Throughout my time in K-8 Math Methods, I have learned a ton of valuable information when it comes to the teaching of mathematics. Looking back, I can say that when i first entered this course, I was scared to death. I had very little confidence my my mathematic abilities. However, I have definitely seen a change in my confidence over the last three months. I am no longer doubting myself when it comes experimenting with different mathematic concepts. My understanding and confidence in the area of math has definitely increased. However, I still have one question. How well will I transfer this new understanding for teaching math into the classroom? When I think about this question, I think about incorporating these new learning experiences into the classroom while trying to meet state standards, preparing my students for state mandated testing, and more. However, as I mentioned above, when i first entered this class, I was scared. Yet over time, my confidence in mathematics grew. I believe the same process will happen when it comes to incorporating these teaching strategies in the classroom. Over time, my confidence in the teaching of mathematics education will increase as I gain experience in the incorporation of these strategies.

Questions and Answers

Many of the questions that I have had have been answered throughout the last couple of class periods. I had always wondered what types of tools are appropriate when instructing students and trying to help them understand a concept. After talking about addition, subtraction, multiplication, and division models and processes, I understand now that there are so many ways to teach these applications. My question still unanswered, is how do you choose which model or method do you teach first? I know no matter what that when I choose method, I'm going to have to teach a different student a different method because not every student will understand the same way, but how do you know which model will be the most successfull within your classroom. This is my only remaining question, otherwise I feel that I have a good understanding of the various ways in which to teach these processes.

New Insights and their Implications

Learning about Cognitively Guided Instruction has really helped me to understand how I can apply the math techniques we are learning to my own classroom. Reading about the CGI classroom was very helpful to realize the importance of the student's learning process and how a teacher needs to take that into consideration. It was very helpful to watch the video of the two different classrooms to see how those teachers integrated CGI into their classrooms. It is helpful learning about it in class and reading about it in our textbook, but it was nice to see a real classroom and be able to see how it all works. I think the CGI approach is one that I strongly believe in and I think it will benefit my students as long as I incorporate it the right way. I also think that reading the article written by Ashlock was very helpful. I never really thought about how important it is to notice not just that your students are getting answers wrong, but why they are getting answers wrong. Working on the error patterns from Ashlock's book really helped me get a hands on experience to start noticing student's error patterns and being able to recognize them so in turn you can provide activities or strategies for them that will help them to overcome these errors. I think Ashlock's book has a lot of valuable information in it and I look forward to reading it and learning more about strategies that I can incorporate into my future classroom.