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.