One of my most eye-opening teaching experiences occurred when I was helping a six-year-old who was struggling with basic addition – or so it appeared. She was trying to work through a book that helped her to the concept of addition via various examples such as “If Nellie has three apples and is then given two more, how many apples does she have?” The poor little girl didn’t have a clue.
However, after spending a short time with her I discovered that she could do 3+2 with no problem whatsoever. In fact, she had no trouble with addition. She just couldn’t get her head around all these wretched apples, cakes, monkeys etc that were being used to “explain” the concept of addition to her. She needed to work through the book almost “backwards” – I had to help her understand that adding up apples was just an example of an abstract addition she could do perfectly well! Her problem was that all the books for six-year-olds went the other way round.
So perhaps the girl you were teaching was a member of the cognitive-decoupling elite you wrote about? The problems you are explaining in that article are reversed in the early years of school math. That is, a strong use of tangibles to explain concepts.
She’s encumbered with all the tangible objects preventing her from answering the conceptual question. In later years she’ll be freed from tangible objects obscuring the real problem. Math will likely be more intuitive for her and she’ll start to soar. And it’s at just that point where the rest of us start to flounder..
I wonder if this concept has been discussed from a learning and pedagogy perspective. Seeking to tailor technical subjects to different types of thinkers?
Strangely, it can sometimes also go the other way!
I think this is unusual though.
So perhaps the girl you were teaching was a member of the cognitive-decoupling elite you wrote about?
The problems you are explaining in that article are reversed in the early years of school math. That is, a strong use of tangibles to explain concepts.
She’s encumbered with all the tangible objects preventing her from answering the conceptual question.
In later years she’ll be freed from tangible objects obscuring the real problem. Math will likely be more intuitive for her and she’ll start to soar. And it’s at just that point where the rest of us start to flounder..
I wonder if this concept has been discussed from a learning and pedagogy perspective. Seeking to tailor technical subjects to different types of thinkers?