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I work with K12 schools in the U.S. and one of our really sad stories is how a calculus students failed to solve a "A t-shirt that costs $15 is 20% off today. How much does it cost after the 20% discount (don't include tax)?" <-- not the exact wording, but you get it.

They responded, "I don't remember the formula for a sale". Only knowing formula's is terrible, it makes knowledge super fragile. So, I for one support your idea of emphasizing understanding over formula memorization!



I feel that way about the % key on calculators that also have a / key. If you need a % key, you have no business using one :-/


Eh, the closer you can get to entering a formula without the mental effort of backtracking and lookahead the better. It's like fraction buttons; obviously you can just think ahead and use parenthesis with division, but a smart fraction button will save a lot of time


What's 20% of $59.22?

    .2 * 59.22
What price is $2.99 milk with 9.2% inflation?

    2.99 * 1.092
What did $5.00 gas cost last year?

    5.00 / 1.092
I'm not seeing backtracking and lookahead.


You'll note that English is written left to right. In the string "20%" there is a "2", a "0", and a "%" arranged from left to right. To type that string into a calculator, one could press "2", "0", and "%" in that order, or "0", ".", "2", in that order. To know to lead with "0." rather than "20", you have to look ahead.

For the others you'd have to do the mental work to append a 1 regardless, might as well stick with decimals




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