One of the ways in which the teaching of Mathematics can go badly wrong is in not providing enough context for why you're teaching something to someone. A classical example is that of the times tables. Times tables are useful for a number of reasons.
Firstly, when taught well the times tables provide the basis of pattern recognition. Look at a grid of numbers in rows of ten. Every time you add eleven, you move up a row and across one, and build a diagonal on the grid. On the other hand, every time you add seven you move up and a row and across three in the opposite direction. This, along with the use of musical rhythm is an important aspect of the topic.
Secondly, and more obviously, times tables assist in the formation of multiplication ability.
Thirdly, learning a pattern of multiplication is immediately useful for learning the basics of division. Witness in wonder:
3 x 6 = 18,
3 x 6 ÷ 6 = 18 ÷ 6,
3 = 18 ÷ 6.
This means that for every line of a times table you learn, you also learn two division facts. Actually for every line of a times table you also learn two multiplication facts, as:
3 x 6 = 6 x 3.
It's not just simple division that runs on knowing tables, though, as short division becomes incredibly easy if you know these facts. Just last week, I demonstrated that by knowing short division and the thirteen times table, you can divide any number, no matter how large, by thirteen. Every real number. What's a real number? Well, that's a question for another day.
How you teach things is important, and it's not wrong to explain why you're doing it.
O.
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