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I teach computer science, and you need to know long division in order to understand the % operator. This is actually an issue I run up against because my 15 an

I teach computer science, and you need to know long division in order to understand the % operator. This is actually an issue I run up against because my 15 and 16 year olds ask to use a calculator for things like 23 - 7 ... And then I want them to do crazy math like 23 % 7.

mkl 7y ago
You need to understand the idea of division, but not the method of long division (I understood % years before long division). Kids learn about remainders from division at primary school, and that's enough to understand %. The idea of remainders, and multiplication tables, make 23 % 7 easy by stepping through the 7 times table. I think multiplication tables are still pretty important, but a lot of my first and second year university students are patchy on them. It doesn't bother me too much when someone learning about modulo arithmetic needs a calculator to figure out that 7 goes into 23 3 and a bit times. Then they can do 7 * 3 and figure out there's 2 left over. Needing a calculator for 23 - 7 is concerning at 16 though!
- abdullahkhalids 7y ago
  I have taught university engineering freshmen in physics courses who routinely used a calculator to simplify fractions as simple as 4/2 or a group of four students who put down 1/3+1/2 = 2/5 and could not identify the mistake when it was pointed out to them. This is what happens when you stop the math drills in school. Requiring math students to know the concepts and not be proficient at the mechanics is like telling a basketball player they just need to know that if they spin the ball when shooting, it is more likely to go in. That doesn't help them become better players. Shooting a spun ball 10,000 times is what does.
  - mkl 7y ago
    I didn't say anything about stopping drilling in general, just that I think long division is at this point merely a historical curiosity. I totally agree that the number sense from drilling fundamentals at school is essential for higher maths. Addition, subtraction, multiplication, fractions, powers, etc. are all very important, as are intuitions about them that only come from practice. Fractions are something many first year university students are incredibly weak at - I've seen the same things you have.

mkl 7y ago

You need to understand the idea of division, but not the method of long division (I understood % years before long division). Kids learn about remainders from division at primary school, and that's enough to understand %. The idea of remainders, and multiplication tables, make 23 % 7 easy by stepping through the 7 times table. I think multiplication tables are still pretty important, but a lot of my first and second year university students are patchy on them. It doesn't bother me too much when someone learning about modulo arithmetic needs a calculator to figure out that 7 goes into 23 3 and a bit times. Then they can do 7 * 3 and figure out there's 2 left over. Needing a calculator for 23 - 7 is concerning at 16 though!

abdullahkhalids 7y ago
I have taught university engineering freshmen in physics courses who routinely used a calculator to simplify fractions as simple as 4/2 or a group of four students who put down 1/3+1/2 = 2/5 and could not identify the mistake when it was pointed out to them. This is what happens when you stop the math drills in school. Requiring math students to know the concepts and not be proficient at the mechanics is like telling a basketball player they just need to know that if they spin the ball when shooting, it is more likely to go in. That doesn't help them become better players. Shooting a spun ball 10,000 times is what does.
- mkl 7y ago
  I didn't say anything about stopping drilling in general, just that I think long division is at this point merely a historical curiosity. I totally agree that the number sense from drilling fundamentals at school is essential for higher maths. Addition, subtraction, multiplication, fractions, powers, etc. are all very important, as are intuitions about them that only come from practice. Fractions are something many first year university students are incredibly weak at - I've seen the same things you have.