| > So, learning what is 3 x 9 is not hard AFTER you have learned n * 10, and this trick. The tricky thing here is that you have a limited amount of working memory, energy, and focus. To do well at math you need: - practice at being focused and confronting things that are hard - an understanding of the problem space you are facing and how your tools work - enough stuff memorized so that you don't have to context switch too much You can have some missing pieces in the third area and do okay. But for a lot of students, needing to context switch to do simple arithmetic throws them off. I encounter students who can do any step of a problem, and can even describe the steps of what to do, but when I observe them thunk down to arithmetic and struggle, they aren't able to find their place again and make mistakes. Most students are better served by getting their multiplication tables firmly committed to memory; perhaps a mnemonic or a simple algorithm of multiplying by 9 helps them get there. But you still don't want to be leaning on that when you're trying to factor a quadratic or cancel things in fractions or whatever. (Seeing patterns, and learning why the pattern works is perhaps more valuable than multiplication tables... but that doesn't mean you don't need the multiplication tables.) |
For me the tricks like above were like a backup solution, using it a few times it became obvious that 9 x 3 == 27. Indelible. It is. For some cases it was like "It can only be 27 OR 26" and then I would use the trick figure out which.
But whether you use a simple trick and a trivial calculation or don't have to do that at all the point is the same it should not take much thinking which would cause you to lose your focus and train-of-thought, as you say.