You and onlookers may enjoy reading the article, "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education"[1] (1999) by Hung-h

You and onlookers may enjoy reading the article, "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education"[1] (1999) by Hung-hsi Wu, for a discussion of what leads to deep understanding of mathematics. Another classic article on the topic is Richard Askey's review[2] of Liping Ma's book Knowing and Teaching Elementary Mathematics, a very good read indeed. [1] http://math.berkeley.edu/~wu/wu1999.pdf http://math.berkeley.edu/~wu/wu1999.pdf [2] http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf