Why do you think we seem to focus on teaching operators in series? Memorizing all of our addition facts before moving on to subtraction, then multiplication, then division? I’m increasingly convinced this isn’t an ideal strategy.
If you have followed this site for any length of time, you probably picked up our minor struggles with subtraction facts. My older daughter has the addition, multiplication and division tables completely memorized, but I still occasionally see those fingers flying as she manipulates through some subtraction fact that should have been memorized, oh, four years ago. Right now I think I’ve used math to prepare her for piano lessons. It’s less and less frequent, still, I cringe. Cringe.
What’s especially frustrating is that I know this is somehow my fault. She’s clearly got every other fact down cold and the inverse relationship between multiplication and division registered almost instantly. In fact, I remember the division timed tests, even the division with remainders sheets, being one of the easier series we went through. It just appears the inverse relationship between addition and subtraction never really clicked the way it should have.
Determined not to repeat whatever happened, I’ve started drilling my younger pupil using a new set of worksheets based around fact families instead of operations. In fact, I’m going to start whipping these out if I see the fingers moving on the older one. Just like most of the other worksheets on the site, these worksheets are structured where they progressively build up facts, but each level adds “fact families” so that the inverse operation gets introduced right away. There are different series for addition/subtraction and multiplication/division, with variants for one minute and two minute drills.
Will it work? Check with me in another four years. After the piano recital.