Walls and windows

Extract

When students work through a written proof what is it that they are attending to? At what level are they taking in and making sense of what they see? The mathematical symbols (i.e. diagrams, equations, etc) that are found in proofs are a result of the writer seeing some generality, attempting to express that generality and to convince themselves and others of its validity. We recognise that students, when reading a proof may work directly with the symbols, somebody else's symbols, without attempting to enter into the process of expressing generality for themselves.