Why is it that teachers keep insisting that 1 is a prime number?

lorddoomicus · 2008-12-05 12:26:34

I've not 1, but *** 2 *** of my son's teachers claim 1 is a prime number. The first one, his second grade teacher actually argued with me about it claiming I didn't know what I was talking about - AFTER I had supplied here with numerous printouts from Ask Dr Math, Mathworld and even the first page of a math reference I have that includes the first 1000 prime numbers ( clearly showing 2 as the first one ).

What's next, teaching him that pi=3.0? And everyone wonders what's wrong with the math and science education in this country today.

ERRR!!!

- Derrik

bossk171 · 2008-12-05 13:27:40

Twice a week volunteer my time in a 6th grade math class. The teacher is a seasoned teacher who is pretty decent teacher (as far a the teaching part goes) who isn't very good at math. Every once in a while she'll make a mistake in class but I mostly bite my tongue, it's not my place to correct her, it would be disrespectful.

The other day the class was discussing equivalent fractions and she told the class that anything over zero was equal to zero. She even wrote some examples on the board including 1/0=0, 2/0=0, 3/0=0. At one point one of the students said, "What about 0/1?" and she said , "No"!!!! I was horrified. First chance I got in private (I didn't want to call her out in front of her students) I told her how wrong she was, and all she said was, "Oh, we go over dividing by zero tomorrow" as if it was really no big deal.

I feel your pain...

mathsyperson · 2008-12-05 13:45:33

I think the source of confusion is due to the 'simple' definition of primes.
"A number is prime if its only factors are 1 and itself."

This isn't right, but it's the way that non-mathematicians tend to remember it. It correctly identifies every prime, but it claims that 1 is prime too.
Some people modify this a bit by saying that a prime is a number with exactly 2 factors. 1 only has 1, so it's no longer prime. Yay!

Primes are actually defined very technically - any prime number p must satisfy the following condition (and any number that satisfies the condition is prime):
"For any two numbers x and y, xy being a multiple of p means that x or y must also be a multiple of p."

The 'exactly 2 factors' rule does the job perfectly well for whole numbers though, the problem's just convincing people that it's that and not '1 and itself' that applies.

Ricky · 2008-12-06 05:23:08

Primes are actually defined very technically - any prime number p must satisfy the following condition (and any number that satisfies the condition is prime):
"For any two numbers x and y, xy being a multiple of p means that x or y must also be a multiple of p."

That definition suffers the same fate as the nonmathematicians you criticized before. Any unit by that definition is a prime. Of course, the easy way to save this is that "For any nonunit p...".

mathsyperson · 2008-12-06 13:23:09

Huh. That's what I get for spouting definitions without actually thinking about them.
Thanks Ricky.

Ricky · 2008-12-06 19:12:12

Also, you must restrict 0. The typical (abstract) notation for this is R* \ U(R). I've always thought there should be a special name for any element of a ring that isn't 0 nor a unit, but I have yet to find a good one.

RaelImperialAerosolKid · 2008-12-18 17:03:34

bossk171,

I really think you should speak up. It's not right to let the math suffer because you're too concerned about the teacher's feelings. After all, the whole point of education is to educate the students. The students come before the teachers. The teachers are there to serve, not be served.

Perhaps you could have told the teacher during recess. Or, if you feel that would be too forward, perhaps you could tell some individual students? In any event, you should not just let it go by. That would be a disservice both to the students and to Mathematics.

Jai Ganesh · 2008-12-18 17:19:38

RaelImperialAerosolKid,
Thats a nice post to start with.
W E L C O M E!

bossk171 · 2008-12-18 18:27:58

Thanks RaelImperialAerosolKid, and you're right. Like I said, I approached her in private, but it was really awkward for me. I'm try to play the long game here. There's a potential for me to get my own group of advanced kids twice a week and I'm afraid that if I step on any toes this won't happen. Is it fair to lose a battle to win the war? I feel that if I got my own group, I'd be able to make a really big difference, I try to take things on a case to case basis.

Today she told the kids that the 9/11 tragedy happened in 2002, and I did correct her. I'm starting to find my voice.

RaelImperialAerosolKid · 2008-12-18 22:42:00

bossk171,

I'm glad to hear it - you made my day! The best of luck to you and your kids!

RaelImperialAerosolKid · 2008-12-18 23:38:51

I got this from Wikipedia:

"Until the 19th century, most mathematicians considered the number 1 a prime, with the definition being just that a prime is divisible only by 1 and itself but not requiring a specific number of distinct divisors. There is still a large body of mathematical work that is valid despite labelling 1 a prime..."

So, to my mind, it's debatable. I personally consider 1 to be prime, for the simple fact that it's not "compound." For me, all natural numbers (the "counting numbers": 1,2,3,4,5,6...infinity) can be put into 2 groups: either prime or compound (reducible to factors that are primes). And there's no way 1 should be considered compound. And having 3 groupings of natural numbers, {primes}, {compounds}, and {1}, seems silly and inelegant.

And I hardly think saying 1 is prime is in any way like saying 2+2=5, or pi=3.0, or 1/0=0, all of which are clearly false.

To be, or not to be (prime). That is the question (for One). I'm sure the validity of Mathematics will not collapse in either case.

Last edited by RaelImperialAerosolKid (2008-12-18 23:55:02)

Ricky · 2008-12-19 07:40:38

I'm sure the validity of Mathematics will not collapse in either case.

No, but it will introduce ugliness into mathematics:

Every nonzero integer can be uniquely expressed as a product of primes (except for 1)
For every prime power, there exists a field of that order (except for 1)
Every prime number has precisely two divisors (except for 1)
The polynomial x^p - x^(p-1) - ... - x - 1 is irreducible if and only if p is prime (except for 1)

And the list goes on. According to Hardy, "There is no room for ugliness in mathematics", and I agree.

Tigeree · 2008-12-20 16:52:02

teachers don't know wot their talking bout these days

Math Is Fun Forum

#1 2008-12-05 12:26:34

Why is it that teachers keep insisting that 1 is a prime number?

#2 2008-12-05 13:27:40

Re: Why is it that teachers keep insisting that 1 is a prime number?

#3 2008-12-05 13:45:33

Re: Why is it that teachers keep insisting that 1 is a prime number?

#4 2008-12-06 05:23:08

Re: Why is it that teachers keep insisting that 1 is a prime number?

#5 2008-12-06 13:23:09

Re: Why is it that teachers keep insisting that 1 is a prime number?

#6 2008-12-06 19:12:12

Re: Why is it that teachers keep insisting that 1 is a prime number?

#7 2008-12-18 17:03:34

Re: Why is it that teachers keep insisting that 1 is a prime number?

#8 2008-12-18 17:19:38

Re: Why is it that teachers keep insisting that 1 is a prime number?

#9 2008-12-18 18:27:58

Re: Why is it that teachers keep insisting that 1 is a prime number?

#10 2008-12-18 22:42:00

Re: Why is it that teachers keep insisting that 1 is a prime number?

#11 2008-12-18 23:38:51

Re: Why is it that teachers keep insisting that 1 is a prime number?

#12 2008-12-19 07:40:38

Re: Why is it that teachers keep insisting that 1 is a prime number?

#13 2008-12-20 16:52:02

Re: Why is it that teachers keep insisting that 1 is a prime number?

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