“You can’t teach algebraic principles to,kids who are still learning basic math.”
But maybe you can teach them that there is more than one way to solve a problem....heck, it worked for Gauss and summations :-)
Remember that what we are looking at here is just a very easy example being used to illustrate a larger concept. So, of course it looks a little silly. But I wish I had been taught more along these lines rather than just memorize, memorize and memorize.
As for what the appropriate age is for this sort of thing...I admit that I have no idea :-)
What in the world is wrong, or so difficult, as learning the multiplication tables, or “i” before “e”? I wasn’t an Einstein in math but I learned then and still automatically use the multiplication tables most every day of my life. I’d hate to think I had to use some convoluted, non-sensical method as I see in the extant example. I’m not aiming my comments at you in particular but this math method is asinine and pure crap.
I saw another example on FR last week. I showed it to an engineer and a college math student and neither of them understood the principle behind it or even how to do it.
You can only really learn the short cuts when you’ve mastered the topic. Using shortcuts before that inhibits the learning process because you have no way to verify if your shortcut is a valid one because you cannot compare with the longer method.
It’s like trying to use a shortcut to drive through an unfamiliar city. That short cut might work, but you won’t know it without having known the longer way first.
Bullshit.
Memorization makes perfect sense for a child at this age because young children have a natural affinity for storing up tremendous amounts of information. Classical education calls it the trivium. The first stage is memorization of facts called the grammar stage. It isn’t until later that the next stage is reached, dialectic, where children are able to use the foundation/pegs of knowledge to reason.