Summary & Synthesis

On Tuesday 9-25, in class we talked about constructivism and how it is a way of how kids learn. To take this further we did an activity to help us understand the area of triangles and constructivism by doing the surrounded activity. In this activity we took a piece of construction paper and we cut a rectangle out of it, then we inscribed a triangle with in the rectangle and then cut out the triangle. We then discussed the different observation that we noticed when we took the two scraps of paper and put them on top of the inscribed triangle. I think that this would be a good activity to have a class do to understand the area of triangles, and help them understand the area of triangles. After this activity I now understand how constructivism is entangled in everything that we learn and the we will teach in the future. It is just a matter of how students learn and how the subject is taught.

Summary and Synthesis

On Tuesday (9/25) we discussed finding the area of a triangle on a geoboard using different methods. We were then given an assignment where we were to use what we learned in class to find the area of several different shapes on a geoboard and come up with an algorithm for it. For me, the easiest way to solve the problem was to find the area of a rectangle that encompassed the shape and subtract away the areas that were not shaded. This involved finding different triangles and/or rectangles that could be made to find the area of the unshaded region. When finding the area of the triangles I used the formula A=1/2BH. After I found the area of each unshaded region, I would then total up those areas and then subtract it from the area of the rectangle and come up with my answer.

After class discussion on Thursday (9/27) about the formula for a triangle, I found out that some students (any age) don't really understand the formula and what the base and height is referring too. This makes it extremely difficult for them to understand what to look for when trying to find the area of a triangle. I think that all the different examples showing that triangles with the same base and same height will have the same area is a good way for students to gain an understanding of the formula. They will then have a better idea on what to look for and it will hopefully be easier for them to solve.

Doing Mathematics

Chapter two of Van de Walle talks about doing mathematics. What does it mean to "do mathematics"?