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“But that would be like telling a student in the 70s to pretend that calculators or computers don’t exist.”

If students of the 70s or today pretended they didn’t exist up to a certain point when they needed them to move forward, like bioinformatics or something, they 100% would be better off. There is plenty of research on off loading thinning providing a worse understanding of the material - eg side rules proving a better understanding than calculators.

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Exactly. I always think about the ways consumers make terrible decisions with everyday purchases at the grocery store etc. If people could easily estimate unit costs in their head for example, a lot of predatory options would have to go away. But calculators keep people from having to get good with everyday math in their head, while those same calculators sit unused in many everyday scenarios where people don't go to the effort to use them.

Quick estimating (which is a different skill from calculating exact answers using pen and paper) is most useful there. People do carry computers with them these days and they do have calculator apps. Some shops I buy from do have unit prices for many items.

I think AI might be more of a problem, at least for some skills because it is not just doing a small unit of work. its more like the problem of doing more complex calculations. An example I have come across with calculators is students learning statistics without knowing how to calculate a variance, because they just put the numbers into a calculator. There is a failure there to learn the concept - they do not really know what a variance or SD is. I can imagine AI doing a lot of that.

“You can use the electronic tuner once you learn to tune by ear” - any decent guitar teacher

If the challenge is held constant, giving people tools is just teaching a different skill set than teaching them unaugmented. The augmented skill set is more relevant to how people do work in the real world, but working through things unaugmented likely help people build a robust internal schema more quickly. We definitely don't need to spend as much time training unaugmented abilities going forward though, kind of like how the number of assembly related classes in CS departments has gone down over time as we've moved up the stack.

I don't know if this was universal, but when I was a student we weren't allowed calculators until I believe 10th grade

You learn stuff by heart, so that when you mess up with the calculator you have a feel that stuff has gone wrong

I liken this to how my own final exams in school were. We had a "cheatsheet" on the front of every exam [1] with all the formulae that might (or might not) be relevant, even simpler stuff like pythagoras' formula was on there that everyone ought to know by that point. We also had access to calculators.

This is, of course, after years of learning without cheatsheets and calculators, where you learned to intuit if a number actually made sense when spat out by the calculator, and when you learned when and how you're supposed to use a certain formula. For example when doing any kind of Physics or Chemistry you're working with numbers that don't make intuitive sense (and often are quite literally imaginary!), like things that are to the ^32 or ^-28, but you still learn to intuit whether the relative scales of the numbers make sense with what you'd expect to see given similar prior experience.

As for the formulae, even with the cheatsheets if you didn't know why or how some of the formulae were supposed to be used, well good luck to you because just knowing the formula isn't even half the picture. I just dug up an example formula reference sheet and despite definitely knowing a lot of the stuff there, I haven't practiced a lot of the maths involved here in years so I wouldn't be able to get anywhere close to answering some of these questions despite my access to the formulae.

AI takes all of this to an extreme. People simply plug in their question into their chat interface of choice and don't even bother reading the output even slightly. It'd be like seeing that the mass of a planet is x^-27 and not realizing you must've input something wrong because you simply trust the calculator without any understanding of what numbers you're plugging in.

[1] - As an example of what I had - https://pmt.physicsandmathstutor.com/download/Maths/A-level/...

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