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I guess I don't see how they can't understand these things if they use a calculator. They still have to know the process and understand how to get the answer. They still have to show step for step their work on assignments. The calculator just speeds up the process. I think there is some misunderstanding that just because a child uses a calculator that they don't understand the work and that just is not true. I am sure the NASA scientists would have LOVED to have graphing calculators to help them put man on the moon and I am pretty sure they use them now. Given that these people are some of the brightest minds in science, I don't think learning to use a calculator hurt them any.
You can't. If the calculator does it for you, you don't understand the steps the calculator took to get to the answer. It's one thing to use a calculator after you know how to do the math yourself and quite another to start using a calculator.
If the apocalypse comes and the power grid goes, there will be an awful lot of people unable to function...which reminds me of the South Park episode when the Internet was gone and they packed up their cars and headed west because they heard there was some Internet in Californee.
But seriously, technology is just a time saving tool not knowledge.
Unfortunately, too many think they don't need knowledge because they have the internet.
What you end up seeing are freshmen in college Math being told "No calculators" and panicing.
I took a Trig class where we had 2 tests..a calculator test and a non-calculator test. Pre-cal ..just a regular calculator for arithmetic.
Not until Calculus could we use scientific calculators with tests.
And once you get to college, you sketch graphs on regular lined paper.
Not having done graphs before kids struggle that entire first semester in College Math.
I took those classes a few semesters ago for refresher classes as I hadn't had college Math classes in over 20 years. What was drummed into my head 20+ years ago all came back while these younger students struggled. Sometimes the old ways are better.
When it comes to graphs understanding the impact of the chosen scale and interval is essential to truly understanding the data. It is through the painful task of wrestling with these variables that one gets a real understanding of the data and what it may or may not indicate.
These variables are often manipulated by the author to fool the target audience. Most people don't even realize they are being played because they rely too much on what they see and don't have enough experience and knowledge on how the data and graph are interrelated.
This is true for a lot of technology. I totally disagree that a calculator is a substitute for calculating conceptually and algorithmically. The former is a procedure that has little to no impact on knowledge whereas the latter is a meta-cognitive experience that enhances knowledge and builds requisite skills necessary for understanding related higher-level concepts.
I'd prefer to scan my items at the grocery store and not understand the technical engineering behind "scanners" and their "adding" methods.
Quote:
Originally Posted by Ivorytickler
You can't. If the calculator does it for you, you don't understand the steps the calculator took to get to the answer. It's one thing to use a calculator after you know how to do the math yourself and quite another to start using a calculator.
I'd prefer to scan my items at the grocery store and not understand the technical engineering behind "scanners" and their "adding" methods.
It's actually quite interesting. So is the engineering behind CD's and CD readers. Actually, they're rather similar.
I'm curious enough that I couldn't stand not knowing the technology behind the scanners. I hope you know enough not to look into the laser.
This isn't the same as using a calculator to do math. Stores want bar code readers and scanners and check outs that figure out your bill to minimize being ripped off (thought I've seen some stealthy moves at the self check out, UGH). This isn't a crutch you're using to avoid math. It's the store trying to make sure they get what is due them and keeping track of inventory. Apples to oranges here.
You can't. If the calculator does it for you, you don't understand the steps the calculator took to get to the answer. It's one thing to use a calculator after you know how to do the math yourself and quite another to start using a calculator.
It's like learning to speak a foreign language by running everything through a machine translator. Or a Home-Ec class where all you do is put TV dinners in the microwave.
Quote:
Originally Posted by Ivorytickler
Stores want bar code readers and scanners and check outs that figure out your bill to minimize being ripped off .
Not the real reason. They want cashiers to be able to enter prices twice as fast, so they only have to pay half as many cashiers to process the same number of shoppers and items. The only person who can "rip them off" is the cashier, who can still just bypass the scanner with an item that her mother is buying.
Actually, it protects the customer more than the store, because the store can't overscan a price. I always check my produce ring, to make sure they entered the right kind of peppers.
It's actually quite interesting. So is the engineering behind CD's and CD readers. Actually, they're rather similar.
I'm curious enough that I couldn't stand not knowing the technology behind the scanners. I hope you know enough not to look into the laser.
This isn't the same as using a calculator to do math. Stores want bar code readers and scanners and check outs that figure out your bill to minimize being ripped off (thought I've seen some stealthy moves at the self check out, UGH). This isn't a crutch you're using to avoid math. It's the store trying to make sure they get what is due them and keeping track of inventory. Apples to oranges here.
I'm not a teacher but I'm a firm believer in FORMAL/traditional education. Internet is fine. Information is fine. Neither, however, will ever replace the cumulation of knowledge that we know to be the backbone of civilized society. Teaching kids to "just do what you want" is plain stupid. If we all just "do what we want" then eventually we'll be a population of blind leading the blind. Learn to do things the right way then if you want to be stupid after that then go for it.
Someone who understands the math can do this, which is how some people make a killing at the market and others (who are not educated in the math behind finance and economics) sit around and do nothing but complain about the market crashing. Knowledge is power, and mathematics drive everything. You DON'T need to know this stuff to make change at a supermarket, but if you want to actually get far and understand what is happening with your money (and be able to play at the same level as a wall street trader) you need to understand math. (Please note I picked finance/economics as one example for simplicity, I could easily make the same argument with any field.)
The problem is that with the over-reliance on technology and calculators, some people are even unable to figure out what the change is IN THEIR HEAD without the help. I go to the store, I'm keeping a running total in my head. If it's within a dollar of what I figured, I'm not complaining, but if it's way off, then there's a problem, and I'll check their input.
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