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In reply to the discussion: Why Would a Math Teacher Punish a Child for Saying 5 x 3 = 15? [View all]Ms. Toad
(34,423 posts)and the child's should lose points if they flip the order - which is what this child did.
It is just that people who don't understand that order is important focus on the result. Flipping the order doesn't change the computational result because the problem happened to be an addition/multiplication one and the commutative principle applies. So because the result is the same, the child should lose points for ignoring the grammatical rules.
But flipping the order does matter for subtraction and division - so if you ignore the grammatical rules when they are violated in addition and multiplication, but penalize them only when they are violated for subtraction and division, you teach the child that sometimes grammar matters, and sometimes it doesn't - and getting the right dictates whether (in hindsight) grammar is important. And a large portion of these children go on to struggle in algebra and above, because understanding the language of mathematics was only inconsistently important. It is like sending a child to a foreign country who was taught the language of that country by someone who has never actually spoken it (and didn't bother to learn it, beacause they hated language - but had to take it to become certified to teach.
Get back to me when you have 2 degrees in math, one in physics, and are certified to teach both, and have taught for more than a decade.
This is not new stuff. I was teaching it in the late 70s - as were other conscientious middle to high school teachers. But by the time students arrived at our doorsteps, they had already been taught by far too many elementary school teachers that mathematical grammar was irrelevant unless it changed the computational outcome.
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