4 ms·
This is obviously cool and all that, but I see one problem with these kind of shortcuts - children (who this site targets) have no idea why this works and how.
by rytis 15y ago
This is obviously cool and all that, but I see one problem with these kind of shortcuts - children (who this site targets) have no idea why this works and how. They memorise it and go about their lives using it. They know it works, but have no idea why.
I'm ranting about it because I have 2 kids who learn all sorts of similar stuff at school, but teachers fail to explain why these things work. (and in most cases I suspect they don't actually grasp the idea themselves)
- budgi3 15y agoThe trick seems to be a combination of both. Learning by rote in combination with an effective method seems to be key to strong number sense in kids. Take a look at the Triple Code Model (Dehaene & Cohen) for some more detail.
- Jach 15y agoI'd correct you by saying that they'll memorize it for as long as it's useful for passing a test because the teacher wants them to solve something a particular way. They'll soon forget it. I learned long division in 3rd grade, relearned it in 6th grade, learned the algebraic polynomial version in 10th grade (then was shown/told synthetic division which is cooler)... and at this point I know I'd struggle doing any of those. I'd rather use a calculator and get back to doing whatever it was that required the answer. In these crazy times where even most elementary kids have phones with calculator capabilities there's no excuse to be parading these mental tricks as "math". I do agree though that a proof of this would be much more interesting than the technique itself. If I have kids I intend to teach them math myself. I don't think I was introduced to the idea of formal proof until 8th grade geometry, and everyone hated those proofs since it was a bookkeeping exercise of writing down every algebraic step and what theorem/axiom allowed you to perform it.