Skip to comments.Do old fashioned arithmetic algorithms really need to be taught any more?
Posted on 12/18/2011 10:06:54 AM PST by 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.
We have the internet for looking up history. So let’s not waste our time teaching our kids.
Oh and spell check is readily available. Screw spelling class.
I remember when we got our first calculator in 1974, I thought, “hey man, this would be good for math class!” I was in second grade at the time. My maternal grandmother said, “if you use that all the time, your brain will rot.” I am still in contact with one of my former high school teachers and he says that calculators are OK, but you should know the theory to do it by brain and hand first. I think those are good things to think about and remember. The calculator is there to save time but I think one needs to know the math theory first.
I believe it still needs to be taught — teaching kids arithmetic instructs them in basic logic and casuality, which is needed throughout life ... my $0.02
No - darkness must prevail!
Who needs knowledge when calculators can think for us instead.
Math is for advanced, scientifically savvy societies. Not ours.
Math teaches a human how to think logically and to use a toolbox of methods to find an answer to a problem. Our society is going downhill because we’ve given up those skills and we’d rather hire foreigners and have them find answers for us.
Teach a child how to enter numbers into a calculator and you have a person who can do menial tasks. Teach a child how to work out a math problem and you have a thinker and problem solver.
I’m sure Roman parents thought the same thing: “My child is made to rule, not to do math problems. We can hire a barbarian for that!”
They still need to be taught. Two reasons:
One of the things you figure out as you get older is that a good portion of what you’re taught in school is not for the purposes of making you more knowledgeable, but actually to “help you think”.
Second, if you need to solve something and don’t happen to have a calculator handy, what are you going to do?
Someone, somewhere has to know those methods in order to create the calculators for lazy people to use. If you stop teaching them they fall out of common knowledge and eventually are lost. We’re not teaching the slide rule anymore, but that’s because it’s no longer needed.
Your daughter is not there to become a self-sufficient, critical thinker. She’s there to drink the Flavor-Aid of collectivism and feel good doing it.
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.
>>Math is for advanced, scientifically savvy societies. Not ours.
Ding Ding. We have a winner!! Well said!
A firm understanding of mathematics is fundamental to scientific and technical excellence.
If all you want to do is prepare people to flip burgers, then you are correct.
If you want to prepare them to be engineers or financially literate human beings.
Eh, I don’t think they need to be banned. I think their use should be strictly limited.
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.
As for computers - if it weren’t for the relatively high tech nature of my highschool I wouldn’t have entered my career path (software development). Same goes for accountants, office workers, administration, IT, networking, etc etc etc.
Yes. The process teaches you how to think logically and about how numbers work. Calculators short-circuit the process, providing answers without understanding.
So if we are hit by an EMP all of a sudden we have huge numbers of people who can’t mange math?I think it is very important for kids to learn math and learn it the same way we did.I don’t see it as a waste of time and think in a way it teaches how to reason things out.
I don’t think they need to be; that way, when I explain something using mathematics, the fools won’t know that I’m lying through my teeth.
Yes they are useful and should be taught .
Anyone can learn to push a button but by learning math , real advanced math you are teaching them how to think (reasoning and logic)
I hear people comment all the time that they wasted time studying math that they will never use ... these same people are the ones who have problems solving common problems that if they had learned the reasoning skills and truly grasped them they could then take those concepts and easily solve their problems.
Kids today do not know how to THINK and that is why they are easily led .
Your other question: “Did you even understand why these algorithms worked at the time you were taught them?”
Some, sure. More often than not, no. Even now I don’t understand why some of what I learned in calculus actually makes sense - but I didn’t continue into an engineering degree path where those things are broken down into a greater understanding.
Regardless, the point isn’t for you to be able to divide giant numbers.
“Did you even understand why these algorithms worked at the time you were taught them?”
If one is never taught them then one never has the opportunity to understand them...
As a mathematician and engineer, I must say that it is hugely important to teach this to children.
I can't respond to to everyone here, so I will will respond to your's.
Does rote following of an algorithm give you a firm understanding of mathematics?
Exactly at what point in in you education did you understand why these algorithms worked or even what an algorithm was?
Yes, for at least two reasons (I teach among others an undergrad physics class for non-majors).
One is that you should never accept blindly what a device tells you. Students have a great tendency to do just that. Did they enter the numbers correctly?
Does the answer make sense I had one student on a homework-where they can use calculators-tell me that due to slippage along the San Andreas fault the cities of Los Angeles and San Francisco would be joined in exactly 635.22723 years! I would rather on an exam that the student show me the ratio of numbers to be divided, for example, even if he can’t do the hand division or does it incorrectly. I don’t take points off if done incorrectly...I just hope he never has his battery run out at an important time.
A more important reason is that electronic cheating by students has gotten very sophisticated and entirely out of hand. Among other aspects, this is a bias against other students who don’t have the monetary resources to invest hundreds of dollars on some of the devices that are now available on the internet. Some of these devices are very concealable and look just like a common calculator.
So im my exams the rule is NO ELECTRONIC DEVICES.
Ok, I will amend my statement, and ban computers until High School.
The Trachtenberg System of speed math!
From Wikipedia: The Trachtenberg System is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp.
If you don’t understand how the math works you can’t put the numbers into a calculator correctly. And you’re gonna feel kind of silly needing a calculator to halve a recipe.
I’m a mechanical engineer by training, I do math in my head as much as by calculator. You need to know whether the numbers you generate have any semblance to reality.
You can’t take an abacus with you everywhere.
Saw six boys at our local library doing homework on the computers. Like hell they were....they were playing games.
Math via computers at grade school level take away clerical errors.
Or to put it more bluntly, the purpose of education is to develop a good “BS Detector.”
Exactly. The underlying reason for HOW and WHY these techniques work is what's important. I will never forget ( or forgive ) a teacher I once had who told us when explaining recursive algorithms that they were very important, and to MEMORIZE them, because we would use them, but don't bother trying to understand how or why they work!
Math? Probably not.
But it might come to this:
It has helped in so many areas. Please encourage (push) your daughter to start math lessons while young.
Many of these same sites are great for home schoolers as well.
Hey, I barely made it past arithmetic and geometry, but I am still way ahead of my peers in my mid-50’s.
In all fields of knowledge (in math this is very important) complex knowledge is built upon simpler knowledge. Also, the building does not have to be strictly hierarchical - often concepts are borrowed back and forth in different areas.
For example, if writing computer programs, having a good feel for how much work is involved in doing certain types of math problems is key to writing computationally efficient programs.
The good mathmetician draws upon all their learning - including the fundamentals - throughout their career.
Also, oftentimes ideas from disparate fields of study can be related or of use together; ideas can be “borrowed” from what would seem like a completely unrelated field.
Education therefore should be “broad” as well as deep. This goes into the making of the so-called “renaissance man”.
Many people doing very advanced work make gross errors in their thinking that reflects the fact that they do not have the fundamentals of the relevant fields drummed into their head.
It is important for people in all walks of life to have an excellent command of the fundamentals of a broad education; they should not be neglected by skimming over them then using a “black box” to provide a glossed over “solver” too soon in one’s education. Only after the student has exhibited a very solid knowledge of the fundamentals should machinery be introduced.
Most general students have no need of computers for k-12 education other than as a typewriter. Other than that, they are simply a plaything.
The only students who really need a computer are those in programming classes.
Using a computer actually misallocates curriculum time away from reading classics, etc. and uses it instead for silliness. How else is that that educations 100 years ago were generally far superior to those today for those who go through the whole system and graduate college.
I whipped out my calculator, pushed a few buttons, and left the $15 on the counter.
Who needs math?
The girl at my register had a calculator, and to cut to the chase, I pointed out that the meals tax (at the time) was 5%, so all she had to do was multiply by 1.05 for the more complex orders that she couldn't remember off the top of her head.
The Feeling of Power, by Isaac Asimov
True. That's where my pocket size slide rule comes in handy.
There was a wonderful Sci-Fi short story called, IIRC, “The A & O Book”. This was a supposed reference to the British bi-level secondary school systems, Ordinary and Advanced. The story was written back at the beginning of the Digital Age.
In the story, set sometime in the future, the young hero is accused of cheating on his A&O exams. The test administrator was described in much the same way as a stereotypical Hollywood nerd is portrayed; overweight, myopic, fingertips turning spatulate due to a lifetime spent at the keyboard.
The evidence for our hero’s cheating was that he had used zero computer time and had a zero percentage error rate. It is revealed that the “A&O” meant Apples & Oranges. The math problems dealt with division and percentages and were meant to be solved with the test computer’s calculator. Our young hero had been taught fractions by his reactionary grandfather and needed no computer time to calculate. Also, because he dealt with fraction through all of the intermediate steps of calculation, he had no rounding errors (i.e 1/3 -0.33333333...)
Ergo, he MUST have cheated and used a stolen copy of the answer book.
I think this was written back in the 1950’s or 60’s. Now, 50 + years later, you are asking this question, “Do old fashioned arithmetic algorithms really need to be taught any more?”
Why not? We shut down Civil Defense. May as well cut off chances of morons recovering after nuclear exchanges or large solar flares against a weak magnetic field, too (poles deviating unusually far).
Give an example of "rote algorithm."
“Were not teaching the slide rule anymore, but thats because its no longer needed.”
I still have one in my truck that I have used for over 50 years, still works and doesn’t require a battery!
The devices are a series of electronic switches. The developers had to talk to them in a language the microprocessors understand -- binary. But the algorithms they used for those devices are the same kids are taught.
Did you even understand why these algorithms worked at the time you were taught them?
Why they "worked?" They worked because they couldn't do otherwise! And you don't need to understand WHY they work anymore than you need to understand Bernoulli's Principle to take an airplane flight. If, however, you don't know that they exist and the batteries run down on your calculator, you are helpless.
Schoolwork builds brain power just like weights build muscles.
It’s no accident that elite schools still teach Greek and trig. It’s not the facts, it’s the effort.
No. And to prove my point, I want you to mail me $2 per day for the next five years in payment for my reply. This is a very reasonable sum, don’t you think? Just $2.
You do realize that all thinking involves algorithms, right?
I guess you're basically saying that thinking is obsolete, other than thinking about things like the Kardashians.
IMO, children should always learn the basics first. No calculators until they can do simple math in their heads.
Everyone should be aware that a missed key-stroke on a calculator can be expected at any time.
Critical thinking skills require independent analysis of data, and that means in math as well as any science.
Absolutely correct. I was with a field chemistry class and the students were measuring water quality parameters. They had a pretty good idea about the kind of values to expect, but when they reported one value off by several magnitudes nobody even flinched. So I asked, “What is a reasonable value for this measurement?”, they all pretty much knew and when they thought about it the light went on. Now we've got a bunch of speculation: plant toxins, pollutants, dead animal upstream, etc. Nobody ever hit on the most obvious (and correct) answer - the meter is broken.
And you are right on about the economic bias...
Oh wow, I remember that story from high school.
You’ll take my slide rule and abacus from my cold dead hands! Seriously the method needs understood first before the simplifying tools are provided. I can’t tell you how many times ive had to backtrack to find input/calculation errors in formulas that the calculator or computer were happy to spit out. It is similar to spellcheck skipping words that are improper grammatically but spelled correctly. Kids need to understand the ideas and processes first.
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