Actually, most mathematics courses do not teach reasoning of any kind. Students are so baffled by the material that they are obliged to memorize in order to pass examinations.
Morris Kline, mathematician
Regrettably, many of us have never been allowed to see what mathematics is. It has been obscured by pointless emphasis on routines rather than ideas. This failure to distinguish what is important has led many people to see mathematics as a collection of totally arbitrary rules which have to be learnt by rote, and performed with the exactness and precision of a religious rite. Ask a person if there is much to remembered in mathematics; if they speak of an overwhelming mass of material, their education in this area has been counter-productive, not merely neutral.
Laurie Buxton, Mathematics for Everyone, Introduction, p. ix.
That which any one has been long learning unwillingly, he unlearns with proportional eagerness and haste.