"Conceptual understanding refers to an integrated and functional grasp of mathematical ideas" of of the ideas underlying a discipline in general. You could not be said to 'know' a discipline unless you have conceptual understanding. Yet, as discussed here (and here, and here) the idea that students should just learn formulae by rote appears over and over again. "There must be something deeply attractive about the idea that children's math success can simply be forced upon them," writes Emma Gargroetzi.
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