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Understanding why each step matters

One of the hardest things for students to do is to keep re-writing steps they already know how to do. So often, we get used to doing something, so we shortcut and skip steps, because *we know* what those steps are. But someone else, reading through your page, doesn't understand how you went from point A to point D without seeing point B and C, too. So one of the easiest steps I make my kids (in my classroom, and those I tutor) do is to write down their process - sometimes even making them write it in words.

For example, when working an algebra problem of 3(x-2)=18, I'd make them do all the work:
3*x - 3*2=18, distribution to get rid of the parentheses
3x-6=18, multiplication
+6 to both sides, to get the x term by itself
so 3x = 24
divide both sides by 3, to solve for x instead of 3x
x = 24/3
x = 8

Now, I wouldn't make them write it down with words all the time, but on a test or quiz that might be a 10-point question. And the first few times they learn a new process, I would *definitely* make them do it. Review the above equation. Can you see how much easier it would be to do the next problem, say, 5(x+3)=52, if you had the one above to look at and get the process from? The words help SO MUCH!


Amen! I know how difficult it is to follow someone's train of thought when he or she has not left at least a "crumb trail." In high school math classes, the teacher emphasized that the process was as important as the answer, because if we did not follow the right process, we may stumble on the right answer this time and keep getting wrong answers after that.