Monday, May 06, 2013

Are you smarter than a fifth grader? I'm not.

My darling sometimes watches TV in the middle of the night when she can't sleep.So I found myself watching (actually listening) to the quiz show
Are You Smarter than a Fifth Grader? They asked the following Math Question:
What number do you need to add to 3 to get a double fact?
I had never heard the term double fact! I really didn't know and there was no way toderive it! I don't recall what my guess was but it was incorrect.See herefor what they are.

Is this a common term? If you Google

"Double fact" math
You get roughly 6,000 hits. (Down from 17,000 a few months ago when I first sketched out this post.)Is that enough hits to be a real term? Is number-of-hits a good measure?

Are there other math terms that are being taught in elementaryschool that are not that well known to people like us? (Though if you have children perhaps you know them.)Note that no matter how much math you know, there may be terms you don't know and can't derive (though you can make an intelligent guess).

My name is Bill Gasarch, and I am NOT smarter than a fifth grader.

1. Is the answer 3 or 1? Is it the _term_ "3+3=6" which is a double fact, or that "2+2=4". It appears to not be a synonym for an even number.

1. The pointer I had has the following on it (though written sideways
and in large print)

A double fact has two addends that are the same.

So YES, a double fact IS an even number.

OH- hmmm- you are right, the answer is ambigous.
On the show it was 3.

2. It's not clear whether "double fact" refers to an even number, or the entire expression "3+3=6." My guess is the latter, but then the question on the show makes no sense: if I add 3 to 3, then I get 6; I don't get "3+3=6."

2. I had never heard of a "double fact" before. But now that I know, here's my opinion:

That expressions like "3+3=6" are taught to children as "double facts" is infuriating. I get that they can be a useful tool for helping kids solve arithmetic problems, and teaching the concept of "doubling" is worthwhile. But "double fact?!" Would not "3+3 > 5" or "3+3 is even" just as correctly be called "double facts?" And what possible good can this meaningless jargon do to help a child understand? (Hell, it's not even proper grammar! "Double fact" means that there are two facts...)

The use of "fact" as a dumbed-down substitute for the perfectly harmless "equation" is but one of countless examples of what makes primary school math education in the US such an embarrassment. It's a fetishization of the irrelevant, invented by those who've never understood math, and taught by those who largely fear it.

1. Agree agree agree. I'd never heard of this before. How amazingly awful. Who the hell came up with the idea to call equations "facts" and to study "double facts"? Good god.

2. It is not an equation either, is it? An equation requires an unknown, so I would venture to just call it an expression.

3. Yeah, it sounds like the expected answer to "What number do you need to add to X to get a double fact?" is always X. They are just asking you to repeat back the definition of the "double fact".

It is a very poorly worded question that tests your knowledge of an obscure term representing a concept too trivial to need a name. My guess is that a member of the show staff found the term "double fact" somewhere in a sidebar of an elementary school textbook and went with it because adults probably won't know the term.

4. "Double fact" is clearly an abbreviation for double factorial, and so the answer is "nothing" (since 3 is already a double factorial: 3!! = 3).

1. Maybe this is for the show "Are you smarter than a freshman?" :)

In general, those "knowledge" shows have been reduced to knowing trivia or usage of obscure wording, in an effort to compensate for using USEFUL knowledge, which would need to be searched and verified by the team responsible with coming up with those questions.

5. 3!! = (3!)! = 6! = 720

1. No, look at the link for double factorial - 3!! isn't (3!)!.

6. Hmm... I'm going to take this from the perspective of a LISP programmer:

A "double fact" (which is a really terrible name) is a quoted addition expression, where the two arguments to + are the same. So '(+ 3 3) is a "double fact".

An even number is what results after unquoting a "double fact" since the s-expression then evaluates.

So the correct answer to "What number do you need to add to 3 to get a double fact?" is TYPE CLASH! The addition function returns a number, not list.

7. This kind of nonsense doesn't end in elementary school. My kids' high school algebra texts are full of terms that have never been used by actual practicing mathematicians, pure or applied. And then there are tests where they're asked to regurgitate those useless definitions. Seeing these (and being asked to help my kids with the problems) reminded me of Feynman's story of reviewing text books for the California.
http://www.textbookleague.org/103feyn.htm