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.
Where to start? I do not agree.
I’m in my early 50s and I’m the only one of my peers who took Latin in HS. And I didn’t know they quit teaching trig - guess I was born too soon...
Log tables and knowing how to use them saved me during a high school physics make-up quiz that I had to ace to graduate-frequent fishing & beer related truancy involved!
My vintage 1976 VHS-tape sized TI calculator died but the log tables in the back of my “College Math” remedial text book saved the day.
Mr. Restall gave me extra credit, the quiz paper showed my work up to the point the battery died and then how I switched methods.
Bad idea. You need to know how to do basic addition, subtraction, and multiplication in your head, because there are times when your pocket calculator or computer isn’t handy. And because they are a part of mental training.
Not most of them, not at the beginning, but with use comes understanding. It's important to teach the algorithm through rote memorization if necessary and then work examples till it sinks in. We learn most of our abstract concepts this way.
I learned the difference quotient as a part of algebra without any idea what it was used for. When I hit calculus and found out it was to calculate derivatives, I was thrilled. I already knew how!
It's stylish these days among "educators" who couldn't give you a definition of the word "concept" if their tenure depended on it to insist that children must understand what they're learning and therefore teaching them the algorithms is not conceptual.
It's rubbish. Man took thousands upon thousands of years to develop these algorithms. It's our responsibility to pass them along to the young. Wasting their time re-inventing the wheel will result in a severely stunted education.
"That's what Greeks are for."
I like that :) Pretty good short story
Good for you. I took first-year Latin and then switched to French. To this day, I wish I'd have taken all 4 years offered. I think Trig is still taught, but in New York at least, it's rolled in with Algebra II -- which makes some sense.
I could not agree more! Witness people bemoaning the fact that half the population is below average!
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.”
Bingo... Couldn't agree more...
Math is not just mechanics but also a state of mind so to speak. Manual math skills are critical even if your most complex task is balancing the checkbook or looking at the ATM balance and determining if I spend $XX more, I will have so many $$$ left till payday.
The state of mind aspect really comes into gear if you go into a math intensive field such as sciences, engineering or some corners of business. You must learn these mechanical basics to even know what to plug into your calculator or program. And, keep in mind that someone has to write the program in the first place. Once, I found an equation and math method in a textbook and things were working out screwy. The book had the author's name and bio in the front pages. I just called up the university and asked to speak with him. Turned out that the book info was incorrect and it was supposed to be fixed in the next printing. If I had been emitted in capability to pushing numbers on the calculator instead of being able to wrap myself into the entire process then a several million $$$ design error easily could have been the result.
It would be nice if somebody knew what division was..
The only way to know that is knowing how to do it..
Then you have your basic ignorance of Calculus..
and even Trigonometry.. Americans are dumber than rocks..
People that flunk out of math tend to go into Law and journalism..
We had to show our work as a means of showing that we actually knew how to do the math.
A correct answer wasn’t enough.
I teach physics and chemistry at a private college prep school.
The BIGGEST problem I have is teaching kids the concept of a REASONABLE ANSWER.
Some of them don’t KNOW, (have not memorized) basic math facts...so they just write down what “the calculator” says, even when it’s a stupid answer.
Latin is the language of science and medicine.
I didn’t take latin but picked up a considerable bit through my interest in science. Those latin root words come in real handy.
I think it would be a good idea if high school guidance counselors would talk to students in their freshman and sophomore years and ask them about what subjects they were having difficulty with, and then take corrective action based on that information, to help prevent these students from ending up with "second choice" or "third choice" majors in college or graduate school.
IMHO, just the process of learning the +, -, * and / tables and seeing the relationships, instills self discipline, something, again IMHO, that is sorely lacking.
I for one would like to hail our new ‘calculator’ overlords......
I for one would like to hail our new ‘calculator’ overlords......
If you depend on the calculator you will forever be dependent on other people to do your thinking for you.
EMP attacks won’t wipe out your memory nor disable slide rules.
Please tell me you aren’t serious. “Them’s just jokes,” right?
I can’t tell you how many ignorant cashiers and waiters haven’t been able to give me proper change because the “machine” jammed, lost power, or just plain broke right in front of them.
Each time, I taught them how to count forward from the amount of the sale to the amount I tendered. Each time they stood there transfixed as if I had shown them a magic trick for the first time.
We have enough stupid people voting for Democrats. Let’s continue to teach basic readin’, writin’, and that other thang ‘bout countin’.
We are becoming so mentally lazy that we call 911 when we get lost in a corn maze, rather than thinking and figuring a way out of the problem.
I still do math in my head, even when on the computer and the “calculator” icon is there. I still taught my grandkids how to tell time on an analog clock with no numbers just by the position of the hands. I’ve run into kids brought up on digital clocks that can’t do that. Dunno how important that is, but it struck my fancy.
So if we are hit by an EMP all of a sudden we have huge numbers of people who cant mange math?
x= # that won’t be able to function w/out electronics
y= # who will starve
Z= total # affected=9/10USA
Thus 1-(9/10USA)=1/10 who can do math and survive EMP
You caught my eye. I have a K&E log-log duplex that I bought in 1944 for a HS Trig class. I worked in a bakery the previous summer greasing bake pans to get the money for the K&E. I was drafted into WWII and came back to school under the G.I. Bill. College expenses were paid including supplies for my engineering education. Picked up a metal(magnesium I think)Pickett&Eckel which had more functions and which I used more. I have a collection of slide rules including circular ones.
I have an idea for you to consider. Lets just teach our kids to run and skip the crawling and walking stuff.
What you are suggesting is a bad idea.
Well, there is an app for that... Abacus
Sure if you want people with no concept of mathematics.
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 heros 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 computers 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...)
I would love to read this story. If you (or anyone else) can think of more details that could help me locate it either in print or online (Google has been fruitless thus far), that'd be great!
Sounds very similar in theme to "The Machine Stops" by C. S. Forester: what happens when the technology you rely on, even for your survival, starts to break down?
This is a drawing of one of the four bit chunks. The different colors represent either conductive metal traces or different doping of the silicon to get the charge to move in the desired fashion.
The whole thing (all four bits) ends up looking like this. I think it's pretty cool. It helps to understand the math beneath it though to really appreciate its beauty.
Then there was the man at the grocery store. The clerk said he owed 10.66.
He responded, “Ah, the Battle of Hastings.”
The clerk was puzzled so he told her that 1066 was the date for the Battle of Hastings.
The clerk fell silent and then said, “Can you do that for any number?”
His beef that when they were doing stoichiometry problems, they were using the calculator to type in molar conversions
...of the form x 1 = ... ÷ 1 = ...
Good job writing that absurd satirical question as if you were serious. Funny.
If you don’t have a grounding in the basics of math, using a calculator is indistinguishable from uttering a magic spell. They will have no idea whether the number appearing on the screen was calculated correctly or not.
Counting in base ten is a rote algorithm. Note that the Greeks didn't have this technology, for all their mathematical advancements, and that it came to Europe only in the Renaissance.
“Did you even understand why these algorithms worked at the time you were taught them?”
Is that relevant? Did you understand how a calculator works when you were first taught to use one? Do you now? Does that stop you from using one?
“”The Trachtenberg System of speed math!””
I always hated math in school but the Trachtenberg System intrigued me and I loved working with it. I’ve tried over the years to remember the name of it - thanks!!
What do I think? I think you should learn that happy kwanza song as soon as possible. What kind of country wants their children to grow up in a world without a happy kwanza song? If it was good enough for our forefathers and the founders of this country, then it’s good enough for us. Algorithms or AlGoreRhythms, what’s the difference? We send our children to school for interaction with others and to babysit when we are at work not for critical thinking skills. They’ll learn that on the job. maybe college . . who knows? The main thing is for our kids happiness. And that means happy kwanza songs and not boring Reading, Writing and Arithmetic. Or history. or economics.
Calculators, like all computers with math functions, could not have been designed by people who didn't know the principles involved backwards and forwards.
So, what base should children learn to count in?
Or should they not learn how to count at all?
we are not discussing math, we are discussing arithmetic.
The author threw in algorithm to appear smart, but the subject is arithmetic
Arithmetic needs to be taught and learned.
Talk about a chick magnet!
That thing is an automatic leg spreader.
I believe it still needs to be taught teaching kids arithmetic instructs them in basic logic and causality, which is needed throughout life ... my $0.02
Logic...causality....the great enemies of liberalism.
Embrace your inner Rand (or Spock) :)
Except maybe for the cursor bezel, which is metal.
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