New Insights and Their Implications + Question

We are now reading the CGI book, which has given me new insight to students' learning of math as well as the teacher's role. Cognitively guided instruction, to me, means that the teacher allows the students to explore ways of solving problems, choose a method that works for them, and explain how they used that method to reach a solution. The book focuses on addition, subtraction, multiplication, and division, giving a variety of examples of word problems that can be used to help students understand each. The CGI book states, “It is when children decide upon a strategy to represent a mathematical situation and implement that strategy that problem solving takes place.” I have now realized that students can develop their own understanding through the use of good problem-solving questions, manipulatives, and other tools. The teacher guides the process by giving appropriate problems and asking the students questions about their thinking and how the problems were solved. Reflecting on their strategies helps students improve their understanding as well as value the thinking of their peers.
As also stated in the book, "Gradually, children come to recognize that their thinking is important, and they come to value the process of doing mathematics." We have been learning from the beginning of this class that students should "do mathematics," and learning about CGI has helped me to verify this in my own thinking. And just as Dr. Reins told us, that we won’t get the class at first but will eventually…I finally have that understanding. My philosophy of teaching mathematics has therefore changed. I will now create a classroom environment that supports doing mathematics, encourages communication, and allows students to actively explore strategies on their own and develop their own understanding so that they can form connections and value their learning. I do wonder, however, why we did not begin the class with the CGI book?? I think the class would have made more sense to me from the beginning if we would have started out learning about cognitively guided instruction.