What does this mark on the piano mean?
This is an example of Mendelssohn's Song of the Boat. There are two fingering marks on the A sound and the #C sound at the same time: 4 and 1 and 3 and 1, which are also connected by small arcs. This is a sign of homophonic anaphora (also called silent anaphora). That is, when the fourth finger (or the third finger) of the right hand plays A (or #C) first, then press and hold the keyboard to prolong the sound. At this time, the palm of your hand is quickly contracted, and 1 finger (big finger) is used to "take over", so that 4 fingers (or 3 fingers) are ready to play the notes of the next bar. When the notes in a phrase are far apart, this method can extend the span of fingers and ensure that the Legato of melody will not be interrupted. This silent finger change needs more practice, and the movements should be relaxed and natural. Remember: 4 fingers (or 3 fingers) can only be moved away after pressing the keys with equal fingers, otherwise two A sounds (or #C sounds) will pop up between finger changes, which will destroy the coherence of the melody.