How can a child who is mastering double digit multiplication, who can describe earth's biomes with accuracy, who can read a full-length novel with fluency - NOT grasp the concepts of "same" and "different?"
I am grappling with this question this week - in part because I simply can't figure out whether the problem is conceptual or semantic. Obviously, Tom can tell the difference between, say, a peanut butter sandwich and a cat. He can even tell you, when asked, the differences between summer and winter, oceans and lakes, and so forth.
He knows that birds belong to the same group - and that the bird group is different from the reptile group.
When I place two equations in front of him - say 7 +2 and 2 +7 - he can handily tell you that each adds up to 9.
When I ask him - "So - do 7+2 and 2+7 add up to the same thing?" He looks at me confused and says "I don't know... um... no."
"But - they both add up to nine."
"And nine is the same thing as nine, right?"
"I don't know..."
"Look, Tom, here's 2 + 7 using the cuisinaire rods. And here's 7 +2. Can you place them one on top of the other?" (He does - and they are identical in length.)
"Are they the same length?"
"I don't know... no."
"Tom! Look at them! They are exactly the same length!"
"OK, I tell you what, show me two rods that are different." (He pulls out a blue and a red rod.)
"These are different."
"Yes, they are. Now show me two the same." (He pulls out two reds.)
"These are the same."
"Right. So... are these two rods (7+2) the SAME length as those two rods (2+7)?"
OK, folks, is Tom just playing dumb? Am I using the wrong words? Or is he truly not grasping what looks to me to be the most basic of concepts? SOMEthing is going haywire here!!