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From: JoeB <email@example.com> To: Teacher2Teacher Public Discussion Date: 2010052823:27:59 Subject: division ___ Students should understand that 2/3 = 3)2 = 2÷3 I clearly recall my elementary teacher's introducing division,only she didn't use the term "division" but instead said,"Today we are going to learn a skill called "gazinto". Clearly she was trying to be humorous and refined the name to goes into. We started with the question, "how many times does 2 go into 6". Why she didn't use the terms "division" and "divide" is a mystery to me. "goes into" is NOT mathematical operation. Have you ever seen a 2 "go into" a 6. What in the world does that mean? I implore all teachers of mathematics to ban the use of "go/goes into". I remember a teacher in an earlier grade using the phrase "take away" to introduce subtraction and that made sense to me as to the meaning of subtraction. For a while she would pose questions like, what is 8 take away 3, which later on she would re-phrase 8 minus 3. I would have been great if she had introduced subtraction as the opposite or inverse of addition, now that's building on something I already learned, addition....it's VERY IMPORTANT to make connections. And later I learned that multiplication was "repeated addition". Now that was a connection that made sense. So why not introduce division as "repeated subtraction". Introducing addition as a shortcut to counting, and then its inverse subtraction followed by the repitition of each operation which gives rise to multiplication and division, in my view, demonstrates connectivity. OK, now let's repeat multiplication, voila, raising to a power..exponents and finding a root as repeated division to unity. For example finding the cube root of 27, could be explained: It is the inverse of raising a particular numer to the third power. Find a number by which 27 can be divided by 3 times to a result of 1.
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