Beliefs

=Why do we count sheep starting at one?=

When I created my syllabus for the spring semester of 2010 (TE 402) I decided that I needed more statements concerning my beliefs in mathematics education. In the recent years, I have come across syllabi that have included beliefs statements or directly addressed the audience as to the qualities of the instructor. I felt that this aspect (my ethos for my rhetoric friends) was missing from the syllabus. From the rhetoric, I come across as a person and participant in the course, but at the same time I come across as an instructor.

With this in mind, I thought I would experiment with my final page of my syllabus. It is a beliefs about mathematics education statement page with a comic strip leading into the statements. It is posted as a document so that the visual aspects remain intact (although the page number has changed). As I am still completing the TE 402 course in which this was used, I am not sure of the impact, although I must admit that many of my fellow graduate students have enjoyed seeing this page.

[|Why Do We Count Sheep from One.doc]

So, I ponder why do we count sheep from one. I recognize that this may seem absurd, but I feel that it is fruitful in a discussion about my beliefs. I believe that we count sheep from one because it is traditional or accepted practice to begin counting anything by one. Children are encouraged to count at a young age, always starting at one. We develop a sense of counting by ones from one, always in the positive direction. Why do we accept these norms of mathematics? Is not a part of mathematics challenging what is accepted.

I think to the creation of zero. Many ancient cultures did not use the number zero, did not even consider it a part of the discourse. Mathematics was counting and counting could be done with the natural numbers. Yet, there were some cultures that embraced the idea of nothingness, that pushed to understand the ideas that there was in fact a value to having nothing and a need to represent it. The value zero is more than just nothing but is a placeholder in place-value arithmetic as well as the antithesis to the infinite. Such a powerful concept, yet one that is taken for granted. Yet in the ancient cultures where zero was not, it was unheard of to need and use zero. My point is that mathematics pushed thinking beyond simply what was convenient or accepted.

I am a fan of Kurt Godel's work, although I must say that I am never as successful in explaining it to others. Here is a man that challenged the ways of mathematics, and I feel turned the tables on accepted practice. Yet his work on incompleteness was quite controversial in his time. It is mathematicians like Godel that push thinking mathematically beyond what is accepted. I feel that he embodies much of what mathematics could potentially be. Instead of just learning to algorithmically perform (such as algorithmically count) we should push the norms of mathematical acceptance.