I have just been inspired in my piano playing to try doing what the Italians did to teach young students, it is a method called partimento, where you compose/improvise over a repeated bass.
As a beginner you can use it once you have well learned a particular scale: say, C major, you could start just by playing the C major chord with the left hand and improvising within the scale with the right, starting with the argpeggios and then moving within those restricted notes; altering the timing, the spaces, etc.
I did it this morning using the A minor scale – it was interesting! I am now looking for a teacher in London who uses this method. It is believed that Haydn was taught by a Naples based teacher using this method. Nicola Porpora. Porpora (1686–1768) was a student of Gaetano Greco at the Conservatorio dei Poveri in Naples.