4 ms·
Perhaps base 10 is the problem. In base 2, you can learn the "multiplication table" in 10 seconds (0 X n=0, 1 X n=n, we're done.) The long multiplication algori
by olooney 7y ago
Perhaps base 10 is the problem. In base 2, you can learn the "multiplication table" in 10 seconds (0 X n=0, 1 X n=n, we're done.) The long multiplication algorithm for n and m is just multiply by n by the least significant bit of m, add to the accumulator, left shift, repeat. You can do subtraction by adding the two's complement (just flip every 1 to a zero and every zero to a one - trivial for a child to learn) instead of using the "borrowing" algorithm. You never have to "guess" when doing long division in base 2. All of these operations can be justified in terms of the Peano axioms with very short arguments: prove the associative and distributive properties, and the multiplication algorithm is obvious, etc.
Arithmetic in base 2 is so easy, you can literally teach your pet rock to do it (assuming your pet rock is a reasonably pure silicon wafer with scattered boron and phosphorous impurities shot through with thin veins of copper.)
And no, I'm not advocating teaching kids to convert between different bases, which they almost universally find confusing - I'm saying we should teach kids arithmetic purely in base 2, and only expose them to base 10 once they understand the fundamental concepts.
Am I being serious? Well, it's certainly a lot easier to dismiss this approach out of hand then to pinpoint what - if anything - is actually wrong with it.
- koonsolo 7y agoThe real world depends on base 10, and so it's way more practical to learn calculations in base 10. I said calculations, not math. I think there is a big confusion between math and calculations. Kids learn calculations, not math. Learning the multiplication table is just a way of how to do quick calculations inside your head. I need to pay 35.15 euros, so how much do I get back? That is calculation not math. In my opinion the most practical thing that kids need to learn first. It's more about remembering than logic. When the get older, math comes into the picture. They can leave calculations up to calculators or computers, and learn the language of math. So in my opinion, there needs to be a more clear distinction between calculations and math, because they are definitely not the same.
- pharke 7y agoWasn't the premise of the article that the reason U.S. students perform so poorly in math in higher grades is because they are only being taught to memorize arithmetical facts and algorithms without properly learning the reasoning behind them? It seems you're prescribing the cause of the problem.
- koonsolo 7y agoNo, I'm saying that they are 2 different things, which seems to both end up in the "math" bucket. Both have their applicability, but knowing one doesn't imply knowing the other. Each one also has a proper age group to start teaching it. Little kids have great memory but limited reasoning skills. That changes when they are older, so at that point you should switch from calculations to math. Dropping calculations for math is just as stupid as dropping math because you think calculations are enough.
- deleted 7y ago[deleted]
- tathougies 7y agoHaving to say one billion one million one hundred and one (12 syllables) to mean 583 (5 syllables) just sounds annoying.