Summary and Synthesis

During class we have been talking about finding the area of any polygon on a geoboard and got to do some hands on activities for this concept. One activity we did was writing an algorithm that would work for any polygon that was made on a geoboard. In class some students talked about their different algorithms and showed the different ways this concept could be learned. After I got to see the different solutions I decided my algorithm needed some changes that would make it simpler. (I could take off a few of my steps. Ex: one of my steps was having a trapezoid, but the trapezoid would be divided into a triangle and rectangle). I think by allowing the students time to discuss their solutions in class, we learn a different view of the concepts and also gives a time to justify our answers.
The class also did a more hands on activity by cutting the triangle out of the rectangle and used string to make different shapes to see what would give more area. I believed the rectangle would have more area because of the length of it. I was wrong though, it was the circle.
I realize by having the students do different activities with one concept; they are getting a more in-depth learning. They are starting to realize why the different approaches work and see a variety of strategies to complete a task. We are not focused on memorizing one formula for a problem, we are allowed to explore and talk about our learning with others. I know in my elementary/high school that is how we learned math, memorized a formula and practiced it for the test. We never did look back at the formula once we got past the test. Now i find myself struggling with math classes in college, the educator show how but next explained why and had us make the connections.