Paul Lockhart, author of A Mathematician's Lament, wrote of math instruction that "it is the story that matters--not just the ending."
New teachers spend hours of work and class time learning about how students develop reading skills. Literacy is situated in gradual stages of development, with classroom activities devoted to engaging with the students as they develop more and more sophisticated knowledge of how words and sentences are constructed. New teachers are taught to think of reading as a complex developmental process, which can be assessed according to certain stages of growth and understanding.
Cognitively Guided Instruction provides teachers with important tools for understanding mathematics and math instruction in ways that are analagous to the development of fluid reading skills. Using CGI, teachers can develop as intimate a knowledge of their students' abilities in math and numeracy as they do in other subject areas. Franke and Kazemi write of their time spent researching that "The frameworks [of CGI] provided teachers the opportunity to understand how this knowledge about the development of children's thinking fits together as the teachers could make it their own."
In my time spent research Cognitively Guided Instruction, I learned that students show a great deal of enthusiasm for instruction that allows them to articulate and share their thoughts with their peers. I also learned that mathematical problem-solving incorporates many skills, which unfold and develop more slowly than I had previously thought. Many problem-solving strategies that adults take for granted, such as the ability to represent objects by drawing them on paper, are too complex to be understood well by early elementary school students. This was supported in my readings about the development of mathematical concepts (specifically, those by Ginsburg), but was not articulated in my readings about Cognitively Guided Instruction (specifically, in the original book by Carpenter, Fennema, et al).
Cognitively Guided Instruction is significant in that it helps teachers unlock their own understanding of their students' thinking. This understanding enables teachers to guide students towards making connections between their own intuitive knowledge and understand of math and the math that they experience everyday outside the classroom. This bridging of an inherent knowledge and the knowledge required to complete a challenging task is at the root of constructivism, one of the most fundamental pedagogical theories of the last fifty years. In being able to understand and pinpoint the development of my student's mathematical understanding, I have become a more capable "guide on the side"-- a teacher who helps her students' bridge their innate understanding with new, developmentally appropriate challenges. With knowledge of how students naturally accomplish certain math-related tasks, I feel more ready to develop a math curriculum for my students that will be engaging, challenging, and applicable to the math-related challenges that they experience every day.
New teachers spend hours of work and class time learning about how students develop reading skills. Literacy is situated in gradual stages of development, with classroom activities devoted to engaging with the students as they develop more and more sophisticated knowledge of how words and sentences are constructed. New teachers are taught to think of reading as a complex developmental process, which can be assessed according to certain stages of growth and understanding.
Cognitively Guided Instruction provides teachers with important tools for understanding mathematics and math instruction in ways that are analagous to the development of fluid reading skills. Using CGI, teachers can develop as intimate a knowledge of their students' abilities in math and numeracy as they do in other subject areas. Franke and Kazemi write of their time spent researching that "The frameworks [of CGI] provided teachers the opportunity to understand how this knowledge about the development of children's thinking fits together as the teachers could make it their own."
In my time spent research Cognitively Guided Instruction, I learned that students show a great deal of enthusiasm for instruction that allows them to articulate and share their thoughts with their peers. I also learned that mathematical problem-solving incorporates many skills, which unfold and develop more slowly than I had previously thought. Many problem-solving strategies that adults take for granted, such as the ability to represent objects by drawing them on paper, are too complex to be understood well by early elementary school students. This was supported in my readings about the development of mathematical concepts (specifically, those by Ginsburg), but was not articulated in my readings about Cognitively Guided Instruction (specifically, in the original book by Carpenter, Fennema, et al).
Cognitively Guided Instruction is significant in that it helps teachers unlock their own understanding of their students' thinking. This understanding enables teachers to guide students towards making connections between their own intuitive knowledge and understand of math and the math that they experience everyday outside the classroom. This bridging of an inherent knowledge and the knowledge required to complete a challenging task is at the root of constructivism, one of the most fundamental pedagogical theories of the last fifty years. In being able to understand and pinpoint the development of my student's mathematical understanding, I have become a more capable "guide on the side"-- a teacher who helps her students' bridge their innate understanding with new, developmentally appropriate challenges. With knowledge of how students naturally accomplish certain math-related tasks, I feel more ready to develop a math curriculum for my students that will be engaging, challenging, and applicable to the math-related challenges that they experience every day.