Recording rough mathematical working
As mathematical problems increase in complexity and length there starts to be a separation between rough working, to support problem solving and the communication of a final solution.
The method a student uses to record rough work should facilitate their problem solving and the skills used during it such as algebraic manipulation, holding in mind of sub-results etc. Since there is no requirement for an outside observer to read or follow the rough work the format in which it is completed need not be a standardised mathematical notation which can be read by others. Hence Writing mathematics for the consumption of others may use different processes.
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