# Dr. Cotter on Flashcards

Flash cards are not a good way to drill the number facts. The only people who like flash cards are those who do not need them. Many adults today, because they could not respond fast enough to flash cards or time tests, became convinced as children that they have no math “ability.” These people often develop math anxiety.

Flash cards are abstract; they require associating a symbol with two other symbols. On the other hand, a child familiar with the AL Abacus thinks about the concrete beads when asked for a fact.

Another problem with flash cards is the false impression they give that mathematics is a subject that doesn’t require thinking, or that it is just a tidy collection of “facts” that everyone must memorize.

The theory behind flash cards, going back to 1910, is based on the erroneous concept that a person learns these facts by associating a third symbol with two symbols. For example, if you see 8 and 7, you think 15. Brain research now tells us our brains do not work well that way. Rather, it is more natural to use a strategy. In this case they might take 2 from the 7, combine it with the 8 and change it into 10 and 5, which is 15.

Also, even if the child did memorize 8, 7, 15, a few years later, the unfortunate child is expected to memorize 8, 7, 56. Many children find this very difficult.

Facts practice should always provide a strategy for the learner to figure out a forgotten answer. The AL Abacus provides a good way through visual representation, based on 5s and 10s.

Another reason to provide the abacus is to discourage counting. Counting is slow, unreliable, and habit forming. Those adding by counting dots on numerals are still counting dots decades later, although now it might be in their heads.

A 5-year-old was asked how much is 11 and 6. After he said 17 without counting, he was asked how he knew. He replied with a grin, “I have the abacus in my mind.”