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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 stude

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.