I am a beginner intermediate flute player. I can read scores to a great extent, but I have a problem. I know the theory that a minim lasts two beats and a crotchet last one beat and all of that. My problem is when reading although I know the pitch and duration theoretically, I have problems producing the correct duration. I don't know how to improve this. My teacher opposes using a metronome, she says that you must 'feel' the duration. If I hear the song, then I can play it with no problem, but from scratch still having problems. Do you have any suggestions how to improve this or how to practise this?
This sort of thing can work well
You need an "internal metronome" - to feel the pulse of the measure in your head as you play. Some people tap their feet to keep that going.
But it sounds as if your teacher doesn't appreciate the role that a real metronome can take in developing your internal metronome.
One really useful exercise is this (it works best with an electronic metronome, as by the end the gaps between clicks are longer than a mechanical metronome can manage):
Start by setting the metronome to click on every beat; that's the conventional way of using a metronome. Play your part along to it until you are comfortable.
Now halve the tempo of the metronome, so that it clicks every other beat. Play along to it at the original tempo, listening for clicks on the 1 and 3 (assuming the piece is in 4/4).
Now halve the metronome tempo again, so the click happens only on the first beat of every bar. Now you're relying on your inner metronome more; the click is an "anchor" reassuring you that you're getting it right.
You can try halving the metronome tempo a bit more. Staying in time with clicks 4 bars apart is tough; lots of good musicians would fail at that.
You can try that exercise with parts you already know, with sections you're learning, or with sight reading.
Also fun is to try playing with the clicks on different beats. One click per bar, heard on the 3rd beat, for example. It's very satisfying when you get it right.
Another way to develop your internal metronome is by attentively listening to music, concentrating on the rhythm. Clap along, play "air-drums", or dance. At the easy end, try following individual percussion sounds in dance music. At the more difficult end, find the underlying pulse in classical music that doesn't have percussion.
Your teacher may well be right. HOWEVER, if, at the stage you're at, you can't feel the pulse, or mark it with some part of your body - tapping foot, twitching shoulder, head nodding, counting in your head - then the humble metronome can come to the rescue.
You'll still need to count, and on flute it'll have to be in your head (mouth is busy!), but on your own, it will keep the tempo going. One which pings on beat 1 is best.
Practise a lot just on one note, forget the melody side, and even before you pick up the flute, tap the rhythm of a new piece as you count - out loud! You may want to sing the timing - one pitch will do. A pupil of mine was helped by giving each note a name - amble = minim, walk = crotchet, run = quaver.
Some folks prefer the 1e&a 2e&a approach to counting, giving semis to each crotchet. You may want to count 1-2-3- in a 3/4 piece, or 1&2&3&, or 12-34-56, it doesn't matter, as long as you count regularly, and attach a sound to the appropriate syllable.
Try writing out some rhythms as single note tunes, and this will help you to put rhythmic patterns into reality.
Eventually, your internal clock will replace the metronome, but for now, use it. It's an aid, and what's wrong with using an aid? Ask your teacher. A drum machine is another idea, but will complicate matters at your stage, I think.
I think you need to take a step back and focus on rhythm.
You can find a simple rhythmic solfege that starts with the basics of the rhythms and study that. It will help you understand the different values of the notes and then you'll be able to feel them.
If people haven't done a study similar to this and jump right into playing songs, they might have a problem (like you do).
Now, like Tim said, I suggest that you start this practice with a metronome and then you can use your foot to keep track of the time.
There are a limited number of combinations of rhythms within a measure for minim, crotchets and their respective rests. Mathematically for a common time measure, taking just crotchets and rests (Quarter notes for us Americans) there are 16 possibilities, with some of them being too easy to worry about very much (all rests for example). Start with them. Memorize what all of them sound like and be done with it. Do it how ever you wish: Use one of the other very good answers here, or imitate to a sequencer or a drum machine pounding out the rhythms.
The next step might be to work on quavers and semi quavers, learning each rhythm combination within a beat. You will find they are the same rhythms, only faster so you are just memorizing a new way to look at something you already memorized above.
(p.s.: Metronomes are good. Use them sometimes (not all the time) when your teacher isn't listening.)
Another thought is that when you are learning a new piece learn the rhythm first. Leaning the notes without knowing the rhythm is a practice time waster, unless of course you are working on sight reading.