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Estonian Schools To Teach Computer-Based Math
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.”'"
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.
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.
It is about time that schools embraced calculators and computers when it comes to math. When it comes to having a competitive edge and actually DOING something with math, the question isn't if you can do 123123.12 x 213123 / 23423.28 in your head, it is about learning to apply mathematical principles in the real world. You quite simply cannot get a job simply because you are good at doing addition, multiplication, subtraction and division. 100 years ago before the advent of the computer that might be true. Today though? Everyone has a calculator on them nearly all the time. 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%, but how to plug in the numbers for that. The question isn't manually computing how to do a PageRank algorithm, but understanding the logic behind that (and improving it!).
Taxation is legalized theft, no more, no less.
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?
Taxation is legalized theft, no more, no less.
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.
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.
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
you insensitive clod!
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.
"The greatest lesson in life is to know that even fools are right sometimes" - Winston Churchill
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.
Sig Battery depleted. Reverting to safe mode.
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.
KERNEL PANIC -SIGFAULT AT ADDRESS #51A54D07
If you need to use that kind of maths a lot, then you'll start memorising the stuff you need. Learning it beforehand is a waste of time.
-- Lattyware (www.lattyware.co.uk)
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.
In my experience, this is the case for everything, from primary school through to university. Memorisation is the way that stuff is taught throughout education, which makes sense - it's easy, makes marking and standardised testing easier, and it makes people seem competent. It also ignores the fact that learning the concepts and being able to apply them is so much more important.
-- Lattyware (www.lattyware.co.uk)
Headline says math[s]. Summary says statistics.
They aren't the same thing.
Let's hope it's Ben Rooney's last submission too.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
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. :)
Please do not read this sig. Thank you.
Oh, and good luck getting a calculator to tell you what went wrong when a number you get isn't right.
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.
My daughter (who now has her own kids) was taught basic algebra at an Aussie HS using a spreadsheet, it was the teacher's own idea and it worked a treat. I think it worked so well because she was doing rather than just seeing or hearing.
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.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
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.
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.
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.
Except most students will not have a need to do the arithmetic by hand except for very basic problems.
/. is very biased towards math/science but in an average occupation, indeed in everyday life there are just some things that you don't need to know such as long division. There's no doubt there will be kids who will do (and will enjoy) doing math by pencil and paper. Indeed, I have no doubt that there are some brilliant (potential) mathematicians who decided not to pursue mathematics further because they didn't like the "gruntwork" of arithmetic.
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
Taxation is legalized theft, no more, no less.
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.
Would the pH of that be 0 (one mole of H^+ or H_3O^+ per liter?) ?
Except that way leads to failure and frustration.
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!).
Taxation is legalized theft, no more, no less.
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.
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.
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.
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.
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 had a 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.)
Got them moderator blues I blieve I walk out the do', With these mod-points I been gettin', I 'most never post no mo'
multiplication and division is Arithmetic and not Mathematics
I disagree! A year after graduating high school, most people can't do basic arithmetic nearly as proficiently as they did when in school. You get rusty at those skills real fast if you're not using them daily. As for trigonometry, basic calculus and stuff you may have had less than a year learning (Maths until final year was compulsory in my school) that's even worse.
"Feeling of Power"
P.S. Why can't computer math be taught as well as teaching kids how to do math on their own?
https://app.box.com/WitthoftResume Code: https://github.com/cellocgw