The phrase 'Invert, always invert,' is associated with Jacobi for he believed that it is in the nature of things that many hard problems are best solved when they are addressed backwards.
This quote of Jacobi comes from Wikipedia.
I believe that inverse and direct may have something of an artificial aspect. Maybe one learns one way or the other by some kind of spontaneous symmetry breaking situation. The first teacher of Arithmetic emphasized sums over subtractions, and therefore multiplications over divisions. Maybe she could have chosen differently.
How could we know?
Design some didactic sequences, i.e., some lesson plans, at the most elementary level possible. Do students become imprinted by the didactical approach?
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