> I think we do a great disservice to students learning mathematics by not emphasizing the power of computers and calculators in modern arithmetic. But all of

> I think we do a great disservice to students learning mathematics by not emphasizing the power of computers and calculators in modern arithmetic. But all of the students who came to the help desk in college were practically addicted to their overpriced graphing calculators. A decent fraction of the time I would look over their work, they'd be on their last try in WebAssign (may it be cast into the fire) with a scared look on their face, and I would say "you entered this part into the calculator wrong". I knew immediately because I learned to estimate these things. You don't have to even know the multiplication algorithm; you can stick to multiplying the first digit, adding exponents in scientific notation, etc. Learning to work with the calculator instead of behind the calculator will make you use it more effectively. The multiplication table has 45 entries that aren't duplicates or multiples of 1 or 0. Kids memorize longer things all the time. The brain is definitely not the limiting factor. >Textbooks still focus things like von Neumann's ability ability to multiply large digit numbers in his head as a proxy for his math proficiency. I don't recall ever seeing that in a textbook. There is a famous story about JvN summing an infinite series in his head, but very few people can do that or would be expected to. He also estimated the yield of Trinity within a factor of four by just looking at it. One should never compare themself to von Neumann. I honestly believe the biggest factor in math anxiety is osmosis. Their parents are afraid of math, their teachers (often!) are afraid of math, and there's a robust body of evidence in developmental psychology that children inherit the worries of their guardians.