My math book sat in front of me, tears brimming in my eyes. The writing on the page blurred. I was fourteen.
“No one ever studies math by reading it!” I remember my mother saying.
Now I’ve mentioned in the past that my mother and I weren’t always on the best terms, but there was one thing I will be eternally grateful to her for and that was teaching me how to study (and by extension teach) math.
I like to think of math as having two levels – the concept level and the mastery/rote memory level.
The concept level is the lower and the mastery level higher. In order to advance in math, it is necessary to step from concept to mastery at each successive step. It is only when mastery is achieved on one level that the concept stage can be reached on the next rung. Think of it as a ladder.
When I sat years ago in tears trying to read my way into a math test, I was stuck at the concept level. I had been confident in my ability to solve problems because I understood what the teacher had been explaining to us on the blackboard. But I had not achieved mastery, which meant that while I could follow along and understand, when it came to actually applying what I had learned, I couldn’t do it.
When just three short months later, I scored 98% I had finally achieved mastery.
There was only one thing I did differently – I practiced. For a measly thirty minutes a day.
I introduce math to my children in some pretty crazy ways. I have cooked with them, done puzzles with them, even had them sort beans and macaroni noodles to teach math concepts. But if I stop there, I believe I do them a disservice. They get the concept, but that does not mean they have achieved mastery, which leaves them weaker for the next rung.
I think schools and every group situation in which math is taught suffers from this problem. A concept is introduced and everyone “gets it” so a little practice is done and the class moves on. It is only later, when the child has to use the lesson learned a few months ago that the chinks in the armor become visible. It is at this point that it becomes necessary to go back and re-learn, or rather, to practice until mastery is achieved.
The good news is that this problem can be avoided. The bad news is that it takes daily practice, progress is slow and you don’t see improvement day over day, but rather month over month.
Just recently I introduced my kids that have been dying to “learn the x-es” (multiplication) to the concept. They did pretty well up until 3 x 7, which is where I reminded them why we need to work through double digit addition before we get there.