Writing a proof is very difficult — even for experts. Here’s an idea that allows students to think about and engage with a proof without starting from nothing.
Take a proof and space out separate sentences (or two or three sentences). For each student or small group of students, print and cut so that each sentence is on a separate strip. Shuffle the strips. Then, let the students assemble the pieces in order to make the proof.
This is an active way of learning as it forces the students to read and understand each strip and then make a decision as to where it should go. This forces them to think about what is there and makes them consider the structure. For example, it should hopefully be clear that the “Let” statements should come at the start.
No doubt this could be done electronically but I’ve only ever done it with paper. If you know of a good piece of software then comment down below!