People have different methods to improve their reading of music. I simply treat it as reading in another type of script.
When we first start to read in any language, we are quite slow, and we can't read complex structures easily. Over time things look up. The additional difficulty with music is that we have to coordinate fingers and the tongue to produce the result we desire.
I have not learnt to improvise. Everything I play is based on printed music. Of course, I now know some passages by heart. That comes handy in fast runs. The range of the saxophone means a limited language compared to many other instruments. Whether you charts or other teaching aids is up to you, but the time comes when you have to able to look at a piece and play it, not necessarily to the highest standard. So, the sooner you are able to free yourself from various supporting mechanisms, the earlier will you find that playing new pieces is fun. Good luck!
You make some good points. Music notation is just another language in another script.
I read bass and treble clef fluently, I don't have to think what the notes are - I know. But I've been reading them since I was about 10. If I play a piece of piano music that I know reasonably well, it's like reading a book - I don't spell out c-a-t 'cat' - I just recognise the word shape etc. When I play sax, which is written in treble clef, I have no issues reading the music. The issues I have are working out the fingering!
The challenge that most beginners face is that hey are both learning to play an instrument and learning to read notation. Just like learning to read you will get more fluent at it.
For comparison, music for tenor viol is mostly written in alto clef (C3 clef - i.e. the 3rd line is middle-C) although you do see octave treble (sounds an octave lower than written in treble clef). I am less fluent with this clef - most confusion occurs reading low notes below the stave as you don't see them very often.
For cello, as well as bass clef I have to read tenor clef (this is a C4 clef - middle-C is on the 4th line up). This is the one I am least fluent with. Again, I find reading lower notes harder because you don't see them that much (except in the Mozart we are currently playing in orchestra!)
For alto and tenor clef, you try to learn where the notes sit and start off playing simple pieces that use a few notes, just like any tutor book, and develop from there. When I went to my first few summer schools as a novice bass viol player, the tutor (a lutenist and viol player) would just throw me a piece of music in some weird clef - alto if I was lucky, baritone (F2 clef - the F is on the 2nd line up) if not. Apart from frying your brain, you do pick it up quite quickly.
I think the 'flash card' method of name and play the note is a good option.
