I'm in a high school choir and we just got a new teacher. He is adamant that we don't listen to rehearsal tracks or recordings, because "real musicians don't." Is there merit to this? Is it better to learn a piece by working on rhythms and notes without hearing them? He likes sight reading with as little help as possible. It is very slow work, even though we're supposed to be the top choir in school, making our performances lackluster.
I'm in a high school choir and we just got a new teacher. He is adamant that we don't listen to rehearsal tracks or recordings, because "real musicians don't." Is there merit to this?
It's certainly not true that real musicians don't listen to tracks or recordings... As Mafii says, many excellent musicians don't actually use scores at all. However, it probably is true that most 'real' choristers can read music to an extent.
Is it better to learn a piece by working on rhythms and notes without hearing them?
There are a some advantages to working from sheet music:
If you have good sheet music skills, it allows you to play a piece from the sheet music without having practiced or learned it before at all. That may not always be necessary in your situation, but it does mean that your teacher is able to introduce material to the class without having to have you listen to it first. The score is also a useful aid to memory even if you have learned a piece somewhat 'roughly'.
in a complex piece, it's going to be much easier for most people to pick out their line from a score than by ear.
In rehearsal, it's much easier for the choirmaster to be able to say 'Ok, let's start from bar 47' and have everyone able to pick up from there, than try to describe things in any other way. It's also good to be able to annotate a score with instructions. It's this practical way of 'working from the score' that your choirmaster probably needs you to be able to do.
Of course, there are some advantages to working with recordings too - it means you don't have to learn to read the score, most people (even proficient readers) can probably get the piece into their "mind's ear" more quickly from a recording, and a recording of a good performance might reveal stylistic subtleties and inflections that aren't obvious from a score - not to mention that you can 'study' a recording while jogging, doing homework, etc.
He likes sight reading with as little help as possible. It is very slow work, even though we're supposed to be the top choir in school, making our performances lackluster.
It sounds to me like you need to meet each other half way. Big ensembles do usually work from scores for good reason, and members of most choirs should probably aim to improve their reading skills. However, if some of the members of your choir don't have sufficient reading skills, perhaps your teacher should compromise a little on the "as little help as possible" bit.
"real musicians don't." Is there merit to this?
As you have stated it, so bluntly, this assertion has no 'merit'. Countless great musicians - including jazz folks, not just rockers - have learned to play from scratch by listening to recordings. Virtually every musician, in every genre, listens to and learns from recordings by great artists, and goes to concerts not just for enjoyment, but to listen and learn. Every jazz instruction book I've ever looked at (about a dozen) emphasized the importance of listening to the masters. Along with almost any instructional music book you get a CD or online audio tracks to help you understand and practice the material.
This example isn't exactly analogous to what you're talking about, but it's something that came to mind now concerning how very prominent musicians can and do use recordings - they learn from them and they are influenced by them. If you look around, you'll find many more examples, and far more dramatic ones. At any rate, nobody can argue that Anthony Jackson is not "a real musician":
Anthony Jackson, (June 23, 1952, New York, New York) is a Grammy-nominated American bassist and session musician based in New York City. Anthony Jackson has been a distinctive voice on the electric bass since entering the scene in New York City. He began playing the piano as a teen before switching to the guitar, and finally picking up the bass after being influenced by legendary Motown bassist James Jamerson (see "Influences" below).
Jackson is a student of Jerry Fisher, Lawrence Lucie, and Pat Martino. He has performed live in more than 30 countries, and has recorded in more than 3000 sessions on more than 500 albums. His bass introduction for the O'Jays' "For The Love Of Money" (on their classic album Ship Ahoy) earned him a co-writer's credit on the song alongside Gamble & Huff. 
In 2010, Jackson released his first leader album, INTERSPIRIT, with Greek bassist Yiorgos Fakanas from Abstract Logix.
Jackson, in 1978 touring the Netherlands with Al Di Meola Jackson devised a six-string bass, tuned B-E-A-D-G-C (low to high), which he called the contrabass guitar...
But we also find this:
He cites his main influences as James Jamerson, Jack Casady of Jefferson Airplane...Jackson was also influenced by Jack Casady. As Jackson said in a 1990 interview in Bass Player magazine. “Casady, whom I'd first heard on Jefferson Airplane's Surrealistic Pillow album in late 1966, had a big, rich, metallic sound with a full bottom and a curious, guitaristic way of playing that I was immediately drawn to. "
Music is for listening - we learn music by listening to music. Books and printed music are only aids to help us to hear the music in our minds and play it for the ears. There is nothing more important for learning music than listening to other musicians who have already mastered the art.
What your teacher means is that "a real musician" doesn't have to hear a piece of music in order to play or sing it. "A real musician" can read a sheet and hear the music in his mind and play it on his instrument or sing it without resorting to recordings.
Maybe your teacher is using some hyperbole to drill the idea into your minds, but he is very correct: "A real musician" does not need a recording to know how to play a piece of music. Assuming we have a proper score, all the necessary information is in the written music itself.
IMO it's important to try and follow his advice - if he says not to listen, then don't listen. He's trying to help you learn MUSIC - not just copy what you've heard from somewhere else. He wants you to read the music and understand it well enough so that you can hear it yourself, without any external crutches - to develop the skills of a real musician.
Because of modern technology that makes learning by ear and with the aid of computers so easy, fundamental musical knowledge seems to be becoming less common than it once was. We need to preserve our musical knowledge and traditions among young people. It's up to you preserve one of humankind's greatest achievements, the art of creating and performing music.
Is it better to learn a piece by working on rhythms and notes without hearing them?
We have to define what is meant by "better": If you're a performer, the only thing that matters in music is the quality of your performance. Whatever improves your performance - makes you play or sing with better style, fluency and execution, with more feeling - is the best tool to use. For most people, listening helps their performance. Listening to others is a valuable tool for improving your own performance. So it's better to listen, even if you are also reading your music for a performance.
But in your case, you're not a bone-fide performer, but a student. Your performance is not necessarily the most important thing, but your musical education. The performance aspect is just one part of your musical education. As part of your musical education, your teacher wants to teach you to read music well, and develop the ability to play written music without hearing it, which is something professional musicians are often required to do. If he thinks the best way to accomplish that is not to listen to recordings of what you'll be playing or singing, that's "better". You should follow your teacher's instructions in the school programs.
That doesn't mean that you'll always have to do that - never listen to anything before playing it. But right now, it's a form of exercise - a way of training you to develop an important skill. I'd venture that for the time being, as a student of this teacher, you'll gain a great deal by following his instructions.
It is very slow work, even though we're supposed to be the top choir in school, making our performances lackluster.
Perhaps that's so, and your frustration is understandable. However, as mentioned, right now your performance is not the ultimate goal, but your education. If there was a sight reading competition, I'd put my money or your group to win it.
It's also entirely possible that once everyone understands the new teacher and gets motivated to "go with the new program", your performances will be back up to par before long. Right now you've got a new challenge with the new teacher, so there is certainly going to be a period of adjustment.
That's a poor argument imo. Many "real musicians" do very much sing or play by ear. They listen to lots of recordings, and lots of other musicians. Some can't even read sheet music, and only play by ear.
It could be however, that he wants his class to learn how to sight read, and how to use relative pitch. He should then however be transparent about that.
I'm really good at playing from sheet music. I've had several complex pieces I just acquired from sheet music, developing my own vision for them. Listening then to the actual original music often left me with ideas and inspiration about how to better convey original intent, with the original intent having elements and character and orchestration that made more sense than my original pitches.
Last time I had this playing an arrangement of film music for accordion, even a two-stage process since the score I was working with was already a major reduction of the original orchestral score. When finally listening to the original versions, I actually got quite more inspiration from listening to the original film music than listening to the original rendition of the arranger even though that rendition (and the score for it) did incorporate several of the elements I adopted after all. They just made less sense to me without listening to the original. Of course, I did retain several elements I had worked out. And of course either version is a long way from the original fully orchestrated version.
So coming back to your conductor: I consider it quite likely that he wants to develop and realize his own artistic vision without having to fight your impression from the original, and he is correct that in the "real world", not having more than the score and a conductor (and if you are very lucky, the composer) is what an orchestra producing original versions has to contend with. I'd be surprised if your conductor himself hasn't listened to versions of the originals, though.
Learning (and memorizing) a piece "by ear" and learning to read it from the sheet music are both very useful skills. In the classical tradition, learning to read from sheet music is the norm, while choirs in other traditions (e.g. gospel choirs) expect to learn by ear and sing from memory. Neither approach should be deprecated, both are valuable, but they are typically used for different musical genres.
As someone who has sung in a choir in both high school and college, you definitely don't need to listen to rehearsal/part tracks to learn a piece and full recordings are useful to listen to periodically to ensure you grasp the intended final sound of the piece but aren't needed to learn your part specifically.
Do you happen to know what the background of your current music teacher is? How long they've been working after graduating with their Masters or PhD? Have they worked mostly with choirs or mostly with orchestras before they started with your choir?
What has helped me learn complex rhythms the most is indeed hearing them, either sung or spoken by our choral director or played out on a piano. Some people, who have composed approximately thirty to forty-five percent of the choirs I've been in, have been able to learn nearly any rhythm from seeing it and singing along with the conductor.
All of that being said, there is definitely reason behind your music teacher attempting to force you to learn to sight read. It is a very good skill to have in order to follow along with your part in early rehearsals and especially with a choir to be able to read the parts being played by accompaniment or being sung by other sections of the choir. My choir just sang Ralph Vaughn Williams Dona Nobis Pacem and there were sections that we had between fifteen and forty measures of either orchestral accompaniment or solos between parts of the piece where the choir sings. Being able to accurately follow instruments from the orchestra, in the score, made following a conductor who conducted entirely differently than others I've worked with in the past a much easier task.