flamark: dittybopper: flamark: When I was growing up we had to memorize multiplication tables up to 12. A couple of years ago I was helping my grand daughter, who was in third grade, with her math homework which was just getting into multiplication. Apparently they no longer require memorization but teach methods based on Common Core. There are several methods to getting the right answer so apparently schools now think methodology is more important than the results. Recently I was driving her to school and she was telling me a story about a teacher who left in 2015 to teach in Guatemala for 7 years but returned to her school this year. I asked her to rethink her statement to make certain her teacher was not a time traveler. I asked her "so what is 2015 plus 7?" I swear it took her half a minute before she finally realized that the math didn't work. Memorization has its place and is far superior to methodology in many cases.

I think the issue is deeper than that.  I've seen symptoms of that not just with the littlebopper, but with the distaffbopper as well.

I think it's an issue of innumeracy.

The idea that math is some abstract thing that has very little application to outside of specialized situations like doing your taxes, buying a house or car, or figuring how much to tip.  And a fear of it, an avoidance in many cases.  The distaffbopper hates math, because she perceives that she's not good at it, but honestly if you can add, subtract, multiply, and divide, you can handle 99% of the everyday issues that require math.  You just have to recognize and accept that it's a math problem.

I don't know how many times I have used the phrase "Have you done the math?".   People no longer think to do the math because the machines will do it for them, so it's not something they do on a daily basis.

The issue may not have been with memorization of math rules, it may have been as simple as not thinking it was even a math problem to begin with.

I agree with you that many people don' ...

Yeah, I dunno. My perspective on these things is irredeemably skewed because I have advanced degrees in math and geophysics. I read some little paperback on innumeracy (discount bin at Half Priced Books) like a decade ago, and my main takeaway was that far more people are utterly unable to abstract numerical concepts than one might suspect.

On that front, I agree with the attempts to push concepts over wrote memorization. However, pretty much all math before calculus is the vocabulary and syntax of numerical abstraction, so a certain degree of memorization is mandatory. It's just like how you can't reach the point of creative synthesis in language without memorizing some basic rules and vocabulary, or in playing an instrument without memorizing which positions produce which notes.

That being said, I feel that the US public education system has failed students when it comes to simplification using the algebraic properties of numbers, approximation, and "the smell test". Exhibits include:

117 x 51 = 117 x 50 + 117 = (100+17) x 50 + 117 = 5000 + 850 + 117 = 5967

1987 x 4132 = A bit over 8 million, because 132 > 13 (the differences in those numbers between 4000 and 2000, respectively). Let's call it 8.2 million, because if we simplified to 2 x 4.1, that 0.1 gives us an extra 10% of 2 in the final result. Actual answer is 8.2013 million.

Is 10000 a reasonable guess for how many people can utilize a 40' x 100' "standing room only" section?
No. Assume 4 sf per person; (4000 sf) / (4 sf/person) = 1000 persons. Probably more in Europe and fewer in the US because of ambient social norms, but I digress.

This text is now purple: olrasputin: Is 10000 a reasonable guess for how many people can utilize a 40' x 100' "standing room only" section?
No. Assume 4 sf per person; (4000 sf) / (4 sf/person) = 1000 persons. Probably more in Europe and fewer in the US because of ambient social norms, but I digress.

I would expect that number to driven by the number and size of doors and the floor structure than by square footage alone.

That's really your takeaway here?

Pretend it's an outdoor concert venue then. Was trying to put forth an easy illustrative example without devolving into a discussion about the airspeed of unladen swallows.