Why do we still teach people to calculate?

Because being able to do basic order-of-magnitude arithmetic in one's head is a critical thinking tool essential to detecting nonsense claims in real time.

Because you need to be able to run numbers in your head for a lot of practical tasks, and inability to do napkin math can cost you very dearly

Yes we should start my six year old with group theory. When we go to the farmer's market I can ask him under what transformations is an apple invariant, and then pay for it by having him solve a Rubiks cube.

to me this seems very ill-thought through, and doesn't feel like they actually remember what math was like. they are suggesting letting the computers do the computation part, but we already do that once that skill has been mastered. i.e.: simple calculators are allowed in calculous exams.

the problem with bad ideas in education is the system might be stupid enough to follow through with it, like that new math nonsense.

It's interesting to discuss mathematical literacy with primary school teachers, mathematicians, statisticians, data scientists. I do periodically.

Primary school teachers respect core fundamentals as kids acquire "mental muscle memory" and realize they have to both create some axiomatic knowledge (axiomatic in as much as you know 9x9 is 81 from rote recall, not because of a belief in inductive reasoning) as well as try to begin an uplift to reasoned knowledge (that 2^2 x 2^2 is 2^(2+2) is 2^4) and some coding/transcoding (1/2 == 0.5) Cuisenaire rods come in and out of fashion. Crows can count. Kids are sometimes dumber than crows.

Mathematicians are very much in davis/hersh "what is mathematics anyway" -I believe Hersh noted that you can be in a field where only 3 other people worldwide can talk to you cogently about your work, and peer review is meaningless.

Statisticians are very comfortable that approximations work, but are less concered with accuracy at times, and very much concerned with methodology. I've had quite remarkable conversations with them about sample size, and how UX people can survive on 5 responses. I neve predict which side of the problem they're going to respond.

Data scientists are almost intuitive at times. sometimes the reliance on codified knowledge (numpy/pandas) and a belief in the p-jacked value or an obvious excel error is frightening. I think they divide sheep/goats into the numerate, and the highly visual.

I consider myself semi literate, mathematically speaking but in fact, I stumble over basic arithmetic all the time, and I struggle with ideas behind complex numbers, trig. I have to re-prove things which should be known, re-induce belief in things which are based on inductive reasoning, I question commutation all the time. How the hell can 2 x 3 be the same as 3 x 2 there's a fundamental left-right ordering in my brain which at times I ask myself is this inside the farsi or hebrew or thai or boudestrophon flow texts, suggesting that not all right-to-left ordered languages obey it yet alas I do.

I also still don't entirely understand why school focussed on trig so much given that very few of us are navigating by sextant. I suspect at times it was dividing us into the ones which drink from the hand, and the ones which lap from the stream.

Do they teach decimal to octal and hex and binary in primary school yet? Will the world be different when the last of the duodecimal measurement learners have died?

To see patterns in things and to extend from the known to beyond.

While numeracy is certainly useful, isn't that only the surface point. The depth in deeper learning (we all learn - Edward Deming - but learn what?) is in shaping self and the internally and externally perceived worlds.

I have rarely skimmed over such a long interview with virtually no content.

Ok, we get it. Wolfram Research has fantastic and somewhat underappreciated products (Wolfram Alpha is far more impressive than LLMs!) and you want to cash in on the AI hype. But please don't take it out on innocent students.

There's two parts:

1. Basic math, eg long division. This is what all the commenters are focusing on, and I largely agree with folks - we need to keep teaching this.

2. HS / College math. E.g. memorizing all the rules to solve integral calculus equations. Or solving all those circuits in Intro to EE. I agree with Wolfram here. At this point, students should be mentally developed enough to start focusing on formalizing and reducing problems rather than rote memorization or hand calculations. It's good to go over all the rules and practice a few times. But to make a whole quarter of it seems a bit much.

He is making a really long winded point I'm not sure I completely understand, so feel free to correct me if I am off here, but I could not really disagree more.

While there is value in emphasizing things like defining/abstracting a problem rather than calculating the result of it, things like the "algorithm" typically taught to elementary schoolers to do long division is pretty much how you would naively/algorithmically program a division operator that can give a remainder. The multiplication "algorithm" given to me at a young age was what first gave me the insight into the connection between addition and multiplication. Abstracting this away in education could not possibly be doing society, math, or computation any service whatsoever, at least not in the way (I think?) he is imagining.

I do think there is value to asking whether a problem needs to be solved or redefined or abstracted in a different manner. I had a calculus teacher in college a long time ago that had a really hilarious way of emphasizing this - he'd often bury "trap" questions into his tests that looked really simple but would test your knowledge of a simple algebraic or trigonometric trick he'd only covered during lecture, and lack of knowledge of this trick would lead one down a hopeless 20+ page response to the problem, to the point where if you found yourself going off the rails with a complex solution, you knew you messed up somewhere. This forced me to look at the problem from a variety angles to see if I could solve it in a more clever, general, or simpler way, or if it could be rewritten (this was usually the correct way to solve it). I really valued that, even years and years later, but maybe that's not the kind of thing Wolfram is getting after in this interview.

Every time this topic is brought up I can't help but think about Asimov's short story: https://en.m.wikipedia.org/wiki/The_Feeling_of_Power

I think that learning some basic by-hand computation skills is useful. The question is where do you draw the line. The current practice seems to be to stop at long-division. To me this seems a reasonable place to stop. There are hand methods to do more complicated calculations, such as computing square roots, that are not taught in school, which is probably fine. I don't think leaving out long-division would save that much time, and I think it's a good mental exercise for kids to have to learn a fairly complex algorithm. If I could suggest one improvement, it would be that in later advanced math courses, they returned to long-division and explained at a deeper level why that algorithm works.

As someone with reasonably good mental math skills (120+ score consistently on https://arithmetic.zetamac.com/, default settings), I cannot really say it helps me much in the real life, at least not on the surface. It sure is nice to be able to estimate some things accurately without having to resort to a calculator, but in no way would anything change in the way I think or conclusions I make if I had to use one, so there might be some truth to what Mr Wolfram is suggesting.

Calculation requires practice which builds intuition. Moreover, it's just more time consuming to input things into a calculator. Its much faster to just have 8 / 4 = 2 in your head.

The only time I said "why don't we just use a calculator" in school was during the oddly specific focus on integration techniques in calculus (trig substitution etc). Seems like the problems were carefully set up to be solvable that way, but IRL you'd actually need a computer.

I hope they stop teaching people to calculate. Then I'll start up my career in fraud and embezzlement.

>Why Do We Still Teach People to Calculate?

I would say it is intended for everyone who can not figure it out for themselves.

Because it’s easy to test and grade?

Because a computer isn’t embedded in our heads yet, wait we have one, why not use it.

My parents used to force me to memorize my times tables and quiz me all the time.

Definitely paid off. Can calculate numbers in my head pretty easily. Definitely used to help with tips or commissions or whatever.

I stopped about a third of the way through, once machine learning cropped up (I'm biased against it, as I'd rather humans use energy to learn and practice than a computer do it, but I accept I might be missing something), but I support the first two points:

1. Define the problem and why we're going to solve it (in D&D terms, I'd say this is a wisdom check)

2. Translate the problem into math language (needs imagination and experience, which is an intelligence check)

2.5. Levitt noted the importance of interleaved practice; why practice a tool intensively for the test only to never use it again? Supported by the authors of Make it Stick: the science of successful learning.

That all sounds better than "here kids, learn these tools out of context".

If we get hit by an EMP blast and get blown into the 19th century those calculation skills would make some rich.

"because you live in a country where the primary purpose for you as a citizen is to go into debt, so you better know how to, at the very least, do financial planning"