I was in grade school in the 40's and science and math was fair then.
To this day I remember telling my grade school teacher that I had figured out how to "take away" a bigger number from a smaller one.
She told me firmly and with irritation (I had responded with a "but...") that it was impossible!
I've subsequently spent a signifcant amount of time searching for ways to teach math to kids.
At this point I'd say that since there are two subjects: arithmetic and math, they should be taught that way. And math should only be taught to the upper 1/3 of the students, at most.
I wish I could convince my bank of that when I overdraw my checking account.
I've subsequently spent a signifcant amount of time searching for ways to teach math to kids. At this point I'd say that since there are two subjects: arithmetic and math, they should be taught that way. And math should only be taught to the upper 1/3 of the students, at most.
You make some good points. Your grade school teacher was restricting herself to the natural numbers with do not include negative numbers. You were ahead of the class and "discovered" the integers which do include negative numbers. It was probably beyond her skill to explain the difference to you.
One difficulty that your story points to is that not everyone is a good teacher. It is not possible to make good teachers come out of college like cars in a factory assembly line. The demand for mass education produces a lot of mediocre teachers.
I do agree with your solution. Let the students good in math go to a more advanced class taught by a better teacher. They won't be bored by a class geared for the average or below average student. But that would mean rewarding excellence and neither the schools nor the public will tolerate excellence. Somebody's feelings might get hurt. It is better to dumb down the class and make everyone equally incompetent.