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ive heard many of my instructors say "blow in the center of the horn" but what does that mean exactly?

You'll know the center of a note when you find it. That has little do with the note being perfectly in tune. But where the note "is" on the tuba. I found that practicing with my Schlipf mute makes is VERY clear to hear/feel when you are above/below the center of a pitch, and to hear what you're putting into the tuba (without all of that "sound" to get in the way). Very helpful as a practice tool, even if you don't require quiet for your neighbors' sake!

I have heard "center of the note" used, but it basically means the same thing. Every note is bendable a certain amount, sharp and flat, before it either sounds like total garbage or wants to try and slip into the next partial. This varies on horns, and is often referred to as "slots." Some horns have narrow slots may only be bendable about 10-15 cents sharp or flat, some are bendable as much as 25-40 cents sharp or flat on each note, before losing the character of the sound. As an example, Alexanders seem to be known for having very wide slots. Many tubas sound best when each note is blown right in the center of that slot. That is why some players pull slides, even on notes close enough to lip - the length of the tubing is being finely adjusted so that the note is always being blown in the center of the slot.
Some players, particularly beginners, may have a tendency to consistently play on the high side or the low side of the note. Playing in the middle is the best place to start, and then certain notes can be adjusted from there.
I do not think your teacher is a bad teacher for making this suggestion, perhaps it was just not clearly explained.

Okay, guys, before jumping to conclusions, let me make a couple of points.

First, to get a good sound from a tuba, the air stream has to find resonance. That means a wide, slow air stream that rings within itself. Most beginners do not use enough air to find that resonance, and that has nothing to do with the instrument, or with the pitch of the note. "Blowing in the center of the instrument" would be the wrong way to say it, but "blowing in the center of the resonance" would be right. The buzz has to have all the harmonic content contained in it, from which the instrument will reinforce some harmonics and filter out others. If the buzz is lacking in air flow, it will not have all that harmonic content even if it is at the right frequency. The resulting sound will be thin and unresonant.

Once a player has learned how to blow a richly resonant note with a good air flow, then you can address the issue of whether the center of resonance for that note on that instrument is in tune.

Rick "for whom a good sound is the foundation on which good intonation is built, no matter what the instrument" Denney

Rick Denney wrote: . . . The resulting sound will be thin and unresonant. . . .

Which is not always a bad result. Sometimes the mood of a performance may benefit from a "chiaroscuro" texture.

gnrguitar64 wrote:ive heard many of my instructors say "blow in the center of the horn" but what does that mean exactly?

Maybe he meant this?