"[Young] children's concepts and skills are largely implicit, informal, and even nonverbal: They cannot talk in any elaborate way about mathematical ideas. At this age level, young children's thinking is something of an enigma." (Ginsburg, pg. 8)
Every classroom is a complex equation of unique factors. Student personalities, specific academic needs, and the limits of a complicated school schedule can make a systematic understanding of the classroom challenging if not sometimes almost impossible. The specific results of my Action Research are thus only relevant to the context in which I conducted my research. However, the conclusions I was able to draw about the importance of informal math instruction (as cited in my Literature Review) and the need to create lessons which link students' preexisting knowledge to core academic skills, are important in the context of any classroom--no matter the grade level.
There are many challenges associated with Action Research. It is difficult to balance the dual roles of teacher and researcher. During Phase 1 of my research, I was consistently trying to balance the need for effective classroom management with the need to observe students' work with the tools as they attempted to solve the problems. The need to do both simultaneously made it difficult to keep a consistent record of how each student was responding to the instruction.
Action Research is, like all classroom instruction, affected by time and scheduling. In an effort to preserve the math instruction already in place in my classroom, the lessons for my project were conducted in the afternoon. I predicted that young students might be tired by this point in the day. While this did not seem to be a factor, parents regularly picked up the students during lunch time for doctor and dentist appointments. This (in addition to absences due to sickness, etc.) made consistent observation of the students' work challenging, and impacted my ability to assess individual students' progress through Phases 1 and 2.
One of the advantages of CGI is also, ironically, one of its greatest challenges. Franke and Kazemi wrote of their interactions with teachers who had spend time implementing CGI, "The teachers discuss CGI as a philosophy, a way of thinking about the teaching and learning of mathematics, not as a recipe, a prescription, or a limited set of knowledge. CGI teachers engage in sense making around children's thinking." CGI is a framework for understanding student thinking, but not necessarily a guide in how to implement math instruction. This can be challenging as a new teacher, as I still have a somewhat limited scope of the various ways math concepts can be modeled and applied. The lack of a clearly delineated method of instruction within Cognitively Guided Instruction necessitated further reading of my own into how students' math skills develop, and how lessons must sometimes be modified to accommodate students and promote the development of skills they aren't familiar with, or to better facilitate the linking of what they already know with what I would like them to work on. While kindergarteners bring an intuitive knowledge of math to the classroom, their framework for applying those concepts is still somewhat limited. It was only as a result of doing greater research into cognitive development that I was able to understand Cognitvely Guided Instruction in context.
Every classroom is a complex equation of unique factors. Student personalities, specific academic needs, and the limits of a complicated school schedule can make a systematic understanding of the classroom challenging if not sometimes almost impossible. The specific results of my Action Research are thus only relevant to the context in which I conducted my research. However, the conclusions I was able to draw about the importance of informal math instruction (as cited in my Literature Review) and the need to create lessons which link students' preexisting knowledge to core academic skills, are important in the context of any classroom--no matter the grade level.
There are many challenges associated with Action Research. It is difficult to balance the dual roles of teacher and researcher. During Phase 1 of my research, I was consistently trying to balance the need for effective classroom management with the need to observe students' work with the tools as they attempted to solve the problems. The need to do both simultaneously made it difficult to keep a consistent record of how each student was responding to the instruction.
Action Research is, like all classroom instruction, affected by time and scheduling. In an effort to preserve the math instruction already in place in my classroom, the lessons for my project were conducted in the afternoon. I predicted that young students might be tired by this point in the day. While this did not seem to be a factor, parents regularly picked up the students during lunch time for doctor and dentist appointments. This (in addition to absences due to sickness, etc.) made consistent observation of the students' work challenging, and impacted my ability to assess individual students' progress through Phases 1 and 2.
One of the advantages of CGI is also, ironically, one of its greatest challenges. Franke and Kazemi wrote of their interactions with teachers who had spend time implementing CGI, "The teachers discuss CGI as a philosophy, a way of thinking about the teaching and learning of mathematics, not as a recipe, a prescription, or a limited set of knowledge. CGI teachers engage in sense making around children's thinking." CGI is a framework for understanding student thinking, but not necessarily a guide in how to implement math instruction. This can be challenging as a new teacher, as I still have a somewhat limited scope of the various ways math concepts can be modeled and applied. The lack of a clearly delineated method of instruction within Cognitively Guided Instruction necessitated further reading of my own into how students' math skills develop, and how lessons must sometimes be modified to accommodate students and promote the development of skills they aren't familiar with, or to better facilitate the linking of what they already know with what I would like them to work on. While kindergarteners bring an intuitive knowledge of math to the classroom, their framework for applying those concepts is still somewhat limited. It was only as a result of doing greater research into cognitive development that I was able to understand Cognitvely Guided Instruction in context.