New Insights and Their Implications

One of the main things that I learned from this class so far is the actual lay out of problem solving and how to get people to think in that mode. I think that this will help me get my students to think through the problems with out step by step assistance.
The algebra tiles are also something that I have been introduced to through this class. While I am not quite as skilled with the tiles as I hope to soon be, I can clearly see how they are a valuable tool that can be used to reach many more learning styles. I hope that I will be able to learn many more such methods to apply to my classroom.

New Insights and Their Implications

I have already learned a lot in this class so far and look forward to learning more. I learned how important a part technology will play as I continue on in my education and as I start teaching. Technology is something that is always changing and so it is very important to understand and be able to use it or at least be exposed to all the different technolgy products that are available. I also learned a new way to explore the lesson of completing the square. This lesson study example gave me a whole new perspective and outlook on a technique that I was taught to just memorize and to use. I think explaining it this way helps me understand the basic concept better and will give me a couple of different ways to approach teaching this technique so that hopefully all of my students will understand this technique one way or the other.

Summary and Synthesis

This semester I have found it very interesting learning all the ways to integrate technology. As a future educator I will definitely try to use some of these techniques as they are available to me. I have really enjoyed learning about the four steps to problem solving and the process of problem solving. It is something that I find very interesting because I tend to do problem solving in a very round about way. I often time don't achieve the answer through the best or easier way possible, but eventually get there. It was fun to learn about the processes and see how all the steps related to myself. Lastly, I have liked learning about the algebra tiles. This was something I had never seen before and I have struggled using them. However, it is something that I think I could get used to and it is a very good visual/hands on learning activity. I can see students benefiting from using the tiles and would like to use them someday in my own classrooms.

Summary and Synthesis

So far this semester, I have been very interested in this course. I really appreciate all we are learning about different technology options to enhance our students learning and the appropriate amount and time for incorporating technology into lesson plans. I am also really looking forward to the lesson study portion of the class. It is something that I, as well as a majority of the class, have not had previous experience participating in. I think it is going to be a wonderful way to gain insight on students' learning styles and how to create good, interactive lesson plans. The interactive aspects of lesson plans is very important, and I really like that we are learning a more active approach to teaching/learning mathematics. I feel that a majority of my education throughout high school was very textbook, lecture, and solving problems with pen and paper, so learning more effective and interesting methods of teaching math has been very beneficial to me. While I understand that every style of instruction has its own place in the classroom and the redundant practice of certain problems with equations may be necessary, I really enjoy learning to take a broader view of problem solving and learning to find similarities between various, seemingly different, types of problems. Finally, this course has already taught me alot about problem solving in general. I have always considered myself pretty good at solving math problems, but I had never given any thought to the actual process I was taking myself through in solving the problems. To really teach problem solving to students, I feel I need to reflect more often on my own problem solving strategies and the actual process I am using to solve the problem and learn.

Summary and Synthesis

So far in the our SEED 418 class, I have been gaining a lot of new knowledge. The biggest area that struck my attention was the problem solving section. I always knew how a went through the process to problem solve but I never really have been asked how I could explain my students how to correctly problem solve. This idea was very time consuming for me, it took a lot of thought and reasoning. Also, in this class I have enjoyed the way we are learning the lessons with a hands on approach. The other day when we did the lesson study, I thought to myself how difficult it may have been to grasp the completing the square steps if we weren't given the pieces to follow along with. I am a very hands on and visual learner, so theses methods have enhanced my learning thus far. Lastly, I am very excited to do the lesson studies. The input that each other will receive from the experience will last forever. The lesson study is going to make me think about each lesson in a much different way due to the opportunity for each group member to have insight on how they would perform a task. Overall, class has gone very well for me thus far.

Summary and Synthesis

Effective teaching comes from adapting to new styles, technology, and new generation of kids. Being able to communicate with your students is one of the first ways of learning how to teach. As a teacher you need to keep involved in learning new styles and understanding how kids think and learn. I learned that using technology in your class can be real fun and fun for your students. As a teacher you need to make learning fun and interesting so that they want to learn. Making learning fun and easy will make your job as a teacher real easy. Students that are unmotivated and uninterested in a topic will have a difficult time with learning. The key is to find out what motivates students and how to get them interested. Using technology can be a fun and very beneficial way to help students learn.

Summary and Synthesis

Effective teaching involves constantly reviewing and developing further knowledge. I learned in completing the square how many steps are part of the process and how easy it is to overlook some information that may seem elementary to us, the potential teachers, but may be crucial to the new learner. An effective teacher must let the students ponder and even struggle a little with the new concepts before offering a solution. I also greatly appreciate the present technology such as the Smart Board. Technology was not a part of my high school mathematics, but it is great to have it present and at our fingers for this classroom.

Summary and Synthesis-So far in the semester, I feel like that we are learning quite a bit, with good teaching practices and technology used in the classroom. The things that we have been shown with the whiteboard and systems that we can use to show math problems are things that I would definitely use in future teaching experiences if the resources were available. In addition to what we are learning by using technology, the idea of lesson study is a great idea for every school. Being able to reflect on the practices that we use on a daily basis is only going to benefit our teaching and the students' learning as long as there is useful feedback on the lesson and how it can be improved. Hopefully all schools with adapt this practice, even if it is only introduced as a teacher workshop about how students learn best.

Questions and Answers

I believe that integrating technology is very critical for mathematics education. When I was in high school there was not much technology in my math courses. So when we discussed this topic during class I expected to talk about the usage of graphing calculators. It blew me away when I found out how much math technology there is. With all the possibilities one would think integrating technology into the classroom would be simple. However, funding is a major problem. Some schools do not have enough money to buy recent textbooks let alone computer programs or calculators for students to be using. I think a solution towards this problem could be the use of smart boards. Smart boards have numerous math tools that would aid teachers in their lessons and students in their mastery of the material. These boards allow students to interact with math instead of solely being lectured over it. Smart boards are expensive but schools can purchase one that can be used in every classroom no matter the subject. I still have many concerns with how to integrate technology into a math course, but I now know how to get started.

New Insights and Their Implications

So far I have been introduced to a couple of new insights to this course which will give me the opportunity to practice them my next field experience. One of these insights was being able to see the use of the SmartBoard, which has broadened my technology world immensely. Most of my generation (I think anyways) has not had to much of a variety of technology in their Math classes in high school. I know growing up in my small school, teachers were limited with their technology resources. And sometimes if they used technology it seemed as though it was forced. (like we said in class) I believe that being able to use technology most effectively would help my students better understand the material. So far seeing the SmartBoard's different options has shown me several different ways to incorporate technology in my future classroom. I look forward to being introduced to other resources of technology in this course in order to analyze where they could potentially be used or which piece of technology would be more effective.

Questions and Answers

After reading the articles on Lesson Study in Japan, I became curious about how this might work in the United States. From the articles it seems that this is very successful in the elementary classes and middle school classes. There were no articles about how this might work in the high school setting. This is what my question was then, How would lesson study work in the United States? First, I believe that this would work in the high school in the United States, however, I think it might take some work to get students to buy into this type of delivery. High school students might be used to a traditional style of teaching and not accept lesson study. I think that if a school were to start students in Kindergarten and continue to teach lesson study through out their school time, lesson study would be successful. I am sure that it would work with out applying something like this, but a great opportunity to research is there for someone.

New Insights and Their Implications

This class has provided me with new insights about technology and how it can be used in a mathematics classroom. Before this course my knowledge about technology use in a mathematics classroom consisted of the use of calculators and possibly PowerPoint and Excel. The class discussions and the readings have broadened my view of technology in the mathematics classroom. I now realize how useful a SmartBoard can be for everyday instruction and that there are several software programs that can be useful in math education. The one thing I will continue to work on though experience and practice is how to best use technology in my classroom so that my students will benefit from the technology. I believe technology is a great exploration tool and can help students grasp difficult topics by presenting the material in a new way.
I've also learned that teaching just mathematics procedures without letting the students discover ideas for themselves is sometimes detrimental. I, myself, do not remember learning the "completing the square" method in high school most likely because I just memorized the process presented by the teacher and then quickly forgot it after not using the process regularly. After the lesson on completing the square, I think I have a better grasp on the subject and will never forget the process. I believe that using a visual representation and being able to discover the pattern first before the teacher gave it to me allowed me to really understand what it means to complete the square. After this experience I think that when designing lessons it is important to let students discover math concepts on their own so that they can gain a greater understanding of the material and will appreciate the problem solving processes and strategies used to arrive at the solution. I hope our future work with lesson study will help me to see exactly how and when to allow students to discover mathematical concepts on their own.
The new insights I've learned both about technology and student discovery have given me new tools in creating a better learning environment for my future students.