After reading Chapter 2 in DMI, I learned a lot about how children think. I saw few examples of children's thinking didn't make sense. For the most part, every case study has logic to it. I have to remind myself about what I learned in the Thompson article: teaching is not about what you want students to be able to do, it is what you want them to understand. Although in the DMI chapter a student insisted on counting tally marks (sometimes more than 100), it is important to understand that this makes sense. There is nothing "incorrect" about how this girl was adding numbers. From there you can aid in showing students a variety of ways to solve problems (especially in more practical ways).
Something I also found useful was how many students added two digit numbers from left to right. From my schooling I have the common addition algorithm drilled in my head where you add the ones first and "carry" if necessary and then add the tens. This is very tedious and confusing and part of the reason I struggle with mental math. As I read the case studies, I practiced some of the addition problems and I added the tens first an then the ones. If I had to regroup it wasn't as confusing as if I had to "carry". This enlightening experience has really motivated me to help my students to understand place value and see how numbers really work. I hope to observe the ways they add and subtract and so on and teach these ways of thinking to other students such as those who count on their fingers, or use tally marks for difficult problems.
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Anne,
ReplyDeleteI definitely have been learning a lot about the ways in which children learn and understand math form the DMI chapters and the biggest adjustment that I have to make is understanding that teaching is not about what you want your students to be able to do, but rather what you want them to understand. This concept is a bit challenging for me because throughout my schooling I don't believe I was ever tested on how well I understood something, but instead was taught a particular way to solve a problem and that is how I would have to do it. I believe that this hindered my math education because I never understood what I was doing because I could never solve it the way which made the most sense to me. I must say, before taking this class I never knew math could be so interesting, but I have truly enjoyed learning about the way children think about math. It is so interesting and I am looking forward to conducting my math interviews this Monday. Have you done your interviews yet?