Summary and Synthesis

Summary and Synthesis - Summarize and synthesize the impact of recent experiences, ideas, and/or issues encountered on Tuesdays and Thursdays in class from your perspective since the previous blog.

During my first blog, I really had no idea where this class was going. I was unsure the point of the way you were teaching, yet I did know it had it's purpose. Now my understanding is that you are teaching us the same way we need to be teaching our students. Asking questions, and finding solutions to our own problems is kind of the way the course is going, and is the way we want our students to be thinking. Instead of being spoon fed information, you are providing us with problems where critical thinking skills are needed, and where we have to be motivated to figure out the solutions to the problems presented. Although it is a different way of thinking, the point is now becoming clear for this course, and our future in teaching math and other subject areas. This course is enabling us to find the reasons behind the spoon fed formulas provided to us in math- the way we were taught growing up. Now I understand a particular concept in math (for example: why area of a triangle is 1/2 bh) and can apply it to many other areas of math (for example, using triangles to find the shapes of polygons). This course has showed me there are many different routes a person can take in coming up with a solution, and our future children need to see this as well. This course is providing me with the necessary skills needed to be able to get my children to think critically, and problem solve in math. The way this course is being taught is challenging, but now I have deeper understanding and meaning behind the math that I originally learned. I now understand how being set in the traditional way of teaching math can offset students in not truly understanding concepts being taught. The whole saying, a mile wide and an inch deep makes more sense now. Because there are so many topics that need to be covered in math, teachers rarely get to touch base with students to know if they are truly understand the meaning of concepts being taught. This new way of learning helps students see the true meaning of mathematical concepts, which can be applied to multiple areas in math, as we are presented with a problem and have to come up with the solution.

New Insights and Their Implications

I really liked what Dr. Reins taught us about teaching new information, and getting students to construct new meaning based upon what they already know. For example as I was learning about polygons, area, and constructivism I was able to draw conclusions, and make connections to build my understanding of the topic based upon my own comprehension. The idea of parroting back information for a test or an assignment seems to be useless for long term memorization and overall comprehension. I believe that the movement from covering information in breathe to covering information in depth is tough for many teachers to try as they are pressured by schools and standards to become accountable for the students learning; yet it is most useful to get students to become accountable for their own learning. Yet, it is proven that students who can create meaning and make it valuable to their lives are more likely to retain in long term memory. I would like to make this part of my own teaching motto, to get students to understand using scaffolding as a motivational tool in the classroom.
I also liked what Dr. Reins has showed us about drawing conclusions based upon Pick's theorem, the chop method, and drawing rectangles to find the area. This helped me move my thinking about area from strictly formulas and numbers to more theoretical and higher leveled think about areas. I truly enjoy learning this new approach to mathematics.

Personal Concerns and Next Steps

Through out the last month I have had a great time continuing to build my knowledge on how to correctly teach math. I am beginning to understand how this method of mathematics instruction can be used to the classroom but do have one concern related to this technique. That one concern is how to teach math using this method and still find time to cover all the standards and continue to stay on pace with the curriculum. I understand that its important to make sure all students get a solid foundation set and then build upon that but it is difficult to teach this way and still cover what needs to be covered. If it was up to me I would spend as much time as possible teaching mathematics the way we have been learning in class but in order to keep my job I understand that I will have to meet all standards and cover all of the curriculum. Teaching mathematics in a constructivism manor may be better for the students but I'm still unsure how I can speed up the process in order to reach the goals that is set forth my the school district I'm teaching in. I look forward to learning more in the next two and a half months and improving my teaching skills.

Personal Concerns and Next Steps

Personal Concerns and Next Steps - You may blog about genuine personal concerns created as a result of the experiences in this course. (Please note: If you blog on this item be sure to provide sound rationale for your concerns and what steps you are planning to pursue to address your concerns. This is not an opportunity to vent, be constructive and professional about it. Don't complain about something unless you offer a better alternative or solution.)

Personally Math has never been a favorite of mine because I have struggled with it. This last test was long and covered a lot of material that I thought I knew, but now I'm not sure that I knew it well enough. I know it's important that I learn and understand this material and I think that I am going to take more notes and make sure I understand the questions that are being asked at the begining of each chapter. I do like that this class is an hour and fifteen minutes because it allows us more time to go over everything and discuss.