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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.”'"
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.
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?
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."
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.
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.
"Science flies us to the moon. Religion flies us into buildings." - Victor Stenger
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.
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
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 but a computer to do it.
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.
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.
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.