4 ms·

I was fortunate enough in college to have a professor who marked me right on questions where I found the answer in an unexpected way- once I came up with a nove

I was fortunate enough in college to have a professor who marked me right on questions where I found the answer in an unexpected way- once I came up with a novel infinite series he had never seen before, and he coded it up, and it converged slowly but it worked! Understanding is more important than memorization.

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candiodari 5y ago
You were very fortunate indeed. What would have happened if, like half of all children, you got a below-average math teacher ? Yes the solution to all learning problems is more intelligent teachers. We know. This has been shown many times. The quality of teachers matters more for educational achievement than the difference between a city-center public school and a private Montessori school. Obviously that doesn't scale and will never be the experience of more than a tiny minority of kids.
- TimTheTinker 5y ago
  An above-average math teacher doesn't start by denying objectivity or calling it by an epithet.
WalterBright 5y ago
> in college Not 3rd grade. Following an algorithm is not memorization.
- fallingfrog 5y ago
  In 3rd grade too. Word problems were always a bit more fun for me, especially if they required a bit of thought to figure out how to approach the problem, but being told to just follow an algorithm 100 times was unbearable. Might be an adhd thing though. Different people learn in different ways.
  - WalterBright 5y ago
    > 100 times Practice is how we cement things into our minds and get good at them. Of course it is repetitive and boring. Someone could teach you how to throw a basketball into a hoop. Want to get good at it? Repeat it 30,000 times, not 100. When it became time for me to implement division for the 8086 processor, I implemented the exact same long division algorithm I was taught in 3rd grade, except using binary rather than base 10. Shift-subtact-add. https://github.com/DigitalMars/dmc/blob/master/src/CORE16/LMATH.ASM#L102 https://github.com/DigitalMars/dmc/blob/master/src/CORE16/LM... Did it again to create the floating point emulator. https://github.com/DigitalMars/dmc/blob/master/src/CORE16/FLOAT.ASM#L598 https://github.com/DigitalMars/dmc/blob/master/src/CORE16/FL... It turns out there are faster algorithms (see Hacker's Delight), but those aren't very amenable for pencil and paper.

deleted 5y ago

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candiodari 5y ago

You were very fortunate indeed. What would have happened if, like half of all children, you got a below-average math teacher ? Yes the solution to all learning problems is more intelligent teachers. We know. This has been shown many times. The quality of teachers matters more for educational achievement than the difference between a city-center public school and a private Montessori school. Obviously that doesn't scale and will never be the experience of more than a tiny minority of kids.

TimTheTinker 5y ago
An above-average math teacher doesn't start by denying objectivity or calling it by an epithet.

WalterBright 5y ago

> in college Not 3rd grade. Following an algorithm is not memorization.

fallingfrog 5y ago
In 3rd grade too. Word problems were always a bit more fun for me, especially if they required a bit of thought to figure out how to approach the problem, but being told to just follow an algorithm 100 times was unbearable. Might be an adhd thing though. Different people learn in different ways.
- WalterBright 5y ago
  > 100 times Practice is how we cement things into our minds and get good at them. Of course it is repetitive and boring. Someone could teach you how to throw a basketball into a hoop. Want to get good at it? Repeat it 30,000 times, not 100. When it became time for me to implement division for the 8086 processor, I implemented the exact same long division algorithm I was taught in 3rd grade, except using binary rather than base 10. Shift-subtact-add. https://github.com/DigitalMars/dmc/blob/master/src/CORE16/LMATH.ASM#L102 https://github.com/DigitalMars/dmc/blob/master/src/CORE16/LM... Did it again to create the floating point emulator. https://github.com/DigitalMars/dmc/blob/master/src/CORE16/FLOAT.ASM#L598 https://github.com/DigitalMars/dmc/blob/master/src/CORE16/FL... It turns out there are faster algorithms (see Hacker's Delight), but those aren't very amenable for pencil and paper.