Homework Sept. 17, Representation

The article by Pape and Tchoshanov is convincing on the argument of the importance of having both a internal and external representation of a mathematical concept.  Figure 1 shows how the internal representation of the concept is different from the external. This demonstrates the difference between street math and school math. The article also convinces me that the way to connect the internal and external representation of the concept is by using different teaching techniques.  Each student will find the connection between internal and external representation in different ways as they have different life experiences. By using different visuals, words or supporting concepts the teacher will be able to connect more students then by just using the same methods over and over. I agree with the article that the connection between internal and external representation is a great teaching tool as some students will have a stronger internal or a stronger external representation of a concept. By making that connection the student is able to strengthen their weaker representation. I do disagree with the article somewhat on the idea that representation is found in social activity. I believe this is true for the more basic ideas, but for more advanced ideas the representation comes from experiences in other courses and objects.

Not all mathematical concepts can fit into an external representation as there are physical limitations to what one can see or visualize. Looking at infinity, it can be a challenging concept as there is not external representation to draw on. This is the same when you move into more them three dimensions. Concepts that are beyond the physical world are more challenging as the students have no external representation.