DMI chapter 5

This chapter was very interesting and it opened my eyes to how important it is to understand how your students think about and understand multiplcation. One thing that I have learned so far throughout this course is providing your students with opportunities to show you what they know and or understand. In the first case Eleanor gives her student a homework page and has them go home and solve the problem in two different ways. It was interesting that she did not give them any ideas on how to solve them, but rather left it up to them in order to see what they know, understand, or dont know. While reading this I started reflecting on my own strategies and the one thing that I realized I need to work on is allowing my students to solve the problem how they think they should or how they understand. I feel as though when I am teaching math I try and teach the students ways in which I learned or understand math. I understand by reading this chapter that in order for me as a teacher to really learn about how my students think about and understand math I need to let go of the leash and allow them to explore different methods and understandings. One thing that concerned me while reading this chapter was that I did not always understand how students thought or solved the problem. For instance, I did not understand how the students used arrays to solve 23 x 4. This method seemed confusing and like I said, I did not understand it. Also I was a bit confused with what was behind Michael's thinking when he tried to solve 25 x 9. While reading this chapter, my biggest concern was the fact that I did not always understand the logic behind students thinking and it made me worried that when I have my students solve a math problem the best way they know how or understand, I won't be able to understand their thinking and be able to guide them in the right direction. I know that I shouldn't have all of these answers right now, but they are thoughts that were going through my mind while reading this chapter. All in all I really enjoyed this chapter and thought it was really interesting.