But I will argue long and loud that they are not useless ornaments pinned onto the average man's education. For me, at any rate, the ability to formulate quickly, to resolve any problem into its simplest, clearest, form has been exceedingly useful. I found higher mathematics the best possible exercise for developing the mental muscles necessary to this process. We must not let zealous people who really do not understand mathematics and its intrinsic values gain control of our curriculum and teaching techniques, because they are prone to downplay the thinking and mastery involved in the learning of mathematics.
Youngsters learn much before they go to school.
They learn from parents, siblings, relatives, and others, few of whom are certified mathematics educators. Television programs are not written by mathematics educators, neither are most computer programs. Sometimes, kindergarten teachers are faced with expanding on or changing previously learned ideas. Visual mathematics begins with undefined concepts such as flat surface. Some examples of flat surfaces are floor, ceiling, wall, table top, and desk top.