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.
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.
http://en.wikipedia.org/wiki/Trachtenberg_system
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.
Of course.
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!
Mark
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.
http://faculty.etsu.edu/stephen/TNADE/mentalmath.pdf
http://mrkhadem.com/Prep%20Materials%20(E)/UIL.htm
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).
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