Eggleton and Case Studies

I have very mixed reactions to this weeks readings. On one end, I'm very understanding and get what they are saying about children making mistakes. On the other end,I feel that as teachers it is our job to fix student's mistakes. At the same time I have questions about everything. I am mostly confused after reading "The Value of Mistakes" by Eggleton and Moldavon. I do agree with some of what they are saying about children needing to make their own mistakes and fixing them. In fact, one of my favorite quotes come from this article. A father says about his two separately taught children, "One son's reaction to a problem might be, 'I don't get it,' whereas the other son's reaction would more likely be, 'I don't get it, yet!'" (Eggleton, 47). It is this type of "go-get-them" type attitude that I want to instill in my students. I would like them to learn from their mistakes because I do agree with a lot of what is said in this article. I believe that children who learn from mistakes made in math will certainly understand and comprehend the math better than a child who is just told what to do. I also agree that student's very rarely think back on these mistakes as negative experiences. In fact, I feel the complete opposite. From my own personal memory, I remember feeling extremely accomplished when I figured out the answer after so many mistakes and so much work. I do wonder though, as a teacher, when is the right time to interfere? How long do you let a child work and wonder before you come in and show them how to do it?
I also really liked the readings from DMI. We have a school day chart like the one talked about in Dawn's case in my placement classroom. I am placed in a kindergarten class and I always wondered why the chart was not ordered by week. I now understand the point and thought behind the ten to each row. I found it interesting that Andrew physically moved to show the rows of ten. With this idea AND the seashells, it just goes to show how many different ways one idea in math can be shown. I think for young children especially, it is important to expose them to concrete, abstract and physical ideas. I also really liked the idea of the division chart in Donna's case. I am always curious about new ways to teach about ten and I feel this would be a new and great way to teach student's about patterns and tens. As I was reading though, I found myself to be frustrated with Marie's case with Lou, Jose, etc. I would have loved to seen how they would have reacted with different manipulatives. I would like to know if it was the place value they were confused about or the actual blocks. If they were more aware of which piece represented which amount, they may have been able to understand better.