As a math major, it was hard for me to wrap my head around the fact that my kid was innumerate, and apparently hard wired that way. But when I spoke to his (3rd?) grade teacher about multiplication and found that he was being required to write out the problem as boxes and then count the boxes. OK, that works, Then he told me that 2X3 was written out as a rectangle two wide and three deep. And 3X2 was ONLY to be written out as a rectangle three wide and two deep. No freaking WONDER my kid was having trouble with such concepts, since the teacher was incompetent. I pointed out that they were the same rectangle, but he didn’t get it even when I grabbed the paper and rotated it 90º. Mind you, my kid really is unable to grasp numeric things, so even an excellent teacher wouldn’t have helped… but it would have made ME feel better.
Just Divide by 2 is the answer! Sorry, a not so in-joke from High School Geometry Class. Only one person managed to get a moderately complicated homework problem correct. After re-explaining several times, the Teacher asked the one person to come to the board and show how they arrived at the answer. They went to the board pointed to some particular angle and said “I picked that one and just divided by 2.” Why that particular angle and not some other one? “That one just looked right.”
If the teacher explains the same problem the same way a 1000 times, then the teacher is not a good teacher. The good teacher would attack the problem from different angles, so that pupils that understand things in different ways all have a chance to understand.
Well Jef, one big reason why it is hard to explain a commutative property of numbers is because NUMBERS are NOT commutative! It is the OPERATORS that exhibit the property (or not).
For example A + B = B + A and A x B = B x A but A / B does not equal B / A. Likewise A – B does not equal B – A.
Yes, the state of math education is indeed atrocious!
While I appreciate teachers, some of them don’t seem to grasp that some kids learn differently than others. You can explain something till you are blue in the face and some children still won’t get it.
Bilan about 2 years ago
She thought so a thousand time, but . . .
Concretionist about 2 years ago
As a math major, it was hard for me to wrap my head around the fact that my kid was innumerate, and apparently hard wired that way. But when I spoke to his (3rd?) grade teacher about multiplication and found that he was being required to write out the problem as boxes and then count the boxes. OK, that works, Then he told me that 2X3 was written out as a rectangle two wide and three deep. And 3X2 was ONLY to be written out as a rectangle three wide and two deep. No freaking WONDER my kid was having trouble with such concepts, since the teacher was incompetent. I pointed out that they were the same rectangle, but he didn’t get it even when I grabbed the paper and rotated it 90º. Mind you, my kid really is unable to grasp numeric things, so even an excellent teacher wouldn’t have helped… but it would have made ME feel better.
KenTheCoffinDweller about 2 years ago
Just Divide by 2 is the answer! Sorry, a not so in-joke from High School Geometry Class. Only one person managed to get a moderately complicated homework problem correct. After re-explaining several times, the Teacher asked the one person to come to the board and show how they arrived at the answer. They went to the board pointed to some particular angle and said “I picked that one and just divided by 2.” Why that particular angle and not some other one? “That one just looked right.”
Sisterdame about 2 years ago
If the teacher explains the same problem the same way a 1000 times, then the teacher is not a good teacher. The good teacher would attack the problem from different angles, so that pupils that understand things in different ways all have a chance to understand.
eromlig about 2 years ago
Jef — great work, Friend!!
Doug K about 2 years ago
The Commutative Property is great, but it doesn’t work or apply if the original equation (or statement in this case) isn’t true.
TheSkulker about 2 years ago
Well Jef, one big reason why it is hard to explain a commutative property of numbers is because NUMBERS are NOT commutative! It is the OPERATORS that exhibit the property (or not).
For example A + B = B + A and A x B = B x A but A / B does not equal B / A. Likewise A – B does not equal B – A.
Yes, the state of math education is indeed atrocious!
goboboyd about 2 years ago
Today, I was yelled at a hundred times. Today, I learned a hundred things. (with apologies to the original author)
Natarose about 2 years ago
While I appreciate teachers, some of them don’t seem to grasp that some kids learn differently than others. You can explain something till you are blue in the face and some children still won’t get it.
DanEP about 2 years ago
Converse .. logically invalid.
kevin87031 about 2 years ago
And then some of my students call it the “communative” property.
Jhony-Yermo about 1 year ago
Oh boy. Another charterer with a name. Hello Kim