Here’s the thing, we all already do this kind of math each and every day. Knowing how to do this is quite useful.
Let’s make the problem a bit more likely, though.
I go to the hardware store to buy something that is $12. I have a $10 and a $20 bill, so I give the person at the checkout counter $30. This person now has to make change.
The teller grabs 3 $1 bills and puts them on the counter, and says, “12 + 3 is 15”.
The teller then grabs a $5 bill and puts it on the counter, and says, “and 5 makes 20.”
The teller then grabs a $10 bill and puts it on the counter, and says, “and 10 makes 30.”
The item is $12. I put down $30. The teller counted out $3 + $5 + $10, or $18 in change. WHICH IS THE CORRECT ANSWER. This is a real life example of what happens in hardware stores across the country each and every day.
Just because you do not understand what is being taught does not mean that what is being taught is useless, confusing, or pointless. I am NOT defending common core. What I am defending is teaching children how to do the same kind of real-world practical math that we do every day.
That not how I do math
30
-12
= 18
So much simpler and faster
Let's make the problem what actually happens. I go to the hardware store to buy something for $12. The clerk scans it, I hand her a credit card, and the register spits out a receipt.
The process you're describing was automatic for us before the advent of technology because we were drilled in fundamentals, and knew the addend or subtrahend of any two numbers since second grade, cold.
When you concentrate on conceptual mathematics to children who don't reflexively know the basics, you are wasting your time, just as you have wasted your time with a contrived example.
If you give the teller a ten and a twenty for a twelve dollar item if are either having a very bad day or you are an idiot.
The teller grabs 3 $1 bills and puts them on the counter, and says, “12 + 3 is 15”.
The teller then grabs a $5 bill and puts it on the counter, and says, “and 5 makes 20.”
Umm. Its only $12 for the purchase. I'd only be giving the $20 in the first place. So, it would be 12+3+5 but this is too complicated.
Without using traditional subtraction:
20 is a decimal count, 2 units of 10. 12 is a decimal count of 1 unit of ten and 2 units of 1. There are 8 units of one between the decimal counts.
8 is the correct answer. The teller has a fiver and 3 ones, that is the change.
QED.
If the item cost $12 and you have a $20 and a $10 why would you give the cashier $30? Since there is no $30 bill? I don’t know maybe they do things different in your part of the world.
I go to the hardware store to buy something that is $12. I have a $10 and a $20 bill, so I give the person at the checkout counter $30. This person now has to make change.
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Why the hell would you give more than the $20?
Your explanation of CC math is severely flawed.
I would also fire the checkout imbecile!
Excuse me. If I’m working the counter and someone hands me a 10 and a 20 for a 12 purchase I grab the 20 and give them 8. I never touch the 10.
Your example does not work.
If the customer says he really wants to give me a 10 and a 20 for a 12 purchase because he is a common core lover, I point him to the sign that says we reserve the right to refuse service to idiots and kick them out of the store.
What common core is trying to do, and I’m assuming a positive intent when I say this, is to speed up the education process by skipping over more basic steps and hope the child will figure out those basic steps on their own.
However, it will be a disaster. If you take a look at older textbooks and compare them to the present, it is clear that the amount that children had to learn has been falling steadily for the past 50years. We’d be better off if we could throw out every math textbook and just reprint the one from the 1950’s.
I can understand the common core math methods instantly when they are presented as I sort of use many of these techniques "naturally" in my head. Others I see as perfectly logical, but with too many steps. There's a Allen West FACEBOOK post going around about 427-316 = 111 that no one seems to understand, but I easily see what's being done. I also understand the common core version of 32-12 problem discussed on this post as well, although it seems ridiculously complex.
So here's the question. Can a natural understanding of numbers that someone like myself possesses be "taught" through the application of these complex techniques? If the answer is yes, then I would be prone to support common core math. But if the answer is "not so much", then can these complex techniques, when combined with a post-modern approach of minimizing the importance of getting the right answer, serve the larger society?
I believe that what most people need is a way to deal with math, and the straight forward techniques of column-based addition, subtraction, multiplication and division have served generations of people extremely well.
What idiot would give the clerk both a ten and at twenty when just a twenty would do?
Yes, I was a cashier before digital cash registers that tell the cashier how much change to give. That is how we calculated the change. And I was shown the method when I got my job. No need to mess w/regular math.
Why wouldn’t I just give the clerk at the hardware store a $20 bill and get $8 back?
Except the teller would have handed the 10 back and then counted from 12 to 20...
Why would you give them $30 in the first place?
So we should teach them to go through all those processes for a simple equation because it will help them make change as a cashier?