Email to my kid's teacher--phrased the right way?

[MandaJo]

@Frylock

Third grade, but I actually don’t know exactly what difference that would make here. Certainly it will affect how complex the material should be, but it shouldn’t affect whether he’s taught things that are actually wrong.

I mean, yes, there is “a sense” in which there are more composites than primes, but teaching it as a simple fact and not a fact “in a sense” will confuse things since in “the standard sense” in math, there are not more composites than primes.

and teaching it as a fact “in a sense” would probably be too complex for third grade*…

So either way, the fact of his age would seem to have little to do with whether he should be taught that “there are more composites than primes.” The answer is “no” whatever his age, isn’t it?

*Ahem but not too complex for my kid…

I think the question becomes “How much energy do you put into making sure they get it 100% right”.

The teacher may say “Under 1000, there are more composites than primes” and the kids keep eliding that to “There are more composites than primes”. If they aren’t really ready to understand about infinty, and how that statement isn’t true for the set of all numbers, then the “under 1000” is just sort of a magic phrase, a token you learn to repeat at the front. Yes, it’s more accurate when it’s said that way, but the kid that repeats it doesn’t really “get” any more than the kid who forgets it. So how much time do you dedicate to making sure they memorize a magic phrase they don’t really understand anyway?

I think generally what one does is to teach it correctly the first time, never say it incorrectly yourself, and hope that enough of a seed is planted that when they do get to infinity, they will be like “Oh yeah. I remember something like that”. But that means a great many kids will think that there are more composites than primes, for a few years.

[Left_Hand_of_Dorkness]

Prime numbers and composite numbers in third grade? Dang. Kudos on your kid’s teacher for an accelerated curriculum.

[Frylock]

@Left_Hand_of_Dorkness

Prime numbers and composite numbers in third grade? Dang. Kudos on your kid’s teacher for an accelerated curriculum.

Well, fwiw it’s an accelerated program… and in this program they do a good job of letting the students lead the learning in many ways, while keeping them challenged and on-curriculum. It’s really an amazingly well done program, given what I’ve heard elsewhere about public education…

[raspberry_hunter]

@Frylock

I have had a reply from the teacher btw. She says this was actually a question the students asked her, and she redirected it as something they can investigate for themselves. She suggested they think about primes under a hundred to start with. She has no idea where the “slipping into composites” stuff came from.

I have already told him, in so many words, “it depends on what you mean by ‘more’” so I think I’ll just leave it at that.

That sounds like a great response, and allays worries I had about the teacher from your OP. It sounds like your son has a great teacher, who’s doing all the things with encouraging them to think for themselves that I’d want a teacher to do. And a great dad, to be concerned when he brought something home that was clearly a bit off.

[Omar_Little]

@Frylock

I have had a reply from the teacher btw. She says this was actually a question the students asked her, and she redirected it as something they can investigate for themselves. She suggested they think about primes under a hundred to start with. She has no idea where the “slipping into composites” stuff came from.

I have already told him, in so many words, “it depends on what you mean by ‘more’” so I think I’ll just leave it at that.

I think you missed an opportunity to encourage your child to have a dialogue with his teacher, without you jumping in.

[Green_Bean]

@Omar_Little

I think you missed an opportunity to encourage your child to have a dialogue with his teacher, without you jumping in.

Kids that young often don’t know what to ask, especially with a complex concept like this. Kids also may not be at all comfortable in questioning whether the teacher is right about something. It is appropriate for a parent to ask for clarification when needed.

[raspberry_hunter]

@Omar_Little

I think you missed an opportunity to encourage your child to have a dialogue with his teacher, without you jumping in.

It kinda sounds to me like the child did have a dialogue with his teacher, which he misunderstood. Which is exactly the point at which a parent should jump in to clarify, in my opinion.

[BrotherCadfael]

There are an infinite number of primes, and an infinite number of composites. However, the infinity of the composites is of a greater order than the infinity of the primes.

Paging Georg Cantor…

[Thudlow_Boink]

@BrotherCadfael

There are an infinite number of primes, and an infinite number of composites. However, the infinity of the composites is of a greater order than the infinity of the primes.

Paging Georg Cantor…

In the Cantorian sense, the infinity of the composites is not of a greater order than the infinity of the primes. Both sets have cardinality aleph-null, as does any infinite subset of the integers.

FWIW, if anyone’s familiar with infinite series, you may be interested in another way to compare the sizes of infinite sets, according to whether the sums of their reciprocals converge or diverge.

When the sums of the reciprocals of a set of positive integers converge (example: the square integers), we think of that set as “small.” When it diverges (example: the positive integers) we think of that set as “larger.” So what about the set of primes?

We will show below that the sum of the reciprocals of the primes diverges, so the primes are a “large” subset of the integers. … On the other hand, it is conjectured that there are infinitely many twin primes (this is the twin prime conjecture, most everybody believes it is true–we just do not have a proof yet). Nevertheless, it has been proven the sum of the reciprocals of the twin primes is about is 1.90216054…(this is called Brun’s constant). So the twin primes are only a “small” subset of the integers (in this sense).