Summary and Synthesis

To be honest at the start of this class I was very skeptical about the methods that Dr. R was teaching us. I wondered to myself how would I ever be able to teach in a manner that I had never learned myself? Throughout the course of these past weeks though, I have started to come around to the idea of it. I have been learning things that I already knew how to do, but did not know why I was doing them or why they worked the way they did! Essentially, I have always had an instrumental understanding of math and now I am beginning to (slowly) have a more conceptual understanding of math. Already I can see the benefits to this type of teaching. I hope with this new attitude I will have a more positive outlook and learn even more from this class.

Summary and Synthesis

I have learned a lot of information so far this semester in math methods. I have learned a variety of new ways to present and teach material to students. I have learned what constructivism is and how to teach in a constructivist manner. It is important to have children learn to solve things on their own without the equation or formula given to them. Students can explore the problem first to try to develop the formula on their own. When students work this way it gives them a better understanding of how to solve the problem, how the formula works, and how they acheived the answer that they got. By working this way, students are making meaning out of what they are doing. Teachers need to make sure to use the students prior knowledge and to connect that to what the students are learning. We have learned different ways in which to teach scale factor to students. We have also learned different ways to approach problem solving and ways to help students solve problems in multiple ways. Right now we are learning about different polygons and finding the area on them. I have learned a couple of different ways to find the area of a polygon; such as, Pick's Thereom, chuncking the interior, and chunking the exterior area of the polygon. We are also learning the different formulas for the polygons. This class has required to think on my own and to use my prior knowledge to connect to new ideas.

Summary and Synthesis

I have learned so many new and interesting concepts this semester through math methods, such as constructivism. I have learned that it is important to be a constructivist teacher when teaching math because students need to learn how to do mathematics on their own. They need support and guidance also, but helping them to actually do mathematics is the best thing for them. When students learn new concepts on their own they make meaning out of it and learn much better. Using prior knowledge to help construct new knowledge is extremely important and can be used to help students develop new ways of thinking about math. Constructivism is just one of the many different concepts that I have learned this semester. Another concept that I have dealt with is finding areas of different shapes and polygons. I have used my own prior knowledge to help me with finding area formulas and coming up with algorithms for areas of polygons. Pick's Theorum is just one of a few methods that I learned for finding the area of a polygon. I found it to be very useful and easy to use. Throughout this class, I have been required to think on my own and find answers to questions that I did not know before. This entire course is based in constructivism and it truly does help in the learning process.

Summary and Synthesis

Since my last blog, I have remebered and discovered new methods in finding area of shapes and what the definition of shapes are. The definition of a polygon is one of the first things that I learned by doing looking at different shapes and figuring out if they were polygons are not. I also learned different methods in figuring out the area of any polygon. One formula I learned was Pick's theorem which as a pattern toit when drawing shapes on a geoboard. There were also other qualifications for quadileterals and rectangles that I had to remember since grade school. Many of my textbooks had defined a rectangle but they defined it in a way that it was so broad and it could be another shapes definition. I think it is important to define shapes well enough so students understand exactly the characteristics of that shape and what makes that shape unique compared to the other shapes.

Summary and Synthesis

I have learned from my instructor that I am not bad at math but was taught math with all of the wrong techniques. I now realize that I should have been taught math through a constructivist manner. I was always taught math content in a broad and general way. It seemed as though I had to hurry and memorize formulas, definitions, procedures, etc. the fastest way possible just so I could keep up with material my teachers would be teaching. I now know that children need to build upon their prior knowledge in meaningful ways in order for them to gain a deeper understanding of the information that is presented to them. I also now realize that I need to implement constructivism into my own teaching style if I want my students to really and retain most of the material that is presented to them. Implications of learning and teaching mathematics is that it can have some very difficult. This is why it is important for teachers to understand how children learn best.

New Insights and Their Implications

I think the biggest thing I've learned in this class is that the way I was taught math growing up is completely wrong! I always had a very traditional way of learning math; my teachers talked about the new concept for awhile, gave us a worksheet to do, and after enough lessons, tested us on it. There weren't many hands-on experiences provided to us students. When it came time to take a test, we just memorized the equations and answered the questions. After the test was done, pretty much everything we memorized was forgotten. That would probably explain why I'm not very good at math now.

I guess I never really knew that there was a different way to teach the information. But thanks to this class, my conceptions on teaching math are changing drastically! Although there are times I get frustrated in this class, I can honestly say I'm learning so much and actually retaining the information because we're doing hands-on activities and working on constructing our own knowledge. I really see the benefits of teaching math in this manor. I hope to be able to adopt this method in my own classroom. I think my students would really benefit from learning this way!

Personal Concerns and Next Steps

My convern in this class is a personal concern which I have struggled with a lot but even more so in this class. I understand the concepts and the materials you are presenting us but I have a hard time explaining it to other people sometimes and think it could be benefital to me how to explain the whys some more rather then just presenting the right kind of problems. To help students understand the right connections.