Summary and Synthesis

Since we have now all taken the exam, I feel that it, as well as preparing for it, is fine to blog about. I usually have a pretty set routine when I study for exams. I read, complete the study guide and review the information until I know it backwards and forwards. I tried to use the same strategy with this test, but soon found that I would need a different approach. For example, I usually would rather do a study guide myself before asking for help, but for this study guide, I felt that collaboration was needed. I usually study alone, and for this test I was studying with other people. For me, and this material, it seemed like there were some questions that I needed to discuss with others to get their take on it. It was helpful to get others' perspectives to widen the way I thought about any one problem. Overall, I did think the test was a little more difficult, but I think I will retain the information that was on this test better than others because of the way I studied for it.

Summary and Synthesis

These past few weeks have definitely been an eye-opener for me. Math has always been my favorite and best subject, so I never really worried about having to teach math. It comes naturally to me and I feel comfortable with it, so I just always figured teaching it would come naturally to me as well. After spending this last few weeks talking about manipulatives and different ways to make students think less about the answer and more about the process, I am now developing doubts that so many of my peers (from college and high school) have experienced for so long. I understand the importance of the concepts we have been talking about as well as the necessity for teaching reform mathematics, but I am feeling more frustrated than ever before and I can feel myself shutting. I suppose this is beneficial in the long run because I can now understand how my future students may feel when they aren't understanding. I have full faith that I will get a grasp on this way of teaching eventually, it's just hard to think of math from a different perspective.

Summary and Synthesis

The past few class periods we have been discussing CGI and what that means to the teacher and to the student. It seems as though a teacher can be doing CGI and not even know it, if they do not know what it means. CGI can be very beneficial to the student and to the teacher. Group presentations are also beneficial to our class as a whole. Sometimes students learn more from their peers.

Summary and Synthesis

After doing research on my presentation for CGI math (addition and subtraction) I gained a deeper insight to the way students comprehend and mentally solve math problems. Students use a variety of manipulatives, drawings, and other hands on objects to help compartmentalize areas of a story problem. The videos that were shown of a classroom using CGI math were helpful because it is easier to see CGI math being done hands on rather than having the concept explained verbally in our class.

Summary and Synthesis

For this first section of the class, I had thought I learned a lot of useful information until it was test time. I put multiple hours of hard work into the study guide and had study sessions with my peers. I feel like I have learned alot from my peers during the LPU's. Their instruction is at my knowledge level and can teach me in ways that I can understand. I have learned alot about making connections and pointing out the process that got me to an answer. These past few weeks have been great and I feel like I am going to start understanding the concepts that will be presented these next few weeks better than I have the previous weeks.

Summary and Synthesis

This week we had a review session and a test. After the test, we had a group present and did very well presenting CGI. I felt that I learned more from group presentations in the class than ever before. The groups are doing a good job presenting the information in a way that makes sense to the whole class. I feel that class should always be like that. On days when groups are presenting I get nothing out of it. Class sessions feel like we are being talked at and not explained to. This is very difficult to learn from because nothing is explained properly enough for me to take the information and put it to good use. Some ways that could be changed is having the material presented in a way that all of us understand. I know this is a new concept to everyone but something needs to be similar so we have a basic understanding when we start. Another way is for the teacher to really help us with our questions. I feel that for me to be more successful in this class we need more help and better explanations of the material.

New Insights and Their Implications

I have learned the more from my peers in this class then I have ever really experienced in a class before. The classroom discussion, the presentations, and group work have helped me to better understand the material being taught. I have learned through other people’s experiences what works and what doesn’t as well as what I need to do better. I have learned that in this class it is important to teach beyond the norm for students. Reaching out to students and having new ways for them to learn is a big deal in this class. I have also learned that being able to justify any mathematical process is a great way of checking your work. All these things are new items of interest for me in the world of math.

Summary and Synthesis

This class has been a very insightful time for me to learn about different ways of teaching kids, and helping them learn new ways to learn connections to different types of math. I've really enjoyed getting to learn all the new ways to help kids learn, and have taken a lot from the class with the different manipulatives I can use in the classroom.

Summary and Synthesis

After many hours filling out the review guide and a couple long nights studying for the midterm, I feel that I did well on the test. By truely learning why you do something and not just how I was able to recall more than normal becasue it was better established in my mind. This completely proves the idea that teaching towards the process and not the product allows students to retain a great rate of the information. hopefully I dont have to eat my words with a bad grade on the test.

Summary and Synthesis

This class has brought out new ways to do math and teach students. The hands on math lessons will help engage the students and allow them to apply knowledge and demonstrate comprehension. It is important that students enjoy learning so they will see math as a positive and exciting subject. Relating math to topics and real world experiences is also important. The way that Dr. Reins has taught this class will allow us to pass this knowledge and method onto our future students.

Summary and Synthesis

For the summary of this first class I would say that I learned alot. This class took alot of thinking, hard work, and more hard work. I feel that this class taught me alot about teaching math and will really help me become a better teacher. Before this class I thought that math was all about answers and steps that were set in concrete. I now know that Math is not about that, math to me is now about challenging students to achieve in their own ways, connect new knowledge, and share what you know with others to try and find new ways of doing things. There were many things that I learned throughout this class, there were alot of things that surprised me, and there were many things that I would not have known to do without this class. I am hoping that this will help me be a better rounded teacher not only in math, but also in other subjects.

New Insights and Their Implications

So far from this class, I have learned a great deal from my peers. I have learned from my peers during the LPU's and from group work and in-class assignments. I have also learned a great deal about making connections from education from my peers. I have learned how others personal experiences have shaped their mathematical understanding and how those can shape my mathematical experiences. From the instructor in this class, I have learned how to go beyond teaching students with an instructional understanding approach and move them to a relational understanding. The instructor of this course has taught me how to teach students not just the how, but the WHY behind mathematics. When we help students understand the why, we are deeming their understanding of the continent. From the readings, I have learned how students learn, and various activities and math experiences that I can use with my students to help the understand the content. I have also learned about CGI and how students need to be given authentic math experiences that provide them with opportunities to use manipulatives, find the answer, and show justification for their process that they choose. This class has taught me that in the past, I have learned a great deal about instructional understanding, but was never given opportunities for relational understanding. The teaching of mathematics in an elementary school classroom is not only important, but essential. It must go beyond the how, and combine with the WHY. The justification process of mathematics is important and gives students that relational understanding.

Questions and Answers

When going through the process of CGI. One question that came up was how is this any different that regular teaching? I understand that students have a variety of different ways to answer questions, but I as a teacher would have my students explain how they came to get answer. However, when I learned more about addition and subtraction. Now, I see how children will solve problems differently. I now understand how CGI, but I believe that I would use a mixed form of instruction and CGI.