I try to avoid polemics, or being divisive. The topic below is one where, I suspect, opinion is already sharply divided and each side views the other with suspicion and some incredulity.
1) It really gets my goat when a teacher reserves an efficient strategy or rule-of-thumb for themselves, yet insists that pupils may only have access to a complex and more confusing version (i.e. The revered “correct” version). What happens in practice is that bright sparks quickly see the underlying pattern, check it for reliability, and then adopt the rule of thumb unimpeded by the teacher’s beliefs. The rest remain confused, experience low success rates in their work and thus low confidence and motivation.
2) If someone uses or shares a heuristic or strategy that isn’t technically accurate, but is efficient and reliable, it is bizarre to assume that they must be an ignorant teacher. Maybe they are. But…
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