Actually there is …
Actually there is much to understand related to the multiplication algorithm. it underlies the partial products used for multiplying polynomials. However, most adults fail to see the connection because they’ve memorized many rules without undersatnding where they come from. Not thinking about what things mean won’t get you very far. Thus, many US students have extremely poor scores on the GRE.

You couldn’t be …
You couldn’t be more wrong. Memorizing is not the key to high level math, deep understanding is. You do need to be able to quickly recall or derive facts, but memorizing them (without understanding) is of little use. I don’t think that you’re memorizing the formula that you describe, you’re recognizing some deeper structure.

You should know how …
You should know how to solve it but for 36/6 once you know why it works you really should be memorizing basic multiplication and division problems not for any real reason it just should happen eventually.

Memorization is key for higher level math.
I don’t know what level your at but im in pre-calc and we can’t solve problems unless we memorize things. Ex
Sin^2x+sin2x+1 we need to know that is a quadratic otherwise it will be impossible to solve.

After having …
After having watched this, I’m so grateful having been in the Austrian school system. Though I never heard of such ways to find the right answer, I see it as a way to keep kids busy (and probably a lot of them confused).

We were only allowed to use a calculator when I was like 14, and even though I’m not a math genius, I passed by applying the “international” way without even knowing this ridiculously playful methods.

My kid starts school next year – without calculator in elementary school!

Not sure why you …
Not sure why you are so angry or how you derived what my “assumptions” are based on this post.

However ridiculously weak my math is, our kids are STILL two grades past (and accelerating) compared to the well-funded upper middle-class local school that teaches this new math.

My math being ridiculously weak, what does that say about the poor kids being taught this joke of a system in the school?

I’d love to have someone as brilliant as yourself teaching my kids math instead of who’s there now.

algorithms you …
algorithms you don’t understand? Why would you want that? But let’s face it, when it comes to multiplication, there isn’t much to understand… Also, you did that, and then you DID substitute 0 into x, and you solved it. That IS an algorithm for systems of the form x+y=a; x-y=a. Also, when having to solve problems under time pressure, believe me: you want to be able to solve simple things quickly. Thinking about “what a quadratic equasion means” won’t get you very far…

You don’t need an …
You don’t need an algorithm if you think, you need to think about the quantities. Thinking and reasoning is not crippling if you know when to use it and when not to. Relying on algorithms that you don’t understand can be crippling. I thought about what the equations meant that you were taking a number and adding and subtracting that number and resulted in the same quantity.

You do need an …
You do need an algorithm. You can say you “see” the solution, but that’s crippling… Are you going to use a calculator for everything you don’t instantly see the solution of? You deduced that x should be 0 BECAUSE it has to be a number that when added to or substracted from another one doesn’t change that number. Then you actually substituted 0 into x and solved y + 0 = 3. Look at that, an algorithm for solving systems of the form x+y=a; x-y=a

No idea what you’re …
No idea what you’re referring to.

No algorithm works …
No algorithm works every time for solving a system of equations. It depends on whether the system involves quadratics, cubics, quartics, etc. The technology is not crippling kids thinking. It is how the technology is used. Technology can enhance or deter, depending on how it is used. Why not go back to slide rules? Didn’t those help kids think? Any technology can be misused.

and many people …
and many people fail purely beause of that…

Some kids are in …
Some kids are in need of an algorithm that’s transparent and works every time. The classic ones kind of have this. Most students who should be using more methods or other ones figure them out by themselves anyway. And I’m quite radically against the huge uprise or technology as it IS crippling many kids’ skills in a couple of areas. Kids start relying on calculators too much, I’m noticing this here too. University is often the 1st place where they’re prohibited for many exams,

You don’t need an …
You don’t need an algorithm to solve this system. You can simply see that if y is 3 and x is 0 that that is a solution. If you’re using an algorithm, you are using a slow procedure.
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I think the point is that you need to know when you need to use a calculator and when not to, not learn that you should never use one. Some systems are very difficult to solve (e.g., possible solutions with two cubic equations. However, there are some nice procedures you can use that involve a calculator.

You know, you’ll …
You know, you’ll need to use at least very simple algorithms to solve this system. You’re nowhere if you don’t know them, or at least are capable of deducing them… You can however solve this easily with your calculator mate, most calculators I know can solve systems quickly. Just put them in standard notation and you’ll get the answers (0 and 3). You’ll generally notice when you can solve it w/o a calc and when you need one, but the point is there has to be A point where you can do it w/o one

Sounds like you …
Sounds like you disagree with the person who made this video, that students need to learn to reason and solve problems. The person in this video thinks that students should learn one way (the supposed only and best way though this is inaccurate) to compute. This video advocates against strategies that encourage mental strategies, but one “one way I learned in school.”

Didn’t you learn …
Didn’t you learn how to solve the system of y+x=3 and y-x=3 when you were 12 years old? Sounds like we can move beyond this. Most students could solve this just by looking at it. Perhaps we should learn when to use a calculator so solve problems.

We were taught in …
We were taught in highschool. Not everybody in highschool knows what he’s gonna study after it…

And we need those programs etc for complex problems. But again, you need to bloody learn what’s behind it all. You sound like you’re advocating that everybody should just grab a computer program and solve all their problems without thinking about them, even the ppl who are supposed to make those programs :s

Sounds like you’re …
Sounds like you’re advocating what is in these books, not just memorizing meaningless algorithms.

Also my friend, …
Also my friend, we’re supposed to learn about stuff. It’s perfectly possible to let a smart 12yo solve all physical problems by making a computer program linked to a database containing all the answers and telling him to just type in the right numbers… We try to understand what happens however, and solve the problems…

Facts? We learn to …
Facts? We learn to solve problems. Also, precision and accuracy have their place in physics. Since you know this all, you know how to process numbers and work with errors, and then it ‘ll be a cold trick for you to realise why you shouldn’t always do this when learning new theories. Also, some people don’t study at all. Take linear algebra. Had an exam on that last exam period. if y+x=3 and y-x=3, what are x and y? You’re supposed to learn how to solve that, without needing to grab a calculator.

So why are you …
So why are you learning any of this if you never need to use it? This is all very confusing to me. Sounds like your taking courses in “useless things that I’ll never need.” A strange degree program.

So most of what …
So most of what you’re learning is a bunch of facts that can be recalled from a list of information. You’re not learning how to solve complex problems or unique situations that real mathematicians or scientists solve? So you’re not interested in precision or accuracy either? You just need to get close to the ballpark? You’re not using how to use technology that can benefit you and allow you to solve messy problems? Sounds like you’re in 1950.

Also, we’ve all …
Also, we’ve all been taught how to work with a pocket calculator just fine. We can use it for certain open-book exams, but generally calcs fail anyway. If you want to solve “real” problems, you’re better off with computers with excel, or specialised mathematical programs like derive or matlab. Which they also teach us how to use by the way… Calculators are handy if you have an everyday concrete problem which you want to solve exactly. Which happens about… never -.-

Dude, you can store …
Dude, you can store any course in your freaking calculator :s. Unless you have an open book-exam, it’s a foolproof way to cheat…

Also, they are numbers that occur in the real world. You just calculate what happens to a mass of 50gk instead of one of 47.598kg +- 0.002kg.

No cheating, easy calculations and easyer to correct for the professors. The numbers we use are real life numbers, 50kg is possible too :s.

So the point is to …
So the point is to use numbers that you won’t typically use in the real world so that you can get good at solving contrived problems? Math at its finest!
Is it possible to learn to use a calculator effectively? Would this be valuable?