Mental confusion occurs because of cross-talk between the addition and multiplication facts.
One interesting consequence of this is that kids’ addition skills temporarily decrease when they start to learn their multiplication facts.
Suppose you were asked to memorize the following:
along with 77 other similar “facts”. This gobbledygook is similar to what young children see when they look at the addition and multiplication tables. These strings of symbols are really our facts:
written in the language of the Gobbledygookites, where
Another problem is with the tables themselves. There is no doubt that filling in the addition and multiplication tables is a very useful way to start learning the facts. The patterns they reveal actually help children better understand addition and multiplication. The problem is relying on them too much. The patterns now become a crutch, allowing one to answer correctly without actually using one’s memory. In real life, the problems appear randomly, one at a time, which is why we designed so much randomness into Amoeba Math.
(S. Dehaene, 2011)