What is math and why do we teach it?

The articles for our first week are thought provoking to say the least.  Previous to reading them I don’t think I ever contemplated what my mathematics philosophy was.  As Hersh points out, “most people, including mathematicians, don't even know if they have a philosophy, or what their philosophy is” (Hersh, p. 4).  My assumptions regarding math were learned from my teachers in school and professors in university.  Math was definite and absolute; there was always a correct answer.  There were theorems and formula’s I could rely on to solve any mathematical problems that I faced. 

In Hersh’s interview, “What is Mathematics, Really?” he refers to three possible philosophical attitudes towards mathematics, Platonism, Formalism and Humanism.  Firstly, “Platonism says mathematics is about some abstract entities which are independent of humanity.  [Secondly,] Formalism says mathematics is nothing but calculations. There's no meaning to it at all. You just come out with the right answer by following the rules. [Thirdly,] Humanism sees mathematics as part of human culture and human history” (Hersh, p. 4).  After spending some time thinking about my own philosophical attitudes towards mathematics I would have to say I have humanistic ideals.  I believe mathematics is a human activity; it is part of our culture and history.  Without humans there would be no math. 

From my own experiences with learning and teaching mathematics, I can relate to and agree with Hersh’s ideas of humanism especially when he states “Mathematics is neither physical nor mental, it's social. It's part of culture, it's part of history, it's like law, like religion, like money, like all those very real things which are real only as part of collective human consciousness. Being part of society and culture, it's both internal and external. Internal to society and culture as a whole, external to the individual, who has to learn it from books and in school. That's what math is” (Hersh, p. 2).  This approach makes math psychologically accessible to each and every individual.  It is not “inhuman or super human,” but something that people can learn because that’s what society does.

In my teaching I try to portray enthusiasm about math to my students.  There are so many negative attitudes towards mathematics in society therefore I try to counteract them in my classroom and provide my students with an environment where learning mathematics is fun.  Hersh states that interaction and communication are key.  I had a professor in university who came into the class, wrote examples and solutions on the board and if anyone asked a question that he felt was trivial he would almost make them cry.  My friend had workings on the side margin of her test and he wrote on her paper that they were trivial and should not be there.  She felt very belittled.  I swore my students would never feel that in my classes.

In my classroom I strive to develop an environment and atmosphere where students feel comfortable taking risk while they are learning.  Relating to them that no one individual learns the same way and that there can be multiple methods to solve any one problem.  I aim to make my students feel like they are connected to the mathematics they are learning.  Whether we are learning about speed or surface area, I try to connect it to something they can relate to in their everyday lives so they can see its importance.  “Mathematics consists of concepts, but not individually held concepts; socially held concepts” (Hersh, p. 3).  It is a social matter and they need to relate to it socially so they can become comfortable with it and feel like they can succeed at it.  I use peer groupings whenever possible so they can work together towards a common goal thus allowing them to discuss with each other solutions in evidently becoming comfortable talking mathematics.      

I want my students to see math as beautiful!

Maggie

Reference:

Hersh, Reben.  (1997).  “What kind of thing is a number?  A talk with Reuben Hersh.”  Retrieved from http://www.edge.org/3rd_culture/hersh/hersh_p1.html on September 29, 2011.