against human nature.rnUse of manipulatives. These are basicallyrntoys of various kindsâ€”counters,rncubes, sticks, marbles, grids, and so on.rnEven the NCTM admits in its Standardsrnthat manipulation of manipulatives is incapablernof proving any mathematicalrnproposition, yet it advocates such arnhands-on approach well into the fifthrngrade.rnThis approach is closely . . .
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