Sad but true. I was at a fast food drive thru when the computers were down. They had to make change the old fashioned way. But the girl could not figure out how much change to give me. She seemed lost as she tried to calculate the difference between what I gave her and what the food cost. She had to call in the manger, who took way to long to compute the change (eventually she found a hand-held calculator).Twenty years of reform math.
Apparently even simple arithmetic is no longer well taught, learned and/or retained. Reliance on machines to "teach math" is only good if one has a machine when it is needed. My daughter had these classes where the calculator was required. The problem was that after smacking the keyboard a few times, she could come up with an obviously nonsensical answer. She would just write it down and move on. I asked her one time how she could multiple two numbers that each were less than one and come up with an answer that was greater than ten. The blank stare said it all (fyi - she failed to enter the decimal points correctly).
Want to terrify a teen-ager? Ask them to multiply 12 times 12. Is the answer immediate or not? Forget adding simple fractions. And we expect these kids to learn algebra and higher mathematics?
Are kids today less proficient even in arithmetic than in the past? Surely we can tell if these newer teaching methods are getting better results or not. As for me, I think my daughter did better in arithmetic in elementary school. After middle and high school, she seems to have "lost" the ability to easily do the arithmetic she learned earlier in life. I blame the calculator.
That's a long time.