Anything you think I should do differently there?
I’m sure you’re well aware that there are an infinite number of both.
As a counter-example to your son, you could add 10 to 3 and get 13, a prime number.
I think a written letter is way, way too formal. IMO, just give him the correct answer and move on. Maybe he told the question incorrectly. Are you sure the question wasn’t “Are there more prime or composite numbers under a hundred?” since the answer seems to be worded that way.
What grade is he in? You have to remember that in the lower grades the teachers are teaching a little bit of everything so it might be hard for them to remember that there’s an infinite number of prime numbers and composite numbers (which can be a hard concept to grasp) as well as what year the Spanish-American war was, whether or not the Sphinx’s nose was shot off during training practice or if that’s an Urban Legend and all the while keep them on track with their reading skills.
IOW, it might be easier to just correct him instead of the teacher if this is the only thing the teacher has made an error on all year. OTOH, if he/she has made a mess of the math curriculum all year, that’s something that needs to be dealt with.
If you do want to do something about it, I think it’s much better to go in and talk to her to about it, not write a letter. I would just say “How was this question worded” and go from there. Basically, start by implying that your son may have had the question wrong, not by accusing her of teaching the class wrong and making putting her on the defense.
Yes, that is the very counter-example he gave me to explain why he couldn’t understand (what he took to be) the teacher’s explanation for her answer.
Do you mean to include emails under the category of written letters here?
No, I’m not sure–which is why I’m asking the teacher what I may be missing here. I’m giving her the opportunity to clarify exactly this point, right?
You’ll note that no where in the email do I state that anyone has said anything that’s incorrect.
First letter of the email say: “I think Jake might be confused about something he heard in class on Friday.” Isn’t that exactly what you’re saying to do? What exactly about the email are you afraid would put her on the defensive?
I forgot about emails. I see my daughter’s teacher(s) every day when I pick her up so when I have a question for them, I just ask in person. For some reason, when I saw this I imagined a nice, elegant, handwritten letter (and then a teacher writing a message on a Teacher Message Board asking how to respond).
You didn’t say how old your son is, but I suspect he’s confusing addition and multiplication to come up with composite numbers.
Possibly, but I doubt it, as he’s told me all about the fundamental theorem of arithmetic (though he doesn’t know that’s the name of it). He seems to have that idea down, and understands the relationship between primes, composites and multiplication. This seems to be something else.
Anyway, I still want to know: Is there some reason you think “I think Jake might be confused about something he heard in class” fails to accomplish what you mentioned about not putting the teacher on the defensive? I put that sentence there specifically for that purpose. Are you saying it doesn’t work?
That’s probably fine, by the time I wrote my long post I more or less forget about the finer details of your letter and started picturing what I would write/do.
It’s tough because I think you already know what the answer is and you (well, I) can hear it in the question. But that could very well just be because we have your whole side of the story. Who knows, maybe you’ll get an answer back twenty minutes later that’ll clear everything up.
Also, you’re right, it is odd that if he has a total understanding of prime factorization (and once that concept clicks, you’ve got it) there’s no reason he should start throwing addition in there.
But I’ll still give him that the idea that there aren’t more composites then primes can be hard to wrap your mind around. It’s like understanding that space goes on forever.
“Are there more prime numbers or composite numbers?” depends on what you mean by “more.”
It’s like asking, “Are there more (whole) numbers that are divisible by 10 or are not divisible by 10?” In one sense, there are infinitely many of each; but in another sense, numbers that are not divisible by 10 are nine times as common (when you look at all the numbers up to any given point) than those that are. The Prime Number Theorem describes the sense in which there are analogously more composite than prime numbers.
ETA: I’m sure some of the people in this thread already know this.
Got it, thanks for the advice!
If the kid is confused, why wouldn’t you want the kid to walk through the details with the teacher?
That seems like the natural course of action, kid asks question because it’s not quite making sense, teacher expands on details, kid counters with his arguments for whether that seems valid or not, etc.
I’m not a hundred percent sure what you’re asking. To help me understand, can you tell me why you think I wouldn’t want the kid to walk through the details with the teacher?
(Oh maybe I understand what you’re saying. The problem is, based on what I’ve heard, I’m not sure yet whether this is something that the teacher will correctly be able to walk through with the kid. In other words, right now, for all I know, based on what he’s said, if he tries to walk through it with the teacher she’ll end up confusing him because she herself doesn’t understand the issue. I don’t know that for a fact, but it seems possible based on what I’ve heard. Hence the email, to suss out just exactly what she did say, so I will know whether this is something I just need to handle here at home or rather whether I can send him back with questions to the teacher.)
I agree completely. I’m just trying to figure out whether the teacher herself is confused, without telling her I think she’s confused. Because she may not be, it may be my kid who’s confused.
That’ll give me useful information both about future possible incidents, and about what exactly to say in the present case when talking about the problem to my kid.
Elsewhere, I’ve written this about it:
Thanks for the link on the prime number theorem. I may be able to show parts of it to my kid, and we can talk about the different senses of “more” involved here. The primes and composites are equally sized sets in the normal “one-to-one lineup” sense. There are more composites in the “what proportion of the numbers below any given number will be composites” sense.
Yeah, I think this makes a big difference. If the kid is in, say, highschool, you probably don’t want to be emailing the teacher at all.
I’ve just skimmed this thread, and (unless I missed it) you still haven’t mentioned what grade Kiddo is in. Depending on that, it might be a bit much to go into the gory details of sizes of infinity, and the seemingly paradoxical concepts like “there are just as many multiples of 10 as there are whole numbers”, and so forth.
At lower grades, teachers necessarily simplify a lot of stuff, and not always quite technically accurately – especially if complete technical accuracy is messy.
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 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.
There are fewer primes than composites, but an infinite number of both. This may be too complex of an explanation for a third grader, but I don’t have kids and I don’t know your kid.