Welcome to the last installment of our Children's Mathematics
book study. If you are just checking this out, it is certainly not to late to join in! Grab a copy of the book and head through the posts at your own pace. If you are looking to join a book study from the start, I will be starting a new on next Sunday on a great new book called Number Talks. Check out the full posting schedule here. Here is the posting schedule for Children's Mathematics:
December 7: Chapters 1- 3
December 14: Chapters 4 & 5
December 21: Chapters 6 & 7
December 28: Chapters 8 - 10
January 4: Chapters 11 - 13
I will post each Sunday morning and share it on my Facebook page. Please join in by leaving a comment on my blog post or Facebook page. If you have your own blog and want to write a post about the book that works too! Add your link in the comments section here. Thank you to all who shared last week!
When I was in 7th grade, I remember learning about the commutative, distributive and associative properties. They were each a section at the beginning of our text book and I remember feeling so confused. I was learning about these properties in such an isolated, text book driven way that I literally had no idea they were things I had been using to solve math problems my entire life. I certainly do not want my students to feel this way so as we use Cognitively Guided Instruction I make sure kids are developing a real understanding of the properties of mathematics. It is truly amazing to see kids develop these big mathematical ideas from experiences and from thinking about how to solve problems. Having a good understanding of the properties of mathematics and helping kids put equations and words with their ideas is one of the most important jobs a teacher can do in a CGI classroom. "One way of making these properties more explicit is to introduce notation to record relational thinking strategies so that there is a written record that can be used to discuss a given strategy." I often find that when kids first start solving problems of a particular type, they might have a mental strategy but will really struggle with how to notate that strategy symbolically. This is when I step in and write the symbolic notation to go along with their idea. This seems to really help all kids in the classroom make sense of the strategy. This chapter also talks about the fact that it is not necessary to use the names of the properties with students but it is important that they understand what the properties allow. I agree with this but I also almost always use the names of the properties with students, even primary ones. I think this is because of my own experience learning the names of properties in isolation and not really understanding what that meant. 
This was by far my favorite chapter. I feel like it really captures what CGI is and what a difference it can make in terms of kids learning to think about the math they are doing rather than just doing it. The idea that knowledge is connected and that all kids benefit from learning conceptually and building upon what they already know is what I strive for in my teaching every day. I have to confess that I have already read this chapter multiple times and continue to find gems of understanding each time I read through it. If this chapter can't prove to folks that teaching conceptually is the way to go than I don't know what can.
December 7: Chapters 1- 3
December 14: Chapters 4 & 5
December 21: Chapters 6 & 7
December 28: Chapters 8 - 10
January 4: Chapters 11 - 13
I will post each Sunday morning and share it on my Facebook page. Please join in by leaving a comment on my blog post or Facebook page. If you have your own blog and want to write a post about the book that works too! Add your link in the comments section here. Thank you to all who shared last week!
Chapter 11: Mathematical Principles Underlying Children's Mathematics
When I was in 7th grade, I remember learning about the commutative, distributive and associative properties. They were each a section at the beginning of our text book and I remember feeling so confused. I was learning about these properties in such an isolated, text book driven way that I literally had no idea they were things I had been using to solve math problems my entire life. I certainly do not want my students to feel this way so as we use Cognitively Guided Instruction I make sure kids are developing a real understanding of the properties of mathematics. It is truly amazing to see kids develop these big mathematical ideas from experiences and from thinking about how to solve problems. Having a good understanding of the properties of mathematics and helping kids put equations and words with their ideas is one of the most important jobs a teacher can do in a CGI classroom. "One way of making these properties more explicit is to introduce notation to record relational thinking strategies so that there is a written record that can be used to discuss a given strategy." I often find that when kids first start solving problems of a particular type, they might have a mental strategy but will really struggle with how to notate that strategy symbolically. This is when I step in and write the symbolic notation to go along with their idea. This seems to really help all kids in the classroom make sense of the strategy. This chapter also talks about the fact that it is not necessary to use the names of the properties with students but it is important that they understand what the properties allow. I agree with this but I also almost always use the names of the properties with students, even primary ones. I think this is because of my own experience learning the names of properties in isolation and not really understanding what that meant. Chapter 12: The Conceptual Basis for Cognitively Guided Instruction
This was by far my favorite chapter. I feel like it really captures what CGI is and what a difference it can make in terms of kids learning to think about the math they are doing rather than just doing it. The idea that knowledge is connected and that all kids benefit from learning conceptually and building upon what they already know is what I strive for in my teaching every day. I have to confess that I have already read this chapter multiple times and continue to find gems of understanding each time I read through it. If this chapter can't prove to folks that teaching conceptually is the way to go than I don't know what can. Chapter 13: Conclusion: Keep on Learning
I have so enjoyed reading this book and will continue to provide my students with the benefits of Cognitively Guided Instruction. I really believe that teachers matter to students more than anything else. It really does not matter what the standards are, what curriculum you are using or what the administration requires if you don't have good teaching. A good teacher who listens and understands her students thinking and ideas and facilitates an environment where kids can build upon their intuitive ideas and learn more efficient and elegant ways to solve problems is what every kid deserves. The standards and curriculum and everything else come second to the power of the teacher and his or her ability to guide students learning.
I hope you have enjoyed reading this book and if you are still haven't read it, I assure you it will be worth your time.
I hope you have enjoyed reading this book and if you are still haven't read it, I assure you it will be worth your time.
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