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.
BUT!
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."
"Yes..."
"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!"
"They are???"
"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)?"
"Ummm...."
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!!
4 comments:
Hi Lisa,
I admire your efforts and regularly read your post on Tommy’s progress. I am sure that Tom is not playing dumb, it is not in his interest. If I were you in this situation today, this is how I might attempt to change my semantics in an effort to help my son master a few new concepts. I am writing as someone who has travelled this road with my own son and hope that my suggestions might come in handy.
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?"
First I would want to ‘test’ Tom’s understanding of the meaning of ‘same’. Same ,in context of categorising has a transient meaning – this is the concept you wish to convey.
For example all females are female : little baby girls, toddles, teens, mothers, grandmothers. Are they the same? Yes they are because they are females yet they are different because they look different.
It is my take, based on how you described Tom’s reaction, that his issue stems from grasping the meaning of same, when same manifests itself as different. Red is red = this is simple. Red and blue is not the same. So make your question literal. See below.
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." change this to
7rods +2rods and 2rods +7rods add up to nine rods. Nine rods make 9 units. We can give value to this number 9. It can be length, it can be weight.. A length of nine rods, a length of nine meters etc. Length is how long something is.
Try 1rod + 8 rods make nine rods … make variations, use your imagination, until he gets it…
"But - they both add up to nine."
"Yes..."
"And nine is the same thing as nine, right?"
"I don't know..."
Lisa here some food for thought: 9, nine, 9, and 9 or even 9they are all nine, but are they the same? If you can somehow show Tom something, anything you can think of, maybe his dinosaurs. They are all dinosaurs and as such they are the same but they are different, herbivores , carnivores , tall, slim, fat etc
If he can accept that then he might accept that 9 lengths of blue are the same as nine lengths of yellow and nine lengths of green even though they are different in colour.
"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."
I don’t believe he understands your question.
"Tom! Look at them! They are exactly the same length!"
"They are???"
and he is amazed at what you are telling him
"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."
This is it , Tom can get same and different at colour level, with a bit of help he will learn more. You could ask him ‘Why are these rods the same?’ He might answer ‘Because they are both red’. They you could ask ‘Are there any other similarities you could think of?’ or ‘How else are they the same?’
"Right. So... are these two rods (7+2) the SAME length as those two rods (2+7)?"
See how complex this question is. Let me attempt to translate what might be going on in Tom’s head: ‘My mother is asking me what? These two rods, which to my understanding are different in as much as:
1. 7 + 2 is not the same as 2+7
2. more blue and less red is not the same as less blue and more red
3. what is nine anyhow?
4. what is the same length?
At this stage in his understanding of concepts, if Tom is this confused or even less that this, then
"Ummm...." is the right answer.
I hope you did not mind my post, my heart and best wishes are with you willing you on in your journey
Florica
sorry, all the different fonts I have used have been lost and as such the meanings I was trying to illustrate have been lost. If you would like a copy of my post in word document, so you see what I meant with 9 (in bold), nine and 9 in italic, write to me at florica.stone@dsl.pipex.com and I will send you the original
such a great blog some how i found you lookin for things on our sons birth defect esophageal atresia
Thank you Lisa for the post and Florica for the response. I used to work as a School Psychologist. My little girl is 3 and is in Speech and Occupational Therapy. We are currently being referred to a Neuropsychologist. I don't think she perfectly fits either Autism spectrum or ADHD....a weird mixture of the two. At any rate, I teach the math portion for our neighborhood preschool group, and I just couldn't understand why she wasn't grasping the concept of same vs. different. This has given me food for thought and some ideas on how I might take a different approach!! I will definitely be reading more of your blog!
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