[FredZarguna]

Let’s make the problem a bit more likely, though.

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.

[LurkingSince1943]

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.

Giving out receipts is the latest challenge for retail clerks. Now they ask you if you want one.

[TalBlack]

“... to children who don’t reflexively know the basics,...”

Exactly! The basics become the mental equivalent of ‘muscle memory and as such form the basis of more complex calculations.

Have you ever noticed how fast the guy at the deli (usually the owner) used to provide change WITHOUT using the change function built into the machine? Back in the day, BEFORE the cash drawer finished sliding open he’d broken down the change to the number of even units and then the fraction then dug out the fraction and then the bills (usually in that order). He sure as heck wasn’t parading ranks of numbers around in his head.

[Principled]

When you concentrate on conceptual mathematics to children who don't reflexively know the basics, you are wasting your time...

Amen FReeper.

[Think free or die]

"When you concentrate on conceptual mathematics to children who don't reflexively know the basics, you are wasting your time,"

And as a teacher of chemistry, I can tell you that trying to teach conceptual chemistry to children who haven't learned the basics of reading and math is also a waste of time. Many of our nation's youth are being promoted through our schools with devastatingly low academic and life skills.

The students who come to me from Asia on exchange programs run circles around our native-born students. They may have weak English, but their fundamental skills are solid, and their work ethic is strong. Our students aren't stupid, but they have weak fundamentals, and they choose to teach themselves the intricacies of non-stop communication on social media rather than academic subjects.

[Monitor]

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 have evidence that the fundamentals aren't also being taught, then provide it. Otherwise, your argument is based on an unsubstantiated assumption.

[editor-surveyor]

>> “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.” <<

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But in the former, someone got paid far more than they were worth, to fail dismally.

“Union Yes!”
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