Imagine you're studying, for example math, and you have to learn calculus, and you're living in a dormitory with a colleague, who's great at integration calculus, and every time you get another integration function puzzle to solve, this guy (or gal) pops up and says "it's 2*e^2/x+C dx", "it's e^2+C dx", "it's sin(x)/cos(x)+C dx" after 5 milliseconds, even before you fully comprehend the function...
I have a question for you
will you be able to pass the exam at the midterm?
They can already do this just by downloading Mathematica.
Solving integrals is the original selling point of Mathematica: https://www.wolfram.com/mathematica/scrapbook/1988/03/04/198...
And yes, I memorized a bunch of integrals for my calculus class and then promptly forgot them all after the final exam. It's not worth it to remember how to do integrals other than simple cases like polynomials or sin/cos on their own.
Do you also oppose calculators for the same reason?
If calculators had a camera on the back that let you take a photo of a word problem on your homework or exam and then provided a complete answer including steps and "work shown" I expect that would have a detrimental effect on students' learning of the subject matter and ability to reproduce it without the calculator.
That's a silly argument, because arithmetic is so simple people pick it up in spite of their use of calculators. Hell, people learn simple arithmetic even if they've never had any schooling (they can tell you that 5 apples and 3 apples makes 8 apples, things like this). And arithmetic with big numbers is so tedious regardless of how well you know it that it's better to just use a calculator, and people have always done this (before digital calculators you had an abacus, multiplication tables, and many other similar instruments).
Calculus or programming or advanced algebra etc are nowhere near the same difficulty, and the same rules don't apply.
There are many differences, one of them is that when you buy a calculator it will serve you well. Other is that calculator does not confabulate the result from time to time and you don't have to pay attention and recheck everything it calculated... And the calculator does not provide you with the most appealing results that are _de facto_ calculated to deceive you
Small update to the differences here: calculator won't ever need a GPU or other device that cost is 50k$ and you'd always need to rent it for seconds. Calculator also won't be embargoed at any point of time (i.e. when next USA president comes into the office, he/she won't be able to prevent your further usage of calculators in your country). Also all the things done by calculator you could do on the paper, just slower.
The integration calculus is a little bit different and more connected to programming - you need to work through as many possible types of integrals as possible to get those good methods of solving into your mind, and then exercise them through and through to get them into your long lasting memory. The same in programming patterns, ways of solving problems etc.
I'm a high school dropout dude...