Puzzle Description:

or was this our past?

#1: Francie (eicnarf) on May 3, 2010 [SPOILER]

Are you a mathematician?

nopers, just a man .... you ever get anyone in chat room francie?

im glad i didnt go to that school
haha

ummmm..bugaboo...your punctuation says you did. lol j/k

No. I think people mostly communicate through these comments.

Of course, Tom. We might make Susie feel bad if we tell her that's the wrong answer. After all, who are we to determine what is right or wrong? ;)

Love the image - when I was growing up I wanted to be a math teacher (never did) but I am sure I wouldn't have taught this 'new' math.

yeah Cynthia! Great puzzle. there is a truth to this. when my son was young, he would accidently punch in the wrong numbers on a calculator and not be able to realize that the answer was wrong.

That was a fun solve. Very enjoyable.

ty bc

Speaking of "new math," there was a period of time about 20 years ago when educators toyed with a new style of teaching math. I think it was called PERC or something like that. Rather than teach math 'facts' to grade school kids by rote, they included other ideas to help the students understand math, not just be able to spit back the facts.

One of those new ideas, a rather obvious one really, was teaching kids to estimate an answer, so they could determine whether their result was reasonable, before continuing with whatever other computations they needed to make. With little kids, for example, the teacher might have two groups of tiles and ask the kids to determine which group looks like it has more tiles, before counting them to find out for sure. I thought teaching understanding this way was a valuable skill to being able to handle math in general and to prepare for further study. But most parents were outraged. Why were their kids being taught this 'nonsense?' Some parents explicitly said their kids should only be taught the addition and times tables and be able to recite them. So after several (but not many) years, this teaching method died out. I don't know whether it's taught any longer.

At the time, I was tutoring math students at NYU. I had empirical proof that this 'useless' skill was an absolute necessity. For example, I had one student come in, seeking assistance with his calculus homework. We worked through a problem together and at the end, his final answer required multiplying two numbers such as 1234 * 0.567. (I don't recall the actual numbers, but I recall one number was largish, while the other was less than 1.)

At this point, the student dutifully pulled out his calculator, punched in the numbers, and confidently told me the answer was 699,678. He began to write the result on his homework sheet.

I was aghast. Clearly, nothing in this kid's head told him that this could not possibly be the correct answer. If he had been taught anything like the PERC reasonable result concept, he would have known immediately that multiplying one number by another less than one results in a value less than the original number. Since this result was much larger, something was wrong with his result.

I think that, just as kids are not often taught how to really understand math, they're also not taught to do anything more than get an answer, and as in Tom's case, *any* answer will do because they don't know how to check their work. They just want to move on.

I hope math education has improved in the US, but I suspect it has not significantly changed from when we were kids, where you got math if you got it, in most cases, not because it was taught properly.

Hear hear David!

And I learned something new just the other day that kinda blew me away - percentages are reciprocal! That is, 25% of 8 = 8% of 25.

Did anyone else know this? I had never been shown that, and I thought I had a solid education ...

Bill: I was never taught that percentages are reciprocal, but come to think of it, it makes sense. 25% of 8 is the same as 25/100 * 8, and 8% of 25 is the same as 8/100 * 25, so either way you have 8 * 25 divided by 100. Which is intriguing!

David: Yes!! Also I miss people being taught to check their work. When I was in school, I was taught to always check my answers to everything. It was so pervasive in everything we did in school that even decades later I find myself applying it to all sorts of other things in life. A few years ago our refrigerator died, and the guy who the store sent to install its replacement looked like he was about sixteen years old. He hooked up the water line to the refrigerator and left, without ever checking his work. Later it turned out that there were several valves that needed to be turned on in order to get water to the fridge, and he had only turned on one of them, so the store needed to send out a repair person to troubleshoot. I was really surprised that the original installer hadn't checked his work before he left by making sure that he could get water out of the refrigerator's water dispenser, because in school I was taught to check everything, so that's the kind of thing I had been taught to do. But then I was thinking that if he was sixteen and spending his days installing refrigerators, then he probably hadn't finished school, so maybe he hadn't stayed in school for long enough to learn that habit. But then I watched my young adult kids and realized that they don't seem to do that either. So maybe teaching has changed.

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