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Why do we still teach people to calculate?

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Re: Why do we still teach people to calculate?

#51

Post by anon291 »

PhasmaFelis wrote: post #16
ggm wrote: post #3

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 t…

> Mathematicians are very much in davis/hersh "what is mathematics anyway" This reminds me of getting my CS degree in the early 2000s, then slowly realizing that my comp-sci program had taught me lots of interesting things about how computers and programs work, and essentially nothing about how to write code for a living. Also reminds me of playing Dominion (the card game) with another student, me saying "Okay, I've…

At the end of the day, writing code is not difficult. Understanding what it's actually doing is the hard part. Moreover, understanding how to write code that reasons about code (and higher) is when you start to need computer science, or really just axiomatic systems (math).

Re: Why do we still teach people to calculate?

#52

Post by abdullahkhalids »

KeplerBoy wrote: post #23
throwway120385 wrote: post #10

Earlier quoted context omitted.

And calculators get broken very quickly on construction sites. And you must be capable of adding and subtracting and finding the LCD and GCD of fractions to read a tape measure in US customary units.

What is going on with your tape measures? Confused european over here.

The metric system has uniform computational cost whenever you add/subtract or divide any two lengths.

The inch-foot system does a tradeoff. Easier computation when your lengths are certain combinations of simple fractions, but difficult ones when not.

Re: Why do we still teach people to calculate?

#53

Post by Baader-Meinhof »

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.

Re: Why do we still teach people to calculate?

#54

Post by johncarlosbaez »

verzali wrote: post #45
johncarlosbaez wrote: post #39

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

I imagine you know more than enough math to already do that!

I know plenty of math, but having more ignorant victims will make it easier.

Re: Why do we still teach people to calculate?

#55

Post by ggm »

anon291 wrote: post #50
ggm wrote: post #3

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 t…

While I can agree that in the later years, the math becomes unnecessarily prescriptive, as a mathematician myself, I am categorically not in the 'what is mathematics anyway' camp, at least not for kids. For children, it is fundamental that they calculate. Learning arithmetic is the first introduction into the idea of infinity, which is a vital concept all children must come to terms with. The natural numbers pop up e…

Nothing I said, nothing whatsoever was meant to imply kids should not learn to count or acquire the times tables, and learn the fundamentals of mathematics we call arithmetic on the streets.

Nothing.

Re: Why do we still teach people to calculate?

#56

Post by cassianoleal »

ComposedPattern wrote: post #36
pklausler wrote: post #22

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.

In the schools I'm familiar with, this isn't really a skill that's taught. The emphasis is on carrying out steps correctly on paper. Making a good estimate without showing work would definitely be frowned upon.

Taking the steps multiple times (practicing) will make it fast and trustful.

Guessing may get you a part of the way if you're very good at it, but repeatability is what really hammers it into you. It also gets you out of trouble when for any reason your guessing instinct is not at full steam (when tired or otherwise incapacitated, anxious, etc) since you can usually relatively quickly rely on the steps you have drilled for.

Re: Why do we still teach people to calculate?

#57

Post by wongarsu »

ComposedPattern wrote: post #36
pklausler wrote: post #22

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.

In the schools I'm familiar with, this isn't really a skill that's taught. The emphasis is on carrying out steps correctly on paper. Making a good estimate without showing work would definitely be frowned upon.

In Germany this was part of the physics curriculum.

It made sense since order-of-magnitude estimations constantly come up naturally in all fields of physics, whether you are asking "is this plausibly possible", "what kind of instrument do I need for this measurement" (and later "can we even measure this in this setup") or "are the results of my experiment plausible". There's a reason we joke that to the physicist g=10 and pi=3.

It's difficult to test this kind of thinking in a written test without turning it into something entirely different, but not everything in school has to be on a test. Typically half of our marks were made up from classroom participation.

Re: Why do we still teach people to calculate?

#58

Post by anon291 »

ggm wrote: post #55
anon291 wrote: post #50

Earlier quoted context omitted.

While I can agree that in the later years, the math becomes unnecessarily prescriptive, as a mathematician myself, I am categorically not in the 'what is mathematics anyway' camp, at least not for kids. For children, it is fundamental that they calculate. Learning arithmetic is the first introduction into the idea of infinity, which is a vital concept all children must come to terms with. The natural numbers pop up e…

Nothing I said, nothing whatsoever was meant to imply kids should not learn to count or acquire the times tables, and learn the fundamentals of mathematics we call arithmetic on the streets. Nothing.

I don't think I said you did say that. It was a response, not an argument.

Re: Why do we still teach people to calculate?

#59

Post by arkadiytehgraet »

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.
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