Of course you can! What an odd statement. Now, I think calculators should be banned until perhaps third grade; when you're that young, all you're doing is basic arithmetic, and it's important that you learn to do that without a calculator. However, when I was in seventh grade, we were allowed to use calculators for some tests and not for others. Surely that's restricting their use!

__________________
Gillian

"Now everyone was giving her that kind of look UFOlogists get when they suddenly say, 'Hey, if you shade your eyes you can see it is just a flock of geese after all.'"

"You can't erase icing."

"I can't believe it doesn't work! I found it on the internet, man!"

I agree.

While I can't support the following with any statistics, my experience with people I know (and know of) shows that many so-called "highly gifted" people don't go into high paying areas or "fulfil the potential" that the lesser gifted might expect them to.

This usually isn't because they *can't* fufil it or because they can't cope with it, it's simply because they don't want to. They don't need it. They already have enough intellectual wealth and are perfectly content to persue their own goals without persuing a theoretical maximum of monetary income.

This is something many people don't understand. They say: "he/she has the potential to do/earn so much, why doesn't he/she use it? what a waste."

No, no waste. It's above and beyond that. They are using it, but not for the goals others might expect. The goals are often invisible to others.

__________________
Ach, mein Sinn, wo willst du endlich hin, wo soll ich mich erquicken? Bleib' ich hier, oder wünsch' ich mir Berg und Hügel auf den Rücken?
Bei der Welt ist gar kein Rat, und im Herzen steh'n die Schmerzen meiner Missetat, weil der Knecht den Herrn verleugnet hat.

I agree with you entirely - an age under which they should not be used (not quite sure what 3rd grade is) and restriction after that. I never meant a complete ban at any age. This does not correspond to what I experienced in the UK where there seems to be no restriction on their use at all. Perhaps other here have more direct experience.

I agree with all this, and several other posts. My original post was really referring to the level of maths which the vast majority of the population actually needs - in my view just basic arithmetic. The calculator comes into force after that, and eliminates a lot of tedium. The posts disagreeing with my ban of the calculator all refer to a level of maths which only a small minority of the population achieves, a level at which the calculator is entirely appropriate.

You are probably right about that, but perhaps this is itself the problem-- maybe such a small proportion achieves a level where math starts to make sense, because we don't teach them that math should make sense (indeed, it is all about making sense). Being competitive in the modern marketplace may have something to do with asking people to understand some things that at present are relegated to a minority.

Mathematics, arithmetic. Lazy minds... So its how to teach the young to learn. Find there way. Only use the machine when you need to. Its a big ask. From my own honest down to earth logic. I will let those around me do the arithmetic for me... the show of's seem to enjoy it., and I will let them have their moment... I am that lazy mind who will let others do the work. I can now argue that makes me the cleaver one... you are free to disagree.

Exactly! I knew the answer in first grade, but didn't understand that if you have six piles of beans, with seven beans in a pile, you have forty-two beans total.

It wasn't until third grade that I learned the meaning behind 6 x 7 = 42, and by way of a similar illustration as the multiple piles of beans.

Are you sure it wasn't because he kept two sets of books? Not exactly what's meant by double-entry accounting, but...

Across the US this holds true, more so with math, from what I understand, than any other college curriculum (ie average salary correlates positively with the highest level of math taken in college).

__________________
If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

No, it was, indirectly, the double-entry accounting.

The Medici introduced semi-modern government administration in a time when that was rare. It allowed them to build up and keep tabs on a state that had a much stabler basis than your average feudal system. (The building is still there: the Uffizi [= "Office"], which is now a museum.)

Instead of just counting your 42 beans, double-entry accounting, among other things, lets you keep track of those beans throughout their stay in your possession, either as something your ordered (credit), have stored (passive capital), have sent to the kitchen (active capital), want to plant (layback investment), sell (debit), etc.

Double-entry accounting is a royal plain in the glass, but it's great for keeping things in order.

__________________
Ach, mein Sinn, wo willst du endlich hin, wo soll ich mich erquicken? Bleib' ich hier, oder wünsch' ich mir Berg und Hügel auf den Rücken?
Bei der Welt ist gar kein Rat, und im Herzen steh'n die Schmerzen meiner Missetat, weil der Knecht den Herrn verleugnet hat.

Yes I agree. I was just being factitious about the post just prior.

In fact equating 'value' with 'money' is probably the worst maths mistake we could ever make!

__________________
"You can't talk to a brick wall but you can do Graffiti"

I'm not sure what the not-US equivalents would be. Agewise, probably about nine. (It varies from kid to kid, in that I was held back a year based on my birthday--it's six days after their cutoff for entering kindergarten.) We were learning division that year; it's one of the only things I remember vividly from that teacher other than that he thought people wouldn't eat food that doesn't appeal to the eye as well. We agreed that he had clearly never eaten in our school's cafeteria.

__________________
Gillian

"Now everyone was giving her that kind of look UFOlogists get when they suddenly say, 'Hey, if you shade your eyes you can see it is just a flock of geese after all.'"

"You can't erase icing."

"I can't believe it doesn't work! I found it on the internet, man!"

You know what I think a lot of this comes down to is the attitude the majority of people have with learning. Please no one take offense to this but most of us where not taught how to learn properly and thus this effects our outlook later on in life. We try to rationalize why we don't need to know math to have a deep understanding of physics. We are happy to think that without doing the hard work that we can know something better then those that put in all the effort.

This doesn't only apply to maths and physics. Go to any sporting event and watch the many fans yell at the players for being stupid while they are sitting there 50 pounds over weight, eating hot dogs and drinking beer.

I realize many people will think my son is an exception because he is "Gifted" but while his genes might predispose him to be better than average academically I strongly believe much of his "Gift" comes from the environment he grew up in where I always promoted him to think about the world around him. Start learning colors before he was a year old, count before he was 2, do simple addition and subtraction, that many adults can't seem to do before he was 4, multiplication and division before he was in school and before he was 6 you could have him multiply 2 two digit numbers together in his head.

He's no math savant. It is all just encouragement and spending the time. Car drives where always filled with talking about something to do with learning. Kids are not stupid as many people treat them as. Get them learning early and they'll thrive. Just look at kids that grow up in multilingual homes. They learn 2 languages just fine often with very different grammar rules without mixing them up. This same learning ability, in my opinion, can extend to other topics like maths.

If a child starts learning maths early then they'll naturally be better at it as they get older for many reasons. The better you are at something the more enjoyment you get when doing it. Thinking that maths can be enjoyable just like sports or performing can be.

Much of the world has a problem in that education has played less and less of a role over the years. It became uncool to be smart. Parents don't get actively involved with their kids education and think their role is limited to parent teacher nights once a year and signing report cards. You'll find many parents that think being involved with your kids is limited to taking them to and watch them play in little league baseball or play soccer. I applaud parents that do this because it is more then many parents do these days and I know much more then my parents ever did with me. But they should think about doing the same with learning. Sit down with your toddler for a half hour or an hour a day to do some educational stuff. The more effort you put in early in their life the more benefit they gain overall.

If you are reading this and saying to yourself "But my kid isn't very academic so it would be wasted" then you are just making excuses for yourself.

My boy might be "Gifted" but I'm a strong believer that much of his gifts where learned behavior and I'd rather him be "less gifted" and more of his talents be "learned" because he'll have more of a drive to use his talents.

So argue that you don't need maths to know physics. It's just lying to yourself so you can feel better about your ignorance. If it doesn't interest you then fine. Maths and physics isn't for everyone. But I imagine that everyone on these boards has an interest in a bit of physics. So if you think you can have this superior knowledge about astronomy and physics without doing the fundamentals then you are only fooling the fools.

All this said don't use the "But my parents didn't encourage me when I was young and it is to hard now" excuse. There are plenty of people out there that have been unfit and overweight their whole lives and then decided to put in the effort. Sure it is harder for them then it is for someone that was fit and active their whole life but it can still be done if you want it.

I'll get down off the soap box now.

For me when I was learning arithmetic in primary school the turning point was an abacus. This was one of those toy ones but the teacher turned it sideways giving it columns with a base ten number system. Excellent because it taught me the concept of base ten weighting, showed me a certain symmetry between numbers of any power of ten. And demonstrated the concept of the zero place holder. I am getting a Russian abacus soon for my daughter. I think this would be a great tool for children in the early arithmetic years.

__________________
"You can't talk to a brick wall but you can do Graffiti"

LoL, you're right. However, my comment about two sets of books leading to the Medici's riches was only partially a joke...

Yes, it is. One of the varied things I've done was taking a turn as the "chief" (read "only") accountant for a small manufacturing concern (filled in for the owner's son when said son got a job in the big city). I love accrual-based accounting, kicked the payroll's but with Lotus 1-2-3, think the depreciation schedules put out by the IRS are a joke, and detest GAAP as being ridiculously over-complicated. In its defence, GAAP is but a small subset reflecting our incredibly bloated end-all/be-all tax code.

__________________
If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

__________________
Everyone is entitled to his own opinion, but not his own facts.

I remember when Apollo 13 (the movie anyways) was in trouble and Tom was having trouble with trusting some numbers. 3 or 4 people at mission control grabbed thier physics books? No! that reached for thier sliderules. The physics part was done already they only needed to apply the specific math

My point is knowing physics does not mean you can apply it to a specific event. That takes math. Burning kerosene provides thurst, physics. How much thurst will I get from 1 gallon, math.

__________________
What comes down didn't go up enough!

A thurst for 1 gallon of kerosene will certainly generate enough thrust to get you into heaven.

I'm actually quite familiar with the term, "double-entry accounting," having taken it throughout high school and college, and having worked a stint as an accountant.

What I'm referring to by "two sets of books" has nothing to do with double-entry accounting. It has to do with keeping one set of books for the government, and a second set which shows one's real profits, including all under-the-table payments and off-the-record deals/work done. The set for the government will show a modest net taxable income, thereby making you look like a respectable, marginally-successful businessman, while the second allows you to keep track of your Villa in France...

By the way, Peachtree uses double-entry accounting. Quickbooks does not.

I use Peachtree for my business.

__________________
If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

Yes, in quoting you I was referring to nauthiz' original comment on the Medici who's somewhat revolutionary introduction of modern accounting and administration to a Renaissance state helped make Florence one of the major forces of its day.

Now, the "two sets of books" you mean should only ever exist on paper (or where ever) in the official version. Writing down the other version is tantamount to delivering yourself to the prison gates. Just ask Al Capone.

__________________
Ach, mein Sinn, wo willst du endlich hin, wo soll ich mich erquicken? Bleib' ich hier, oder wünsch' ich mir Berg und Hügel auf den Rücken?
Bei der Welt ist gar kein Rat, und im Herzen steh'n die Schmerzen meiner Missetat, weil der Knecht den Herrn verleugnet hat.

Don't you mean a pane in the glass? Just kidding, couldn't resist.

__________________
Let's put together the pieces of The Grand Puzzle . (website - now revised)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

But you're equating calculating with mathematics.

Getting past numbers to actual mathematics is the main hurdle, mindless drilling of calculation actually gets in the way of that.

Using a calculator to find 6*7 frees the mind to look at the real problem.

__________________
‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

6*7 is one that's never stuck in my head. For whatever reason, I have to take a detour through either 6*6+6 or 7*5+7 instead.

I think there is a clear difference between the task of multiplying, say, 6.3475 * 7.64796 and the integers 6*7. My comments were in the context of school children unable to perform even the basic arithmetic. For most of the population, this is what mathematics is. If you need a calculator for 6*7 you are very unlikely to see a mathematical problem beyond that.

6*7 could take some Deep Thought. Do you know the answer to "What is six by nine?"

Do you mean in base thirteen?

__________________
Forming opinions as we speak

Hmm. Apparently I do.

Upon noting, further down the thread from where I posted, that we are now short of an OP, this is now edited to say...

Take the simple situation of a pendulum, swinging freely. Without the maths, you can't even work out how long its period is. You'd probably be quite surprised, too, to find out that for small perturbations, the period is independent of the displacement.

Taking a simple example a bit further, the maths tells you what happens when the displacement is not "small", and what difference you will get when it starts swinging on bigger arcs.

If you cannot approach even this most basic problem without the maths, then how can anyone hope to make a new and serious contribution to physics?

It seems to start off at a very, very basic level. For example, it explains vector addition in one of the lectures. Surely this is assumed knowledge before university level, isn't it?

Despite not doing the additional maths at high school that others did (it was not offered at mine), I was certainly comfortable with dot and cross products, how to calculate the closest approach of two lines in 3d space, angles between arbitrary vectors, and so on, long before university.

The first lecture I ever sat down in was a "refresher" on vector calculus, where they ran over the definitions and standard proofs (i.e. What is div.grad(v)) very quickly before launching straight into the more serious stuff.

And, although it is maybe not the best time in history to mention this, it is also the reason why many of us deserted physics for finance.

If we could leave aside the, er, unpleasantness exploded on the world by a small percentage of my former colleagues, maths was absolutely essential to everything that we did, including understanding exactly to how much risk we were exposed.

From understanding how to most efficiently locate and fix the source of a Cholesky error in a covariance matrix, through to both visualising and managing all of the partial derivatives of a price which was a function of fifteen different underlyings, it would have been inconceivable to become a succesful trader in recent years without really being very familiar with university level maths.

So its use, of course, goes far beyond "just" physics.

If the OP were still here, maybe the understanding that he would be equipping himself for a brighter future would encourage him to put in the hours of study that he eschews.

OK, last anecdote, I promise, but...

A few of my friends and I used to work on the checkouts in a supermarket. By the time I left, we had the modern scanners, but at the start it was electronic tills with buttons, so you typed the cost of each thing in by hand. On the whole, you never looked at the buttons, but just shifted the items off the belt with the left hand, and typed in the prices with the right.

Sometimes, rarely, you'd make a mistake with the buttons, such as typing in £21.56 instead of £2.15. The accepted methodology to fix this was explain what you'd done (you'd feel the mistake happening when you hit two buttons at once) to look over the remaining items on the belt, and then to come up, quickly, with something like;

"I'll put your dog food, flowers, wine and milk through for nothing, and your beers for 65 pence to correct the mistake."*

Then on you'd go with the rest of it.

Admittedly, we were all reasonably bright lads, but everyone was able to do this with no problem.

We all slowed when scanners were introduced, as the limiting factor became orienting the goods with the bar code down, as opposed to just passing them from the belt to the bagging area.

Ah, happy days...

*yes, we could have cancelled the incorrect price, but that required a supervisor, so was slower, and where on earth is the fun in doing it that way?

I don't understand. What do you mean by "work out" how long
the period is? Do you mean predict what the period of a pendulum
will be, given the length and so forth? I can generally estimate
the period of a pendulum by watching it. No math is involved.
If I want to be more precise I can use a stopwatch. Still no math.

That's pretty obvious, to a rough approximation, anyhow, just by
playing with a pendulum for a few minutes. I'm sure Galileo wasn't
the first to discover the relationship.

What "basic problem" involving pendulums did you mean to say can't
be approached without maths?

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves