I'm pretty hopeless at improvising (in Big Band solos) but I try anyway

. I usually just 'wing it' by playing something based on what I hear. But for longer, less predictable chord sequences I've found it useful - as your teacher suggests - to sketch out the chord
structure/pattern.
I would go one step further and play/listen to the basic chords (triads) in the pattern - leaving out the 7ths/9ths, etc. - so you get a sense of the 'shape' of the chord sequence. I often use a guitar/keyboard for this but a sax will work too. Many chord sequences are fairly predictable (I II IV V) but some chords are less so. I've found it useful to make sure that I know when these 'less predictable' chords occur in the sequence.
With my limited experience/ability my tips are:
- keep your improvisations 'musically related' to the head (melody/rhythm) in some way; variations on the head (melody/rhythm) are usually more interesting to listen to than random demonstrations of 'playing technique' that match the same chords
- like
@Jazzaferri, I'd suggest starting with a few variations on the head (melody/rhythm); variations on rhythm, especially, are often overlooked as a source of improvisation. One, two or three notes played in different rhythms are often more interesting than endless 'arpeggios'. The more you play the improv for a tune, the more you can experiment, learn and expand; develop your variations from a solid base
- experiment and make "mistakes"! Learning to improvise on a head is IMHO learning what works and what doesn't and what you like and don't like. If you try to avoid making "mistakes" you probably won't learn as much. Don't overthink it. Learn by what you hear.
- when all's said and done your solo/improv is about you; there are no rules and no standards to live up to. When you play something (however small a variation) that you felt (in the moment) you wanted to play - even if it didn't sound so great - it's musical. If you're playing constrained by 'rules', it's probably not.
When I'm not just winging it, I try and remember where the 'blue notes' are in a chord and include them.