was those complicated maths at the time. Later in school, I was fortunate enough to learn calculus from a teacher that applied it to every day applications.

The same applies for programming languages. I learned by deciding on a goal and making it happen. I had a references with the commands and figured it out. Later by sharing my work I learned more efficient ways to accomplish my goal.

mips
November 20th, 2014, 11:13 PM
As an Applied Mathematician and a developer of calculation intensive software for one of the largest multi-national Actuarial firms in the world, my two cents:

Mathematics is the fundamental language on which our understanding of the entire Universe is built. This even applies to shopping -- what is presented to you and how it is displayed are both the result of mathematical modeling by someone who is interesting in making you buy something, even if it is not what you need or want. Understand that and you will not be taken to the cleaners.

When I was learning Math early on, I was less interested in rote memorization of rules and formulas and more interested in why the rules and formulas were what they were. In High School, that led to straight A's -- and I am far from a genius -- and more than one lecture that ended with "so just do it that way and stop being difficult!". But I understood the "why" and that always served me well when the perfectly formed rule escaped me during a test. A quick review of the "why" in the margin got me going again.

Same thing at the University level. I was fortunate to have two Professors who were also interested in teaching the "why" first and then memorizing the rule second. One of them was a particularly hilarious guy named Chen. Everyone seemed to enjoy his classes.

Since I understood "why" because I sought those answers out, I was well prepared enough that I gained a reputation for falling asleep in class, waking up only long enough to ace quizzes and tests. The entire Math Department had a running joke something to the effect that maybe everyone should sleep in class to improve their grades.

Dr. Chen had me teach one of his undergrad courses for credit one term. He would proctor by sitting in the back of the class and fall asleep (or feign it, as it turns out) almost immediately. At the end of the term, he brought me in for my evaluation and told me he was getting a "B".

I coughed. "How can you give me a B? You don't know what I was doing because you always fell asleep in my class!"

His expression didn't flinch. "Ah. You fall asleep in my class all the time."

"But I get As!"

He smiled wryly. "OK. A it is, then!"

So, here's my take: Mathematics is taught wrong, particularly here in the States. Rote memorization preceeds understanding the concepts. It may be several terms down the road before one suddenly encounters the answer to the "why" in a higher level course.

The "why" should be taught first, which not only aids the memorization of the formula or process but serves well in the case where one does not immediately remember the rule. It also make the process much more interesting and fun.

When my kids were in school I helped them by teaching them why the rules they were asked to memorize were what they were. I taught them to take a breather in tests and make margin notes to re-derive the rule if they forgot it in the heat of the moment. They both got excellent grades in Math classes.

(The same process, by the way, helped them learn when we were working on cars. Instead of "Part A gets bolted to part B and then gets slid into part C", I taught them to understand how and why something like an engine works. The assembly process then became relatively trivial. Learning how the engine and all of its various parts work together was a lot more fun for them than just memorizing the steps in disassembly and reassembly of the water pump.)

To this day there are formulas I don't bother to remember or fill my head with. I take 30 seconds to derive the formula from my understanding of the underlying concepts. That is,
I understand the MATH and don't bother remembering the particular steps in order (except, of course, if it something I use often enough that I can't help but remember!) Math is not a series of formulas. Those are only the convention we use to express concepts.

If a student is having trouble remembering what all the formulas in Trigonometry are, for instance, teach them to use the Unit Circle to conceptualize them. They'll not have to remember the specifics of dozens of formulas. They'll understand the Math, not an inscrutable, disjointed series of formulas they will surely conflate and use incorrectly.

All of the preceeding is to say that I don't think that it is so much that Math (to a certain point -- it is certainly true that each person has their own aptitudes and strengths) is hard to learn as that it is not taught correctly.

Just one professional Mathematician's opinion.

I'm gonna reply to this later but QIII is almost right on the mark and it probably gonna devolve into a us vs them scenario.

flaymond
November 21st, 2014, 07:41 AM
+10

bro2
November 21st, 2014, 09:08 AM
Mathematics being the most important thing to learn in the world we living by now. But, it has been the most hated subject in the world to learn by majorities of the teenagers and younger. Many people including me :( don't like to learn it because the difficulties to get success on some topics. Do you know anyway to make the 'hatefullness' of teenagers to Maths wiped away? Any tips to share? Also, any 'powerful' motivation quotes or words that you can share with us to increase kids motivation to learn Maths?



* I love programming, but I like to learn Maths more and more. I actually don't love to learn it, but with programming, I can wiped the 'lazy' and 'duh' feels.... ( the reason is I found the power and beauty of it in programming works)

1. People have different levels of aptutude BUT

1b. Math in general is harder then other high school subjects like English or History, where you just need to pick up the "gist" of whatever you're doing. In math, you need to concepulize things, then build off those. You don't do that as often in other subjects. TLDR: Math is harder, thus lots of people hate it.

uRock
November 21st, 2014, 05:19 PM
1. People have different levels of aptutude BUT

1b. Math in general is harder then other high school subjects like English or History, where you just need to pick up the "gist" of whatever you're doing. In math, you need to conceptualize things, then build off those. You don't do that as often in other subjects. TLDR: Math is harder, thus lots of people hate it.

The lack of students learning proper English is just as bad, if not worse than math. I've seen cashiers have a hard time making change for a purchase and I've seen even more folks who get "then" and "than" wrong on a regular basis.

QIII
November 21st, 2014, 05:33 PM
Then it seems as though English teachers are a somewhat less effective than they should be.

monkeybrain20122
November 21st, 2014, 09:19 PM
The lack of students learning proper English is just as bad, if not worse than math. I've seen cashiers have a hard time making change for a purchase and I've seen even more folks who get "then" and "than" wrong on a regular basis.

Well 'then' or 'than' is only a convention therefore is somewhat arbitrary anyway. English is not the native tongue of most humans and it changes over time. Mathematics is universal and timeless (and perhaps transcends humanity if you want to get philosophical, 1 + 1 would be 2 even for aliens) :)

1clue
November 21st, 2014, 10:01 PM
QIII's post is exactly correct IMO.

People might be better at learning "pure" math but first they need to know WHY they should be even interested.

I hated math as a kid. It was extremely difficult, I didn't know why I needed to know this stuff, and the story problems were inane and made everything even less pleasant. Train A and train B, what? Why should I care about the @$@%^ train?

OK for the high school kids: Your parents are kicking you out of the house when you're 18. You make minimum wage and are guaranteed 30 hours a week. Rent is $500/month. You need $200 a month for food. You need $50 a month for incidentals like clothes or whatever. Your utilities will cost about $100 a month. How much is left for recreational purposes?

Answer for my location: $25. You need a roommate, or you will live like a drone. I think a more realistic number would be a negative one. So the next story problem, something about how to divide the unequal sized rooms fairly. Or how much that car actually costs you to own, and whether you can afford it.

I struggled through college, finally got to third-semester calculus where the teacher explained the why for the first time. He made it interesting. He would pick somebody, say mechanical engineers for example. He would ask them what they were learning, and then he would derive the formula they were using on right up on the board, just off the top of his head. He was legally blind so there was no chance of him reading it from somewhere.

After college I found myself building houses. Not from an engineering standpoint, I was the guy swinging the hammer. I was astounded at how much calculus and limits applied to every-day living. The reason for the angle of your roof, for example, based on what kind of materials are used, their characteristics and their cost, even how strong the wind blows in that area. The roof angle is described as pitch, which is a tangent: 4-12 pitch is 4 feet rise for 12 feet run, this is applied trigonometry!

Every aspect of house construction I came across, I could reverse-engineer the logic as to why it was done that way. This was far more interesting than math classes ever were.

uRock
November 21st, 2014, 10:16 PM
Well 'then' or 'than' is only a convention therefore is somewhat arbitrary anyway. English is not the native tongue of most humans and it changes over time. Mathematics is universal and timeless (and perhaps transcends humanity if you want to get philosophical, 1 + 1 would be 2 even for aliens) :)

"then" and "than" have been the same in every dictionary as long as I remember. Most of the people I see using those wrong were born and raised here in the US. "than" is a mathematical term, so I think it is very important to be able to distinguish the difference.

uRock
November 21st, 2014, 10:18 PM
Then it seems as though English teachers are a somewhat less effective than they should be.

I can't say much in regard to that without getting political, aside from saying "I agree".

QIII
November 21st, 2014, 10:52 PM
Was subtly distinguishing between then/than in the English language, not teachers from the UK, of course. ;)

monkeybrain20122
November 22nd, 2014, 05:45 AM
"then" and "than" have been the same in every dictionary as long as I remember. Most of the people I see using those wrong were born and raised here in the US. "than" is a mathematical term, so I think it is very important to be able to distinguish the difference.


What I meant was that all human languages are conventional and therefore somewhat arbitrary. There is no intrinsic reason why "then" and "than" have the meanings they designate, it is just convention. Dictionaries are based on convention of usage ("grammar" on the other hand has a universal, intrinsic core ,-- to be differentiated from conventional grammar of natural languages such as English or Japanese. In a deep level grammatical structures are universal to all languages. This was discovered by Noam Chomsky)

carl4926
November 22nd, 2014, 05:53 AM
After college I found myself building houses. Not from an engineering standpoint, I was the guy swinging the hammer. I was astounded at how much calculus and limits applied to every-day living. The reason for the angle of your roof, for example, based on what kind of materials are used, their characteristics and their cost, even how strong the wind blows in that area. The roof angle is described as pitch, which is a tangent: 4-12 pitch is 4 feet rise for 12 feet run, this is applied trigonometry!

Every aspect of house construction I came across, I could reverse-engineer the logic as to why it was done that way. This was far more interesting than math classes ever were.

The practical application element of teaching is often under supported and not always a viable option given the circumstances.

Your comments are no surprise to me at all.

Well done on your development of such important life skills, they are of great value.

QIII
November 22nd, 2014, 07:05 AM
I also have a degree in Modern Languages and Literatures (German, specifically). So I can continue to pontificate. :)

No. Human languages and their various vocabularies are not arbitrary. What you may be correct in saying is that a language's words -- the sounds articulated and the symbols used to represent them -- have no immutable and intrinsic universal value when divorced from the context of the societies and cultures from which they sprang.

They have evolved over tens (perhaps hundreds) of thousands of years to effectively communicate ideas in a manner most likely to be understood and least likely to be misinterpreted within the communities in which they are used. They have evolved every bit as much as have our ears and noses -- neither of which is arbitrarily assigned a function.

This is true both of highly analytic languages (such as Mandarin Chinese) and highly inflected languages (such as Latin).

"Then" and "than" have evolved in Modern English to represent entirely different concepts that are not arbitrary.

"Than" is comparative.

"Then" is associated with time, order, consequence or case depending on context. Words may mean different thing in different contexts. But, then again, the context is well-defined and not arbitrary.

If words were genuinely arbitrary, we would not be playing on our computers, surfing the web and reading about probes landing on comets. We would be running away screaming inarticulately because we had just watched Grog get eaten by a bear because we were not able to agree how to let him know to watch his back.

"Run, Grog! There is a bear coming up behind you!" works because the grammatically well-constructed series of non-arbitrary words with accepted definitions conveys a very well-understood message. And that is why using language correctly is important. Friends don't let friends get eaten by bears.

Thus ends my sermon for now...

carl4926
November 22nd, 2014, 07:33 AM
Words in context
English is crazy sometimes

'Do you have a invalid parking ticket?'
Is that because it expired or because you are and invalid?

QIII
November 22nd, 2014, 07:38 AM
George Carlin was the master of pointing out the silly nature of some expressions.

"Get on the plane? <expletives which, in the interest of the forum rules, I will interpret as>No, thank you! I'm getting IN the plane!"

uRock
November 22nd, 2014, 06:36 PM
What I meant was that all human languages are conventional and therefore somewhat arbitrary. There is no intrinsic reason why "then" and "than" have the meanings they designate, it is just convention. Dictionaries are based on convention of usage ("grammar" on the other hand has a universal, intrinsic core ,-- to be differentiated from conventional grammar of natural languages such as English or Japanese. In a deep level grammatical structures are universal to all languages. This was discovered by Noam Chomsky)I get what you are saying in the sense that one's brain would calculate two apples in his hands even if he couldn't communicate it verbally. :)


I also have a degree in Modern Languages and Literatures (German, specifically). So I can continue to pontificate. :)

No. Human languages and their various vocabularies are not arbitrary. What you may be correct in saying is that a language's words -- the sounds articulated and the symbols used to represent them -- have no immutable and intrinsic universal value when divorced from the context of the societies and cultures from which they sprang.

They have evolved over tens (perhaps hundreds) of thousands of years to effectively communicate ideas in a manner most likely to be understood and least likely to be misinterpreted within the communities in which they are used. They have evolved every bit as much as have our ears and noses -- neither of which is arbitrarily assigned a function.

This is true both of highly analytic languages (such as Mandarin Chinese) and highly inflected languages (such as Latin).

"Then" and "than" have evolved in Modern English to represent entirely different concepts that are not arbitrary.

"Than" is comparative.

"Then" is associated with time, order, consequence or case depending on context. Words may mean different thing in different contexts. But, then again, the context is well-defined and not arbitrary.

If words were genuinely arbitrary, we would not be playing on our computers, surfing the web and reading about probes landing on comets. We would be running away screaming inarticulately because we had just watched Grog get eaten by a bear because we were not able to agree how to let him know to watch his back.

"Run, Grog! There is a bear coming up behind you!" works because the grammatically well-constructed series of non-arbitrary words with accepted definitions conveys a very well-understood message. And that is why using language correctly is important. Friends don't let friends get eaten by bears.

Thus ends my sermon for now...I concur. :)

QIII
November 22nd, 2014, 06:54 PM
Hee hee!

Compare two sentences that might be directed at Grog:

"The bear is bigger than you are!'

"The bear is bigger then you are!" (Which should be written "The bear is bigger, then you are!")

The first sentence compares the bear's size to Grog's, giving the clear impression that running might be a smart course of action for Grog.

The second indicates that at one point the bear is bigger than Grog, but at some later time Grog is bigger than the bear. This might lead Grog to turn around to confront the bear. This, in turn, would lead Grog to forfeit the genetic legacy he would otherwise have passed on to his progeny.

Following the bear's feast and the hasty retreat of Grog's friends, the linguistically adept humans might hunker around the fire in their cave and discuss the fact that it was not their fault that "then" and "than" are arbitrary.

As in Mathematics, understanding the concept first -- and then the form used to express the concept -- keeps everyone from being eaten alive either by bears or by University Professors.

(By the way, as a student of language I am quite well acquainted with the work of Noam Chomsky. That largely forms the basis for my understanding of language. Language is innate because we have evolved to use it -- and it has evolved with us. I am of the opinion that our innate understanding of Language and Mathematics are two sides of the same coin and are inextricably linked. That Mathematics is innate is demonstrated by our ability to catch a pop fly or hurl a spear at a running animal and hit it in the chest. Both require innate calculations of ballistic flight with consideration of the relative motion of two bodies in space/time. That is rocket science. Furthermore, a good outfielder is an even better Mathematician that most, as he is able to compute also the motion of a third and fourth body in motion -- and, after catching the fly, hurl the ball to the third baseman to put out the guy who tagged up on second base and is running to get to third. Without a supercomputer anywhere to be seen, the left fielder constantly calculates the motions of the ball, his body, the runner and the baseman; the future state of the system and the necessary flight of the ball after catching it to intercept the runner.)

Geez. A decade of University studies has served me well to discuss subjects both arcane and esoteric, but I still can't figure out my TV remote.

Paulgirardin
November 22nd, 2014, 08:50 PM
1. People have different levels of aptutude BUT

1b. Math in general is harder then other high school subjects like English or History, where you just need to pick up the "gist" of whatever you're doing. In math, you need to concepulize things, then build off those. You don't do that as often in other subjects. TLDR: Math is harder, thus lots of people hate it.

Yes.Just imagine if English had to be precise,the whole internet would cease to exist.

....Yes,I'm looking at you,Mr Bad Speller/Bad Grammar :lolflag:

Paulgirardin
November 22nd, 2014, 08:59 PM
Words in context
English is crazy sometimes

'Do you have a invalid parking ticket?'
Is that because it expired or because you are and invalid?
Yes ,but was the ticket ever alive?If not how could it have expired?Or become an invalid?

rewyllys
November 22nd, 2014, 11:23 PM
Carl asked, "Do you have an invalid parking ticket?", and then asked, further, "Is that because it expired or because you are and invalid?"

Where I live, parking tickets (i.e., citations by the police) never expire; the longer one ignores them, the more costly is the fine when one finally has to pay it.

Carl's alternative is that I am expired and invalid. But if I'm dead, then by definition I am now invalid as a person, and it seems superfluous to mention that fact (viz., my invalidity). Furthermore, whether or not I was an invalid prior to death is now a moot point.

PJs Ronin
November 23rd, 2014, 02:13 AM
@ QIII

I suddenly have an urge to inquire "Who's on first?", but shall for the moment refrain. Nonetheless, catching the flyball and throwing out the runner (that doesn't seem right, somehow) is, imo, no supercomputer feat. Said outfielder has been involved with countless pop flys and as we all know of the brain's penchant for jumping to conclusions the majority of the calculations boil down to "do I run right/left/out/in or stay put". After that, the rest is ingrained mechanics... which is math, hmmmm.

As to your/my caveman friend. I'll guess for a moment and assume he can't write but has excellent hearing. Unfortunately, if said caveman was here in Australia, or perhaps England, he would be questioning why you're shouting at a bottle of booze and why you were concerned about his naked rear (bare). Poor lad can't have a beer and a poop without someone yelling at him.

Just in case:
Grog:
noun


1.
spirits (originally rum) mixed with water.

QIII
November 23rd, 2014, 03:27 AM
Not throwing out the guy who popped up. He's out when the ball is caught. Throwing out the guy on second who might make it home on a pop fly after tagging up on second ...

You ferriners not understanding baseball. Sheesh! Next you'll tell me you don't watch NASCAR!

Grog? He always was a drunkard, which may explain why he was foolish enough to be hanging around a bare bear with a beer while searching for his TV remote.

flaymond
November 24th, 2014, 12:59 PM
:lolflag:

lisati
November 25th, 2014, 03:06 AM
Isn't language wonderful, with all its flavo(u)rs..........

WinEunuchs2Unix
November 28th, 2014, 04:51 AM
I've had a few kicks at the can with Binary, Octal and Hexadecimal math for Assembly programming on different mainframes. But what surprises me these days is the number of people that can't do multiplication tables such as 5 x 12 is 60.

Many people in the blue-collar field will suffer in job promotions for this lack of skill. And I mean A LOT OF PEOPLE.

echotech2
November 28th, 2014, 08:23 AM
I always had problems with the 1 times table. It doesn't make any sense. You multiply something and you end up with the same number you started with.

Dave_Tom
November 30th, 2014, 11:07 PM
Maths is a tricky subject because the majority of the time you need some background to learn something new. When kids don't grasp it from a young age they are on the back foot when it comes to learning new things a little later at school, and an already tough subject becomes even more so when you don't understand the building blocks needed for more complicated areas.

Like with anything in life, it is whether or not you can make things interesting that ultimately dictates how much effort you will put in. If you really enjoy a subject you are more inclined to work at it than one you don't. So relating Maths to things kids enjoy, in the modern day computer games are very popular for example, would be my suggestion. However, everyone has strengths and weaknesses, so you will always have people struggling with maths and others where it comes to more naturally.

tjeremiah
December 3rd, 2014, 04:49 AM
my first go @ college I failed math 5 times in a row. I was so bad, clearly, that I was placed in math 1 (adding,subtracting, etc). I felt so stupid that I couldn't progress. Took a year off, went to a newer college and was introduced to an awesome professor who made it all look fun and doable.

Started in math 1, then 2, did so good in 2 they put me in 9 (college algebra), passed that then moved to Pre-Cal (B+), and now im in Calculus 1 all in a year and a half!

Never give up, keep going. Find someone who is good at teaching and keep practicing writing the same problems over and over and over...

princecharming
December 3rd, 2014, 08:15 AM
It is a very interesting question that why Mathematics is so hard to learn??? A number of students are saying that this is very difficult subject for all of us to learn, because there are so many difficult sums as well as questions, which are our overhead pass.

taipan4000
December 11th, 2014, 12:53 PM
One of the issues with mathematics is that it gets learned for more or less for the sake of learning. Vary rarely do teachers of mathematics tell students how they can use or apply what they are learning outside the classroom. With subjects like physics, chemistry and biology it is easier to give practical examples of how to apply what is being learned.


The other problem is that about two-thirds to three-quarters of what we are taught we will never use, or come across outside the classroom.


During my university days I had to study a mathematics unit on eigenvectors – it was a compulsory unit. It was the most useless subject I have ever had to learn. More than thirty years later I still don't know of a practical application of eigenvectors.


To make students appreciate mathematics try to give them a sense of why they are learning it and where they might put into practice what they are learning.

sudodus
December 11th, 2014, 01:59 PM
It is never too late. Browse the internet with the search phrase applied eigenvectors and you may find some surprising applications :-)

taipan4000
December 12th, 2014, 01:27 AM
I just Googled eigenvectors - interesting stuff about computerized vision and eigenvectors. If the internet had of existed when I was studying I would have known more & been more positive about eignevectors at the time.

monkeybrain20122
December 12th, 2014, 11:55 PM
Only philistines ask 'what is the use?' Would you ask what is the use of music? :) Eigenvectors are very important in physics and engineering (physicists call them 'normal modes' for whatever differential operators under investigation) Yeah eigenvectors are important for understanding music as well, in that context they are related to harmonics.

RabbitWho
December 13th, 2014, 11:52 AM
I am thinking because the teachers don't understand it. They just memorized some stuff they don't understand. I don't know anything about this new "project maths" but I'm hoping it will be better.

I remember them telling me about "carry the one" what the hell? Where did that come from? You can't just do that!
I asked them why and they'd say "you just do!"
Then a year or 2 later with long division.. you just drag the zero from the top to down here where you need it... WHy!? You just do.


And it just went downhill from there.

Feynman has a story about helping his cousin with algebra, he tries to show his cousin how to get the answer and his cousin says "Yeah, but you did it with arithmetic, you're supposed to do it with algebra!"
It seems to me that if you can understand why you are doing things to the numbers then maths will still be difficult because there is eventually a lot to keep in working memory, but it won't be impossible because it will make sense.



Only philistines ask 'what is the use?' Would you ask what is the use of music? :smile: Eigenvectors are very important in physics and engineering (physicists call them 'normal modes' for whatever differential operators under investigation) Yeah eigenvectors are important for understanding music as well, in that context they are related to harmonics.

I got a infraction once for saying pretty much exactly what you just said. "Insulting other members".

OpenSaucer
December 14th, 2014, 04:11 AM
Philistines were a civilized and cultured people who got a bad reputation from people who didn't like them.


There is no such thing as a bad or dumb question and if anyone is uncomfortable with answering a question such as 'what is the use' is shows the failings of the person of whom the question is being asked. We learn by asking questions.


For most people, other than some historians or linguists, knowing Latin, ancient Greek, or Aramaic is no use. Likewise, most people have no use of quantum mechanics in the daily lives. I have even met people for who music has no relevance.

taipan4000
December 24th, 2014, 01:14 AM
I came across the following webpage yesterday. You might find it useful.

http://www.abc.net.au/radionational/programs/philosopherszone/why-mathematics-matters/5983140

Noah_Kiger
December 26th, 2014, 06:40 PM
I've always had troubles in math, it just takes more "brain power" to learn than most subjects.