# Estonian Schools To Teach Computer-Based Math

#### samzenpus posted about a year and a half ago | from the new-math dept.

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First time accepted submitter Ben Rooney writes *"Children in the Baltic state of Estonia will learn statistics based less on computation and doing math by hand and more on framing and interpreting problems, and thinking about validation and strategy. From the article: 'Jon McLoone is Content Director for computerbasedmath.org, a project to redefine school math education assuming the use of computers. The company announced a deal Monday with the Estonian Education ministry to trial a self-contained statistics program replacing the more traditional curriculum. “We are re-thinking computer education with the assumption that computers are the tools for computation,” said Mr. McLoone. “Schools are still focused on teaching hand calculating. Computation used to be the bottleneck. The hard part was solving the equations, so that was the skill you had to teach. These days that is the bit that computers can do. What computers can’t do is set up the problem, interpret the problem, think about validation and strategy. That is what we should be teaching and spending less time teaching children to be poor computers rather than good mathematicians.”'"*

## Both! (0)

## Anonymous Coward | about a year and a half ago | (#42864797)

That is what we should be teaching and spending less time teaching children to be poor computers rather than good mathematicians.

We should be doing both. They are not mutually exclusive and they are both important.

## Re:Both! (4, Interesting)

## hedwards (940851) | about a year and a half ago | (#42864859)

The US has been focused more on mathematics for as long as I can remember. That's one reason why the US is usually behind China in terms of math, China places a ton of value on turning children into calculators rather than understanding any of the math they're being expected to rote memorize.

I'm not so sure that going the computer route is such a great idea. It's all well and good to use computers and calculators, but if you don't know your times tables and you can't do long division, you're going to be stuck having to have a calculator at all times. Which is more reasonable now than it used to be, but you'd be surprised how much faster it can be to do things on paper sometimes.

Oh, and good luck getting a calculator to tell you what went wrong when a number you get isn't right.

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42865001)

Mentats. Someday soon there might be a very good reason to teach people to think like computers, rather than teaching computers to think like people.

(Spacing Guild, and Benegeserit, etc. will always be fantasy IMHO)

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42865051)

california doesn't focus on math. to graduate high school you need 2 years of math and 3 1/2 years of p.e.

## Re:Both! (1)

## pclminion (145572) | about a year and a half ago | (#42867093)

california doesn't focus on math. to graduate high school you need 2 years of math and 3 1/2 years of p.e.It's not like after learning 2 years worth of math you just forget it instantly. But with P.E., if you stop exercising, your body goes straight back to tubby-land. You are comparing apples and oranges in a most ridiculous way.

## Re:Both! (1)

## sirlark (1676276) | about a year and a half ago | (#42870933)

## Re:Both! (4, Insightful)

## Darkness404 (1287218) | about a year and a half ago | (#42865071)

And yes, there's a reason why China is behind the US in terms of math, because, like you said a lot of the value is placed on rote memorization, but that is also the reason why China has lagged behind the US in terms of real innovation.

Oh, and good luck getting a calculator to tell you what went wrong when a number you get isn't right.

Except this is what Estonia is having students learn: what the numbers really mean and how to use them. Which is a more useful skill, to be able to compute the A^2+B^2=C^2 your head or to be able to recognize a right triangle when you see one and be able to use that formula to find out useful information?

What most education systems are doing is teaching kids to memorize formulas and be able to do them with pencil and paper (or in their head) but not telling them when to use it or what the numbers really mean. You can ask most students what the Pythagorean theorem is and they can tell you, but how many of them can actually practically use it?

## Re:Both! (1)

## Darinbob (1142669) | about a year and a half ago | (#42867061)

I think students need all of it. Learn how to do the arithmetic by hand, plus learn the formulas, plus learn what the formulas mean. If you focus on just one area the student will lose out.

## Re:Both! (2)

## Darkness404 (1287218) | about a year and a half ago | (#42867203)

To use a car analogy its a bit like riding a horse. Back in the days before cars and trains, if you needed to travel long distances you had to ride a horse. If you didn't know how to ride a horse you were at a distinct disadvantage compared to someone who could ride a horse. Knowing how to do complex math by hand in today's age is a bit like knowing how to ride a horse today. It might be an interesting skill to know, indeed it might be required for some professions, it might become a hobby, but it isn't essential.

I know

## Re:Both! (1)

## Darinbob (1142669) | about a year and a half ago | (#42867401)

In the US we don't divide the curriculum based on what we think the students will do in the future. Some countries do this however. They may have a pre-college high school separate from a trade oriented high school. In the US though we give the same education to everyone, rich or poor, with educated or uneducated parents alike. So we do want to teach good math and science to everyone, because you can never predict who will need it in the future. Over time the student decides that they can't handle the college track perhaps.

I think this is in conflict with many corporate leaders who would prefer that schools just churn out a compliant and viable work force.

## Re:Both! (1)

## Darkness404 (1287218) | about a year and a half ago | (#42867565)

A guy who really enjoys history is likely to be thrilled by the prospect of an in-depth class on the political environment of the Italian Renaissance. On the other hand, there's people who couldn't care less about such a subject.

There are people who enjoy Trig or who will use it in their expected careers. Then there are others who simply loathe it and will never use it in their life.

The idealists and supporters of the US school system believe that this current way exposes everyone to everything and so everyone can be equally good. But really what ends up happening is that everything gets dumbed down to the point where everyone is equally bad.

There are very few students who can be Renaissance Men. There are very few people who have expertise in all the traditional areas of schooling, few are good at math and science and history and English and art. On the other hand, there are many students who excel in one or two of those areas and so it makes sense for those who are really good and really enjoy art to devote the vast majority of their studies in middle and high school to art. There are those who are really good at math, it makes sense for them to devote the majority of their studies to mathematics. In doing so, we breed better artists and mathematicians rather than starving the artists and mathematicians in courses that they will never fully master and bringing down those who are good at that subject.

The US education system apparently has not come to the realization that ability differs.

To use a sports analogy, its a bit like taking Apolo Ohno and Peyton Manning and telling them to throw a football 20 yards. Ohno is unlikely to ever need that skill (being an ice skater) and indeed not being a football player he might not even have the ability to do that. On the other hand, Manning isn't really challenged by this and is unlikely to really improve (because there's no support for learning to throw the ball any higher). Both Ohno and Manning are both brought down by this, Ohno because he has no motivation and little ability, and Manning because it is too basic. Instead, Ohno should be improving his speed-skating skills and Manning should be improving his passing skills (beyond just 20 yards!).

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42867863)

Your comments ignore the fact that it's very good for you to be frustrated every once in a while. It builds character. It teaches you that some things require real work to accomplish, and it shows you too that not everything you do in life follows from your main goal. These are some of the best life lessons and by limiting coursework to that which fits a student's chosen path you're denying them those experiences.

If I had a kid I wouldn't care that he doesn't get the math 100%. It would be far more important that he learn to invest time in something difficult but worthwhile. It's also very important for me that he learn that not everything should come naturally to him.

In short failure and frustration are critical parts of learning.

## Re:Both! (1)

## hedwards (940851) | about a year and a half ago | (#42868649)

No, ability is primarily driven by effort put into it. I wasn't good at math when I was a kid, I was terrible at reading. I could barely read at all until I was 8, certainly well behind my peers. The logical extension of your view is that I not be required to read or write because it was frustrating.

After many years, I did eventually manage to master reading sufficiently well that I can read without needing to hear the words in my head as I go along and I actually enjoy reading. The parts of my brain responsible for it eventually were able to figure it out and now I can read quite well.

The same thing goes for other subjects, we make students take those classes so that they can develop those portions of the brain that they wouldn't otherwise develop. This is one of the reasons why Americans, even ones with poor health generally, are in better condition neurologically into old age than people in other countries.

Had the educational establishment taken your view on this, I would never have been able to get the satisfaction out of helping other people learn how to read and do math. I would have been severely disadvantaged even though I have only a minor learning disorder.

## Re:Both! (1)

## hedwards (940851) | about a year and a half ago | (#42868625)

The problem is that you rarely, if ever, see somebody that can't do basic arithmetic who is able to understand things well enough to use a calculator. I tutor developmental math students on this stuff, and by and large I don't see very many of them that understand the concepts without being able to perform basic arithmetic. It's far more common for them to get the arithmetic, but be completely unable to do math.

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42868203)

It's actually fairly simple to prove, not simply apply.

## Plus, it's very appropriate (0)

## Anonymous Coward | about a year and a half ago | (#42868369)

After all, it's e-Stonia we're talking about!

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42865211)

Many times, to understand how a process works, you need to observe every step of it (i.e., hear and forget, see and remember, do and understand). Since the intelligence of most children surpasses the teaching skill of even the best teacher, it is often superior to just have kids do the actual process. They learn the meaning, rather than just the route process. However, being able to do mental arithmetic, while a fun parlor trick, is not terribly valuable. Also, people who actually need or use this will develop it naturally. This "understanding how to set up the problem" is far more important (and is the actual skill you refer to in understanding why "the number comes out wrong"). Long division especially falls into this category; practically it is much better to learn how to rapidly estimate orders of magnitude than be able to execute this particular algorithm.

## Re:Both! (2)

## fufufang (2603203) | about a year and a half ago | (#42865253)

The US has been focused more on mathematics for as long as I can remember. That's one reason why the US is usually behind China in terms of math, China places a ton of value on turning children into calculators rather than understanding any of the math they're being expected to rote memorize.

I'm not so sure that going the computer route is such a great idea. It's all well and good to use computers and calculators, but if you don't know your times tables and you can't do long division, you're going to be stuck having to have a calculator at all times. Which is more reasonable now than it used to be, but you'd be surprised how much faster it can be to do things on paper sometimes.

Oh, and good luck getting a calculator to tell you what went wrong when a number you get isn't right.

The problem is that solving complicated algebraic equations require you to have good mental arithmetic skill, otherwise everything becomes a pain. If the students can't do basic arithmetics quickly, they will find it hard to reason about complex problems. I feel the new approach by Estonia might backfire on them once students reach high school.

## Re:Both! (2)

## TapeCutter (624760) | about a year and a half ago | (#42866279)

A lot of kids have trouble with algebra because they don't get the basic concept of variables and references, they do understand those concepts in general they just don't link it to algebra. I had the same problem teaching grown ups C pointers many years ago, in a lab class of ~50, less than 10 would get the basic concept on the first lesson. Seems hard to believe but in my experience most students get stuck because they have missed something very basic, often because the teacher thinks it's so obvious that it's not worth spelling out.

## Re:Both! (1)

## icebike (68054) | about a year and a half ago | (#42865485)

Much beyond simple mathematics (addition subtraction multiplication and division) is seldom encountered in the lives of many people.

However people working in the trades (electricians, carpenters, mechanics) usually need a little more.

But your first sentence seem to contain an internal contradiction. You claim china speed too much time on memorization and not enough

time on understanding. Yet you state that China leads the US in this regard.

So, by your own example Understanding is less important than memorization.

Maybe I just misread what you typed.

## Re:Both! (0)

## Hognoxious (631665) | about a year and a half ago | (#42865647)

What do electricians need to calculate beyond the basic operations? Working out how much cable to go from point X to Y via Z? Addition. What current is necessary for a given power? Division. I doubt carpenters use integration to determine the volume of newel posts, and as for mechanics most of them can barely add the bill up correctly.

Yeah, that'd be a change.

## Re:Both! (1)

## Blaskowicz (634489) | about a year and a half ago | (#42866509)

So, you've never heard of the cos phi? Or a complex impedance? Electricity is reasonably dead simple if you're only dealing with DC voltages or currents but once you're dealing with AC you'd better have a basic understanding of trig, complex numbers and exponentials.

## Re:Both! (2)

## lattyware (934246) | about a year and a half ago | (#42865765)

## Re:Both! (3, Interesting)

## Obfuscant (592200) | about a year and a half ago | (#42866075)

This.

When I was in graduate school I was TA for a chem lab. For one of the quizzes, a student said he'd forgotten his calculator and asked to borrow mine.

His: TI.

Mine: HP.

Grading him extra points off when he came back with the answer "1.000" for a concentration problem: Priceless.

He knew how to operate his calculator, probably. He didn't know how to operate mine ( "number enter number enter divide" is different than "number enter number divide"). And he demonstrated a complete lack of feeling for the concentration of hydrogen ions in a solution. Unfortunately, it was the latter that he was supposed to learn in this class, not the former. By going with the answer 1.0 "because the calculator said so", he screwed himself and showed a failure to grasp the course material. Had he not been dependent on the calculator, he could have realized that "1.0" is a really really really strong acid, and the buffer he was calculating would never be that strong. The correct answer was five orders of magnitude away, at least.

The sad part of today's "find a calculator" climate is that people have lost the ability to ballpark anything.

## Re:Both! (1)

## colinrichardday (768814) | about a year and a half ago | (#42867429)

Would the pH of that be 0 (one mole of H^+ or H_3O^+ per liter?) ?

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42878579)

Guessing the ballpark answers was one of the most useful skill the uni taught me.

Looking at a problem and guessing the answer is "around 200", even if after a careful calculation it's 287 is still close enough. Invaluable in day to day life. I knew it wasn't gonna be a million nor 7.5. And if the calculator told me otherwise I would triple check that. Sadly many students trust the silicon too much.

## Re:Both! (-1, Offtopic)

## juopguta (2838635) | about a year and a half ago | (#42866143)

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42868425)

China places a ton of value on turning children into calculators rather than understanding any of the math they're being expected to rote memorize.

but if you don't know your times tables and you can't do long division, you're going to be stuck having to have a calculator at all times.

This seems somewhat contradictory. First you start by deploring the rote memorization you allege occurs in China, just to turn around and laud the merits of rote memorization as a necessary tool to be good at mathematics.

My own experience agrees with your remark that Chinese students are taught by rote memorization, but after that it diverges from yours. The Chinese students that I encounter are routinely at the top of the class in all mathematical disciplines (and many others). You can rationalize America's lagging mathematical skills by waxing about how Americans are among the few who "really understand it" but the truth is that solving most mathematical problems involves choosing a goal and then making systematic steps towards that goal by following a strict set of rules. You need some general understanding to locate the goal but after that you don't need a global picture to get there. The student who can bang out the Laplacian in arbitrary curvilinear coordinates without a second of hesitation is going to get to the goal faster than someone who has to sit there and rederive it from scale factors and other general formulae. That student is not a mindless drone either without any awareness of what he is actually doing. The "rote memorization" process usually involves a lot of problem sets, not just memorization of rules that are to be applied if a problem appears.

Here's a car analogy. You may need to know the local geography to decide the best route to your destination and you will likely enjoy the roadtrip more if you are aware of your surroundings, but the guy with GPS and far more experience at driving fast through various terrain is going to get there first unless you know a great shortcut that he will not find. If your goal is to enjoy the experience, then you win. If the goal is to get from A to B as fast as possible so you can get on with your work, then you lose.

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42868605)

But, Americans aren't lagging, which is sort of the point. You're talking about the few Chinese that manage to make it out of China. Those are the best of the best typically, or ones that have plenty of money for private tutoring.

It would be a bit like judging the status quo of the British system based upon the graduates of Oxford of Cambridge.

Also, I recommend you google "death by GPS" to see the problem with your choice of analogy. People get killed when they rely upon a GPS unit but fail to pay attention to the directions its giving them.

## Re:Both! (1)

## hedwards (940851) | about a year and a half ago | (#42868617)

There's no contradiction there. There is some declarative knowledge that you have to learn in any field. If you don't know your times tables, it's difficult to function at all in society where math is being used. It was expected of myself and my classmates to be permitted to move to fifth grade that we know our times tables up to 10x10.

In fact without some declarative knowledge you'll never advance very far. It's declarative because there isn't really anything to understand other than the fact that it is what it is.

But, what I'm talking about is that they'll be expected to do question after question extremely quickly without being asked to understand why or be able to come up with the equations on their own. It's basically completely worthless in the real world as nobody ever gives you a problem like that to solve outside of the academic world.

## Re:Both! (1)

## mjwalshe (1680392) | about a year and a half ago | (#42870131)

## Re:Both! (0)

## Anonymous Coward | about a year and a half ago | (#42872181)

I still haven't to this day (I'm 28) memorized a multiple table or any similar cheat sheets. I do and have always considered it a complete waste of time, much to the dismay of my teachers in school. Instead I spent my time in math classes developing a real understanding of mathematics.

I don't remember: 4 * 3 = 12 because of a table. No I remember it as: "4 + 4 => 8 + 4 => 12" or "3 + 3 => 6 + 6 => 12". Notice the second solution optimizes out redundancy, a silly example of it but I take that to an extreme when crunch numbers in my head.

## Re:Both! (1)

## unixisc (2429386) | about a year and a half ago | (#42869163)

I agree w/ 'both', but one does have to prioritize. Things like binary arithmetic and Boolean algebra are simple enough to be taught in, say, 5th grade. From then on, they can start learning things progressively, such as the truth tables of various circuits, even while in Physics, they start getting introduced to electrical concepts. So that by the time they're out of high school, they have a good sense of how to design or program things.

When I was in the 5th grade, we did learn a bit about base '5', and told how the same concept can be extended to base 2 and so on. I think that we can introduce binary, octal and hexadecimal math. (While on this topic, I do think it would be nice to introduce new symbols to replace A-F in hexadecimal that could be captured on a 7-segment display like 0-9) Once kids figure out how to do these, the basis of teaching them how to design arithmetic and logical circuits is laid out.

We did discuss in another thread the use of various things in math that are taught but never used in day to day life - trigonometry, calculus, complex algebra and so on. But Boolean concepts are used, from things like circuit design to doing searches online. It would therefore be more useful to teach those things at a more primary level, and only introduce higher level math later, after the basis of computational learning is established. That way, students can apply some of those concepts they learn in programming exercises, since it's increasingly computational devices, rather than people, that use those things

On the Estonian experiment, however, it is important for people to grasp the concept of numbers, and as long as the purpose of computers or calculators is to help them speed up their calculation of what a 10% surcharge would result in, it's fine. However, I've seen people who can't do the most basic calculations w/o pulling out a calculator, and that is sad.

## Up to the parents now, as it used to be. (1)

## Anonymous Coward | about a year and a half ago | (#42864843)

How sad it would be to ask someone how much two plus two is and they tell you I don't have my computer. I don't know.

## Re:Up to the parents now, as it used to be. (0)

## Anonymous Coward | about a year and a half ago | (#42864901)

I understand where you're coming from with this comment, but honestly, I think that if you're taught how to solve problems like TFS seems to indicate, you'll be able to work your way to solutions for today's "standard" math problems from first principles. Not saying we should throw out arithmetic, since that may very well be the "first principle" that we have to work from, but I think the general idea of working more on the concepts, rather than rote memorization of mechanics, could be a very good thing.

## Re:Up to the parents now, as it used to be. (2)

## omnichad (1198475) | about a year and a half ago | (#42865111)

rote memorization of addition tables and multiplication tables would still be important to understanding the results. And also shortcuts. Otherwise, the concept of 43+43 is the process of counting to 86. Not knowing you can add the digits separately and the concept of a carry digit would seriously hinder people.

## Re:Up to the parents now, as it used to be. (1)

## Darinbob (1142669) | about a year and a half ago | (#42867227)

If you use an abacus, a very ancient device, these ideas come naturally. Even though the abacus is just a calculator it does not hide things from the user. With a digital calculator you essentially have a function that turns two numbers into a third number. Similarly with slide rules, you could do multiplication by using logarithms and it wasn't hidden from you. Further with the slide rule you got a very good feeling for the scale of the inputs and outputs, how you got more precision on one end and low precision on the other end. Whereas today I see programmers not understanding the basic concepts of precision and scaling and they treat floating point numbers as magic entities.

Are we going to have problems with calculators that are unable to display how much of their floating point results are accurate so that the student thinks that those 10 digits printed out are all precise? I see programmers who don't understand this stuff.]

Yes, at a certain point you can stop learning the arithmetic. In college you don't have to do long division anymore. But in college you should understand the concepts behind long division well enough that it's internalized.

## Re:Up to the parents now, as it used to be. (3, Insightful)

## i kan reed (749298) | about a year and a half ago | (#42865017)

1. When's the last time you were more than 10 feet from a computer? How often do you think it's going to be in the next generation.

2. I'd rather have graduates who can do calculus with a computer, than those that can fuddle and almost do Alegbra without. That may be the choice we have to make.

3. Do you seriously think they're going to teach by saying "the computer always solves any problem", without broaching the mechanics at all?

## Re:Up to the parents now, as it used to be. (1)

## Desler (1608317) | about a year and a half ago | (#42865083)

2. I'd rather have graduates who can do calculus with a computer, than those that can fuddle and almost do Alegbra without. That may be the choice we have to make.

That's such a bullshit false dichotomy. If they can't do algebra there's no way they're competently doing calculus.

## Re:Up to the parents now, as it used to be. (3, Insightful)

## i kan reed (749298) | about a year and a half ago | (#42865593)

Sentence 1 of your reply has no relationship to sentence 2, so I'm going to argue against what I imagine your point to be. This might be pointless:

If they aren't doing algebra, its going because they're stuck algorithmic bullshit like memorizing the quadratic equation, then they'll never make it to calculus, which was exactly my point.

No one needs to waste time learning to do square-roots by hand. No one needs to memorize multiplication tables. No one needs spend a ton of time on the algorithmic execution of concepts in math, except those developing re-usable algorithms to that effect(mathematicians and programmers). I can't remember the last time I did long-division by hand(except of course, of polynomials, but that hardly counts). Either precision matters little enough that I can approximate, or precision and accuracy matter enough that I wouldn't want anything

buta computer to do it.## Re:Up to the parents now, as it used to be. (0)

## Anonymous Coward | about a year and a half ago | (#42866119)

You can do square roots by hand without calculus?

Also, "memorizing the quadratic formula" and "solving quadratic equations" are two different things. Obviously, any adult should be able to derive the quadratic formula as a method of solving quadratic equations. Since you end up using it often, you'll probably end up memorizing it.

I think the danger people are pointing to is that if one simply learns to put quadratic equations into a computer, they may not even be able to derive the quadratic formula.

Where "able to derive the quadratic formula" actually means "have some understanding that symbolic mathematics exists and can save you a ton of time"

## Re:Up to the parents now, as it used to be. (0)

## Anonymous Coward | about a year and a half ago | (#42866773)

No one needs spend a ton of time on the algorithmic execution of concepts in math, except those developing re-usable algorithms to that effect(mathematicians and programmers).

Your understanding of the extent of Math use in hard sciences and engineering is ... shall we say very large only when seen from very very close up? And as a hint, programmers are not among the heavy users, not by a long shot. And as a second hint, the types of problems where computer use is a (more distant) secondary helper are far more frequent (and frankly more interesting, as in challenging) than the ones where it is the sole tool. Nevermind that in the vast majority of cases computers offer

approximationsand the limits of those approximations cannot be understood without understanding the actual algorithmic execution behind them.But hey, your point definitely stands if all your needs can be satisfied with a computer that uses a spherical approximation for a cow.

## Re:Up to the parents now, as it used to be. (1)

## davester666 (731373) | about a year and a half ago | (#42868471)

So basically this generation is the last who needs to know how to do math?

The next one just needs to know how to punch it into a computer and hope the answer is right?

That is, well, stupid.

For one thing, this would make financial fraud, well, much more widespread than it already is. Being able to tell whether a total is even approximately correct has repeatedly saved me money, as well as being able to determine how much change I should get.

## Re:Up to the parents now, as it used to be. (1)

## cellocgw (617879) | about a year and a half ago | (#42873115)

So basically this generation is the last who needs to know how to do math?

The next one just needs to know how to punch it into a computer and hope the answer is right?

(must be my day for showing off my SciFi knowledge :-)

"The Machine Stops, by EM Forster." Thought by some to be the inspiration for THX1138.

Which is to say, I agree with you.

## Re:Up to the parents now, as it used to be. (1)

## CastrTroy (595695) | about a year and a half ago | (#42867259)

## Re:Up to the parents now, as it used to be. (4, Funny)

## Yakasha (42321) | about a year and a half ago | (#42865067)

How sad it would be to ask someone how much two plus two is and they tell you I don't have my computer. I don't know.

Actually I'm envisioning them replying: <clack clack> "3.999999 you dumb troll."

## Re:Up to the parents now, as it used to be. (2)

## vlm (69642) | about a year and a half ago | (#42865085)

We're pretty much at this point with retail cashiers right now.

Back when I worked retail management as a starving student (admitted a couple decades ago, now) we had to fire a girl because she didn't know how to make change. Like the cash register reads 37 cents, now which coins to you hand to a customer? She simply could not figure it out. Even after trying to teach her to count up, she simply couldn't add numbers fast enough. I'm sure she's probably a CEO or accountant now.

## Re:Up to the parents now, as it used to be. (1)

## similar_name (1164087) | about a year and a half ago | (#42865155)

## Step in the right direction (0)

## Anonymous Coward | about a year and a half ago | (#42864863)

## Calculators redux (1)

## Half-pint HAL (718102) | about a year and a half ago | (#42870017)

So we're back to the old calculator debate, but in new clothes. When I was at school the argument was all about whether to use calculators or not. For most of my school career, I survived without recourse to a calculator. I

hada calculator, but I never used it, because the course materials were always designed in such a way that we didn't need one. We didn't need to "calculate" the final answer, we just reduced equations, and that led us to exactly what the quote in the summary calls for: mathematicians, not calculators. OK, so statistics has a lot more number crunching in it, but that's already stuff we switch to the scientific calculator for after the first month or so: factorials, n-P-r, n-Choose-r etc.I am very dubious about how you can abstract any further without losing a fundamental and important understanding of what the maths actually is, and how can you decide which mathematical tool to employ if you don't fully understand what the tool does?

Furthermore, going back to winning argument in the 1980s/90s calculator debate, it's really only this manual stage that develops our skills of approximation, and when working with a computer, we need to be able to look at a result and guesstimate whether it's in the right ball-park or clearly way off the mark.

(Incidentally, I took CS at university and we did lots of geometry and algebra, and we didn't need graphics calculators -- in fact, we were actively discouraged from using them, partly because it would have been onerous on the exam invigilators to have to go round and physically reset everyone's calculator by hand to clear the memory before the start of an exam. If I remember rightly, the rules literally banned them outright, but individual invigilators often let them in and forced the reset themselves.)

## About time... (4, Insightful)

## Darkness404 (1287218) | about a year and a half ago | (#42864957)

## Re:About time... (3, Funny)

## vlm (69642) | about a year and a half ago | (#42865167)

100 years ago before the advent of the computer that might be true. Today though?

A large part of the modern educational system is geared precisely toward that. We are easily the best prepared 1913 workforce the world has ever seen. Our 10000 man factories will be staffed by fully qualified drones, our draftsmen are fast and precise when hand drawing blueprints... The more you think about it, the truer it is. The bell rings, just like a factory whistle. Rows of desks just like rows of (hand/human operated) machines on the factory floor. Not much has changed in over a century.

## Re:About time... (3, Insightful)

## Darkness404 (1287218) | about a year and a half ago | (#42865691)

For example, in Kindergarten I learned print handwriting. In first grade I learned D'Nealian (basically a bastardized version of cursive, not quite print and not quite cursive) by third grade teachers required that everything should be written in cursive. The idea was that somehow, despite the fact that computers were everywhere and few people actually used cursive that it was a required skill to learn and that we'd be using it the rest of our lives. Wrong. Aside from a time from 3rd to 5th grade when teachers required it, I never used cursive, it was really a waste of time.

There's a whole host of useless things I learned, each with a rationale that we'd be using this "skill" the rest of our lives. Which might be true if I lived in 1950, but I don't. I remember at some point we were forced to keep a pen-and-paper agenda and my request to use my PDA to keep track of things (I mean, nothing fancy just my dad's hand-me-down monochrome Palm Pilot) and that request was flatly denied. There were all sorts of things that I could have been (and should have been!) taught in elementary/middle school, things like computer programming, basic electronics, etc. but those were overshadowed by much more "important" things such as learning to write in cursive...

I'm glad to see this mentality that calculators don't exist banished from classrooms.

## Re:About time... (1)

## Compaqt (1758360) | about a year and a half ago | (#42868801)

I think the way you're arguing, school districts could just sell all the schools, fire the teachers, and just buy every kid an iPad with a subscription to Siri, and be done with it.

Is there anything you'd teach in the schools?

## Re:About time... (1)

## GravityStar (1209738) | about a year and a half ago | (#42875313)

School should never devolve into "keeping the children busy during the day". If it does, then yes, either overhaul the curriculum or close the damn schools.

## Re:About time... (1)

## Anonymous Coward | about a year and a half ago | (#42865793)

The question is not if you can accurately calculate how much that $7.99 shirt is going to be if it is taxed at 7%

You're right, that isn't the question. The real question is how to save money on your shopping trip. So, when you're in the store and want to know what the better purchase is, the box of 14 for $12.95 or the box of 32 for $29.99, I assume you never choose incorrectly for any of the similar selection of 20 items your picking up this trip since you're always using your handy dandy calculator!

Since I never see anybody using a calculator when I'm out shopping, I'm going to go out on a limb and guess that being able to mentally perform basic arithmetic is still a valuable skill. Literally.

## Re:About time... (1)

## SydShamino (547793) | about a year and a half ago | (#42866329)

If they don't print the per-unit costs on the label, then when you think I'm looking at my shopping list on my phone, I'm actually using a calculator to figure out which of those is the better deal. Usually, though, the per-unit costs are printed on the label on the shelf.

## Re:About time... (1)

## fatphil (181876) | about a year and a half ago | (#42866645)

Which reminds me, I have some photos to send to the consumer protection board - those shelf tags can sometimes be hilariously wrong. Having said that, maybe I should send them to the supermarkets first, and see if they reward me with a free supermarket sweep. Blackmail's not below me, when there's the possibility of free food - do I look stupid?!?!

## Re:About time... (1)

## houghi (78078) | about a year and a half ago | (#42865975)

To be fair, in Europe we do not need to do that. The taxes are included. If they are not, you pay the advertised price.

Understanding the logic behind it is much easier when done without the calculator. Otherwise for many it is just like using any other program: Mindless repetition, without understanding.

I have sen this in action when I wanted to rent a car. When looking online for prices, for one day and then for 10 days, in 50% of the few times I liked it up, it was 10x the day price. In the other 50% it was the week price plus 3 times the day price. This was lower (as expected) as the 10x day price.

So I phoned the company and asked them to quote me a price. Apparently they got the same wrong configured server and quoted me the 10x day price for 10 days. I asked them if a longer period was cheaper compared to a day price. i.e. if 10 days would not be cheaper then 10x 1 day. They said yes, but the computer told them that was the price. I asked them if they could calculate it by hand and they were unable (not unwilling) to do so. Even though the website clearly stated what the week price and what the day price was.

I have seen business presentations where there were serious errors in the Excel sheet and the person making them did not notice, because he had no idea that and increase of 25% in staffing could not mean a decrease of 10% in staffing budget.

This all happens, because people have not learned what numbers mean. They know how to type them in, but have no clue about the ballpark the outcome should be.

I knew that 10 days should be cheaper then 10x 1 day.

I knew that +25% staffing would mean around +25% in budget and so I would know what ballpark we would be talking about.

Sure, for the specific numbers I use a calculator.

So by all means, please embrace the calculators and computers. But do this into addition to what we already do, not as a substitution.

## Re:About time... (1)

## Half-pint HAL (718102) | about a year and a half ago | (#42872651)

My mum was out shopping once. She bought two or three things in a shop, at £x.99, £y.99 and £z.95. There was a fault in the electrics and the cash register was out. The shop assistant attempt to calculate the total by long addition and was taking ages. My mum was a maths teacher. She showed her the "divide-and-conquer" algorithm for adding multi-digit numbers ((x+1) + (y+1) + (z+1)) - (0.01+0.01+0.05). The woman behind the counter was very grateful, because she'd never been shown this at school.

And in fact, nobody taught

methat at primary school: my mum taught me it at home. Teaching people to be mathematicians instead of calculators can start in the first year of schooling, if they just teach kids how to think in terms of divide-and-conquer, rather than giving a brute force "technically correct but massively suboptimal" way of working.## Re:About time... (1)

## Hentes (2461350) | about a year and a half ago | (#42866259)

We have moved quite a bit forward from calculators. The question now is not whether to teach arithmetic, more like whether to teach calculus and equation systems, or just use a symbolic program. I still think it's useful to at least learn how they work, but cutting back on doing repeated exercises might be a good idea.

## Re:About time... (1)

## Darinbob (1142669) | about a year and a half ago | (#42867031)

We need both. If you can't calculate by hand you don't actually learn many vital concepts. Ie, how does a computer do division? The same way a person does division. The person who designed the chip to do the division is unable to do so without first knowing how to do it the long way. Even if you're not designing a chip you still learn some fundamental concepts by understanding the process.

Do you even understand what 7% tax means if all you know is how to plug in numbers into a calculator? If you just use a calculator maybe everything just end up being opaque magic numbers that have no meaning? Do we want future workers to all be like the dysfunctional programmers of today who can't do a basic algorithm without just copying from somewhere else, and they can't do any programming more involved than gluing pre-existing modules together?

How do students even know when the calculator and computer are wrong because it got bad input? If they punch in a wrong number and the computer says 7% tax on $57 is $8, will they recognize that it is wrong?

In the past people used slide rules and I think those had a big advantage because you got a feel for what logarithms were. I think calculators have taken that away so that you have a much more vague idea of what they mean or how they relate to multiplication and so forth. And that's with an advanced idea of logarithms, if we simplify even basic arithmetic how much more do you lose?

And yes, pragmatically speaking not everyong needs to know the hard stuff, and most of these "let's do education differently" programs are really about making better factory floor workers or IT service job workers. That's not necessarily what we want from education.

I've been at a computer store where a network was down, and the staff was barely functional and unable to do basic arithmetic or bookkeeping. They had one person with a calculator, one person reading instructions, and one person reading off the prices of each item. Today I very often find people who can not do arithmetic giving me the wrong amount of change.

## Re:About time... (1)

## Darkness404 (1287218) | about a year and a half ago | (#42867423)

And no, its not "dysfunctional" to get your algorithms and just put them in your program, its called efficiency. Why re-invent the wheel (and introduce potential bugs) by re-coding something that is already done (and tested)? I mean, sure a programmer could spend 85% of their time re-coding existing code, and the remainder working on new stuff, or they could just take existing, working code and focus on adding the new stuff.

and most of these "let's do education differently" programs are really about making better factory floor workers or IT service job workers. That's not necessarily what we want from education.

Um, have you even been in an American school? The entire program right now is to make factory floor workers! We focus on obsolete gruntwork rather than focusing on the big picture. We prepare students for life in 1913 rather than 2013. We ignore many technological advancements for the sake of a "complete" education. We waste time teaching students print, cursive and keyboarding rather than just print and keyboarding. We waste time trying to cram in dates and years rather than teaching the principles behind history so we can learn from it. Its the same with math, we can either focus on the gruntwork and spend 95% of our time teaching kids how to do long division and things of that nature, and only 5% discussing the principles behind it. Or we can spend 95% of our time discussing the principles behind it and only 5% discussing the gruntwork behind it.

The idea of the human calculator and the human encyclopedia is over. Real-world success isn't being able to quote dates or do multiplication in your head, its applying those concepts to the world around us. Its not knowing 400 digits of Pi but being able to use Pi to model the world.

## Re:About time... (1)

## Half-pint HAL (718102) | about a year and a half ago | (#42872717)

And no, its not "dysfunctional" to get your algorithms and just put them in your program, its called efficiency. Why re-invent the wheel (and introduce potential bugs) by re-coding something that is already done (and tested)? I mean, sure a programmer could spend 85% of their time re-coding existing code, and the remainder working on new stuff, or they could just take existing, working code and focus on adding the new stuff.

[...]

Um, have you even been in an American school? The entire program right now is to make factory floor workers! We focus on obsolete gruntwork rather than focusing on the big picture. We prepare students for life in 1913 rather than 2013. We ignore many technological advancements for the sake of a "complete" education. We waste time teaching students print, cursive and keyboarding rather than just print and keyboarding. We waste time trying to cram in dates and years rather than teaching the principles behind history so we can learn from it. Its the same with math, we can either focus on the gruntwork and spend 95% of our time teaching kids how to do long division and things of that nature, and only 5% discussing the principles behind it. Or we can spend 95% of our time discussing the principles behind it and only 5% discussing the gruntwork behind it. The idea of the human calculator and the human encyclopedia is over. Real-world success isn't being able to quote dates or do multiplication in your head, its applying those concepts to the world around us. Its not knowing 400 digits of Pi but being able to use Pi to model the world.

Well then let me ask: have you ever been inside a

non-US school? Because it is not just a choice between mindless rote repetition on one hand and throwing all the paper away and working on a computer on the other. You can learn the fundamentals of how numbers and probabilities and algebra and geometry work meaningfully, and once you've learned it, you can apply it.If you object to teaching the fundamentals, and instead focus on plugging numbers into a precoded algorithm, then you are indeed teaching for 2013, because you will produce a generation completely adept at saying "computer says no"....

## Oh great! (0)

## Anonymous Coward | about a year and a half ago | (#42865129)

Another article on how other countries are doing something different (i.e. "better") than us!

There is nothing more to say.

## Reminds me of stats in the '60s (4, Interesting)

## Ungrounded Lightning (62228) | about a year and a half ago | (#42865323)

Especially since it's sepcifically statistics that's involved in the push.

Back in the last half of the 1960s hand calculators were just becoming available and affordable. There was a bunch of pressure to ban them and maintain the old curricula, with hand computation everywhere.

The big mover to calculators was the statistics department. That's because the arithmetic involved in statistics calculations is long and tedius. Assignments could only be toys. Computing a chi-square test using pencils and paper was a group term project. So the students had to eat a semester of theory and have hands-on experience of doing the work ONCE.

With hand calculators a chi-square on a reasonably-sized dataset could be done for a daily assignment. The students could move on from crunching and actually SEE the tools work, getting a "feel" for the processes. That, in turn, meant they could learn MORE tools in the same time.

With computers the computation can be faster than the delay can be perceived, so students can apply another factor-of-many multiplier to how much of the subject they can cover and how well they can comprehend it.

There are some subjects where the number of computations small enough that manual arithmetic is occasionally useful at a professional level, complex enough that understanding all the steps to set it up is important, and powerful enough that a small number of complex computations does something important - rather than bogging you down in an impossibly large number of simple, repetitive, and error-prone steps. Statistics is NOT one of these subjects.

## Re:Reminds me of stats in the '60s (0)

## Anonymous Coward | about a year and a half ago | (#42867921)

Contrast Stats with Physics, where it's really important to understand how the relationship works, and not just how to apply it. In upper-division Physics my problem solutions would frequently be a page or two long per problem. This was actually valuable though, as up until then we hadn't seen how the math can really fit together to describe a physical situation.

We could have done that in a CAS, but the CAS would have deprived us of the ability to stop in the middle and contemplate the meaning of what we were doing, which is really the value of doing the algebra.

## I still have a slide rule ... (1)

## Kittenman (971447) | about a year and a half ago | (#42865395)

I mean really - back when I took Maths 'O' levels you weren't allowed calculators in the exam room. I'd do the maths and then check my answer on the slipstick. Slide rules aren't great for accuracy, but ok for quick checks.

BTW I haven't used it for years.

## sh"1t.. (-1)

## Anonymous Coward | about a year and a half ago | (#42865609)

## Mod up Estonia (1)

## futhermocker (2667575) | about a year and a half ago | (#42865761)

In addition, learn kids not to use and learn only a single OS or particular programming language. Use them all, get to know them, learn their pros and cons.

## I think this is a good idea. (2)

## TsuruchiBrian (2731979) | about a year and a half ago | (#42865785)

I think after establishing a base of being able to do simple arithmetic with adequate competency, there is diminishing returns in making people better human calculators. It's not that I don;t think this is a useful skill, but rather that I feel the lost opportunity cost from not teaching them more useful things like how to think about problem solving is not a good tradeoff.

We make kids do the same kinds of math problems over and over again. I can barely remember how to do long division nowadays (although I could probably figure it out fairly quickly). Is the reason I can figure it out based on the fact that I was forced to do it over and over again as a kids? Not really. I can figure it out because I know what it is that long division was meant to achieve. I can apply what I learned alter on to rederive long division, although memory can speed this up a a little bit.

Knowing how to think is more versatile than memory. Knowing how to think allows you to do more than just long division. In the same way that we wouldn't dream of making kids use books of logarithms in light of how much better using a calculator is, why not let them use calculators for basic arithmetic, once they've mastered it (and by mastered I don't mean do lightning fast, but just reliably). All the time saved by using calculators means that we can teach them how to do new things sooner.

## This is a basic problem with all education. (1)

## lattyware (934246) | about a year and a half ago | (#42865791)

## Reatarded headline (1)

## Hognoxious (631665) | about a year and a half ago | (#42865821)

Headline says math[s]. Summary says statistics.

They aren't the same thing.

Let's hope it's Ben Rooney's last submission too.

## Teach them to think, or teach them to calculate (1)

## gestalt_n_pepper (991155) | about a year and a half ago | (#42866045)

I have to admit my bias for the former, but teaching rote calculation in one's head has some value, if only as mental calisthenics. That said, I applaud the Estonian school system for getting more reality based, unlike so many school systems here in the USA.

Full disclosure: I'm half Estonian, do some math in my head, and I still write in cursive, occasionally. Keeps the kids from understanding it. :)

## Re:Teach them to think, or teach them to calculate (1)

## fatphil (181876) | about a year and a half ago | (#42866737)

Certainly, being able to use the commonly-available equipment in order to perform tedious calculations is a more useful skill than being able to manually perform those calculations most of the time. However, the ability to detect an significant error in those calculations is vital, which means that some kind of mental arithmetic skills will always be necessary.

## You did not read the article did you? (0)

## Anonymous Coward | about a year and a half ago | (#42866557)

The article talks about teaching STATISTICS. Yes, children and adults too, need to learn about how to interpret statistics and methodologies for collecting and analyzing data. This is s good thing and doing it by hand is often a stupidly tedious task. When it comes to learning arithmetic by rote, it's not a bad idea. Rote learning is often misunderstood, it does not mean mindless learning, it means that you become familiar enough with the material so that you have a good understanding of the underlying principles. I teach HS physics, the students are allowed to use a formula sheet on tests as I believe memorizing formulas is not the best use of brain cells, but guess what, the students that do the best seem to have them in their head because when approaching a problem they are able to call on a knowledge base in order to narrow the possible solutions without wasting hours looking up formulas and seeing if it fits. Ya its neat that you have a computer near you at all times, but I'll still rely on the guy with experience and knowledge to save my life during a plane crash, rather than the lame dude looking up the stall speed in the manual.

## As always, Asimov. (1)

## cellocgw (617879) | about a year and a half ago | (#42873043)

"Feeling of Power"

P.S. Why can't computer math be taught as well as teaching kids how to do math on their own?