Do old fashioned arithmetic algorithms really need to be taught any more?

[no gnu taxes]

I'm talking about the old multiplication and long division calculation methods. I know what you are probably thinking. That I am some public school advocate, even though I was pissed as hell when my kindergarten daughter asked me if I knew the happy kwanzaa song.

But are these really useful anymore? I mean you can buy a calculator for $1 that does all these things and the software developers didn't use those methods for creation of the devices. Did you even understand why these algorithms worked at the time you were taught them?

Not trying to be controversial; just want to know what you think.

[Nowhere Man]

Me, I’d allow calculators/computers at perhaps the junior high level or at the latest, senior high. I did not really use a computer until 7th grade, then again it was a TRS-80 Model-I back then, it was 1979 after all. 1982 was a real watershed with it came to computers, I was in 10th grade and used the number of Apple ][+’s we had plus I got a TI-99/4A for Christmas that year. I think that would be a happy medium but the theory must be taught and understood first.

[susannah59]

I think calculators and computers are being used far too early in school.

I had a very poor math education, hated math, and was never good at it. I still am not a "numbers" person.

I taught at a community college for a couple of years. The area I taught in occasionally involved some fairly basic math. It was scary to see that I could do certain mathematical things in my head better than some students could do with calculators.

I agree with something others have mentioned: the answer must be right if the calculator says so. They aren't thinking. Plug in some numbers, pull out other numbers, go on to the next problem. That is not a good thing! Young folks aren't being encouraged to learn to think and reason and I find it frightening.

[dr_lew]

I personally have nothing against rote algorithms, or rote learning. It’s just a question of balance. Rote learning was dominant at one time, and so there was reaction against it to the point where it is now thought of as a thing evil in itself.

Also, of course, counting in any base is the same rote procedure. I actually taught me kids once, in the guise of a game, how to hand emulate repeated incrementation of a binary accumulation register using pennies. They caught right on and thought it was great fun, but I doubt they even remember doing it by this time.

[NVDave]

Exactly. What older engineers are able to do is have an “instant BS detector.” When someone in public policy whips out some idiotic number or estimate, guys like you and I who come from the older school of “back-of-the-envelope” estimation can yell “bullcrap!” (or words to that effect) before the clown finishes his sentence.

There’s no shortage of people who are so innumerate that they will believe ANYTHING they are told - no matter how mathematically absurd it is.

In the midst of this financial charlie-foxtrot, want to become depressed? Go on a street corner and ask people “how many millions in a trillion?”

It’s amazing, I tell you.

[Erasmus]

this is a schematic of a 4-bit adder which can add two numbers, 0-15 and produce a result from 0-31.

Pardon my analism, but let me amend that to

"this is a schematic of a 4-bit adder which can add two numbers, 0-15, plus a carry, and produce a result from 0-31."

[smokingfrog]

I know, I know!

Man, it's really tough sometimes trying to keep up with demands from all the ladies ...

[dr_lew]

... Go on a street corner and ask people “how many millions in a trillion?”

Sounds like a good way to get arrested.

[Harmless Teddy Bear]

Yes.

For one thing you are not always going to have a calculator with you. For another thing it teaches you logic and the relationship numbers have with each other. Lastly you can do math in your head much faster then you can with a calculator.

I was once showing a young lady how to fill out a spreadsheet, every now and then we would have to subtract $400.00 from one cell and add it to another cell.

She either had to stop and work it out with a calculator or do a formula in the cell. I did it in my head and just punched in the correct number.

Not only was I faster but I was more accurate.

[dr_lew]

That’s not an equation, only a formula.

[editor-surveyor]

What are you going to do when your last battery is dead? (assuming that your cheap chinese calculator survives the EMP Noot says is coming)

[editor-surveyor]

>> “I would ban computers and calculators from school....the point of education is to train the mind on what to do with facts, and not just teach people how to use a calculator.” <<

.
Amen!

We’re headed for a huge failure.

[smokingfrog]

You don’t expect me to give up ALL my secrets, do you?

[editor-surveyor]

Thanks for posting that.

As a young teen, I was an avid Asimov reader, but had forgotten that one.

[editor-surveyor]

You don’t have to go back 100 years; 50 will do nicely to illustrate the disaster.

[Gandalf_The_Gray]

Eh, I don’t think they need to be banned. I think their use should be strictly limited.

I agree they should be used sparingly in primary grades, more intensively in mid and high school. Most schools misuse their computer equipment as adjuncts to a typing (keyboarding) course.

While you *can* figure out most derivations by hand, it takes forever. Once you’ve gotten the concept and methodology down, it is instructive to be able to quickly show the result of a derivation and how alterations affect them.

Not quite sure of what you are deriving. Multi-digit multiplication and long division are not really derivations, they are algorithms based upon multi-digit addition and subtraction, which in turn are based upon single digit addition, subtraction, and multiplication. While you can count "gummy bears" and other manipulatives (including fingers) to arrive at correct answers, the most effective way to process this information is rote memorization of the various "math fact tables" along with the associative, commutative, distributive, and equality properties.

Having the basic "math facts" in memory allows one to build from simple (short) division with that unsatisfying "remainder", to long division and normalization of decimal points. Fractions follow naturally from division and rules for manipulation of them is again best memorized. The continuum of integers, the notion of zero as a number, negative numbers (and their rules) lead to concepts like infinity. The associative, commutative, distributive, and equality properties come to the fore again when algebra is introduced. Infinities are a good place to start discussions that introduce differential and integral calculus.

All mathematics builds from the sublimely simple to the ridiculously complicated, one step at a time, building more structure from simple facts. Digital computers are amazing tools but their internal mathematical operations are really primitive. Digital inputs are converted to base two and fed to hardware logic circuits (or software simulations) that perform addition. If subtraction is called for they perform a "ones compliment" on the subtrahend and add, multiplication is provided by multiple additions and division by multiple subtractions. The blinding speed of computers allows them to use these simplified methods to process data at prodigious speed.

Computer algorithms for performing basic math functions are not particularly useful for us poor humans who think at a much less then gigahertz clock rate. However we do get to write the instructions for our hyper speed idiots and so still serve an important function. A computer program is built from smaller logical blocks like mathematics itself, it is always wise to start with the basics when dealing with complicated subjects.

Regards,
GtG

[E. Pluribus Unum]

I personally have nothing against rote algorithms, or rote learning. It’s just a question of balance. Rote learning was dominant at one time, and so there was reaction against it to the point where it is now thought of as a thing evil in itself.

The "reaction" is mainly from unionized, affirmative-actioned teachers, many of whom are barely literate themselves, if they are literate. We can't know for sure, because we aren't allowed to test them.

Get rid of government schools. Make people pay to send their kids to school. Do that, and you can subscribe to any New-Agey education BS you wish.

You want your kids to know grammar; have them diagram sentences for the first four our five years of their language education.

You want them to have a basic grasp of math; have them memorize multiplication tables until they know them.

You want your kids to have high self esteem for no apparent reason, tell them that they already know everything they need to know and if something is hard, it's because it's useless.

[taterjay]

Do you mean like when someone tells us there are 57 states?

[MortMan]

Mathematics is the ground floor in the problem solving skyscraper.

[NVDave]

Yea, something like that.

[ctdonath2]

I teach beginning programming. Many fail because they do not grasp the basic nature of numbers, operators, and variables. Relying on “magic” calculators prevents this grasp; learning to do things the hard way, even if soon abandoned, sets the groundwork for understanding the basic concepts of programming. We risk losing a generation of potential talent precisely because such basics are not taught, in turn hindering advancement of such things as calculators.