I was excited to get into some of the case studies in the reading this week. In school, it was always hard for me to understand math out of a book and I have experienced some of that even doing just readings about math. When I read the CGI readings they became much more real to me. The case studies in DMI book gave me a lot of concrete ways to think about some of the ideas that we are learning about. I really liked case 6 where Lucy was working on how to translate the algorithms that she knew on paper where she had to "carry" to making the same problem with unifix cubes. This reminded me of the discussion that we had in class last week where we were debating the merits of the "borrow and carry" method. Once Lucy had gone through the entire problem with the blocks it really seemed to solidify the idea in her mind and that just reinforces the idea that borrow and carry does not have any real math connotations other than what we assign to it.
When I was reading the post before mine I really enjoyed the real world example of the toddler that was "naming" the crackers that she was eating. Before I read the "What You Need to Know About Beginning Number Concepts" article I had never really thought about that before. I don't really remember my thoughts about math when I was that young and I suppose I just haven't spent much time working with very young children about math. It does make sense though that children would try to use numbers to name things around them just like they use words to name other objects that they see. It makes things more concrete instead of the abstractness of numbers.
When this article also talked about the conservation of number I was thinking about ways that I had seen this demonstrated in some of the younger elementary classrooms I had been in before. I had seen students before when the objects they were looking at were bigger they assumed there were more of them than if they were really small.
I'm looking forward to continuing to work my way through the casebook to find some examples that I can try to integrate into field or possibly my student interview in the near future.
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Anne-
ReplyDeleteI really like what you have to say about carrying. I know we talked about it in class last week, but this is definitely the perfect example to show when speaking about the negative use of the term "carrying". I truly do feel that a young child who has not been taught any other way could easily mistake the term "carrying" for physically moving the numbers. The fact that the child physically moved her manipulatives showed that she had the same idea. Even though she eventually figured it out, I can't help but wonder if the problem would have gone differently had she been taught a new term.
I also agree with you when you say you don't remember your thoughts about math and numbers when you were a child. I can not remember for the life of me ever thinking about whether all the objects were INCLUDED in counting or whether one was. It's definitely a struggle trying to think back that far, but I think with more practice and education we can learn as much for the sake of our students. :)