October 30

As class began students were assigned parts in Lakatos' "Proofs and Refutations" and all class members participated in an enactment of most of chapter 1. As mathematical questions arose, and they often did, we stopped to make sure everyone in the class understood the mathematics involved.

The board was filled with multiple interpretations. Boxes were removed from the shelves to make a model of a polyhedron bounded by an inner space and outer space. (The class had read the chapter earlier and many were confused by not only the mathematics involved but the message that Lakatos was trying to convey.) He was trying to provide an illustration of mathematics as a process. By the end of the reading, most had gained and understanding of his perspective although a few were not in agreement with such a definition of mathematics and could not imagine such a process taking place in one of their classrooms.

We then returned to a discussion on problem posing since a variety of perspectives had emerged from readings from various sources. We accepted each of the multiple perspectives and decided that when writing about problem posing, we need to make sure we express our own perspectives to let the reader know the basis of our writing.