These exercises can be quite challenging. I recommend starting with simple melodies before improvising.
Set your metronome to a slow tempo change your perception of the beat so the metronome clicks on the “ands.” If you are having trouble hearing the clicks as off-beats, slow the tempo way down.
Once you are comfortable at a slow tempo, gradually increase the speed. You need a strong internal pulse to be successful at a brisk tempo.
A challenging variation is to set the metronome to click on the second and fourth sixteenth notes (the “e” and “a”)
2. Use the light
With a digital metronome or app, turn off the sound and watch the blinking light or visual display. Once you have internalized the time, close your eyes. When you open your eyes, see if you are still synchronized with the metronome.
3. One click per measure
Set the metronome to click only on beat one of each measure. (If you metronome doesn’t go slow enough, check out Web Metronome. It’s free to use and can go as slow as 1 beat per minute.)
Next, shift your perception of the beat so the click is on only beat 2. Then shift the click to start on beat 3, beat 4, then each of the four off-beats.
A challenging variation is to set your metronome to click once every two or four measures.
Play a song in 3/4, and set the metronome to click every two beats. It will click on beats 1 and 3 in odd measures, and beat 2 in even measures.
In 4/4, set the metronome to click every three beats.
In 4/4, set the metronome to click every three eighth notes. The metronome will land on beat one every three measures:
This only scratches the surface of polyrhythmic possibilities. Good luck!