Journal+Entries

After each unit covered in class, we reflect on the unit with a Journal Entry. Following are each of my entries for the units we have completed thus far:
__Arithmetic:__

In studying arithmetic the past four weeks in class, I have been extremely intrigued learning about the roots of our base ten number system and other culture’s number systems. I had no prior knowledge of where our number system originated from or even that it was called the Hindu-Arabic system.

I believe that learning this basic information on our number system will be an interesting lesson to teach in my future classrooms. It is not something commonly taught, as it is not in the Michigan Grade Level Content Expectations. However, I do recommend that students learn what I have learned so far in this class because it really opens my eyes to the development of our mathematics and number systems. It makes me knowledgeable as well about place value problems and common misconceptions people have. This will be helpful in my future career as a teacher.

__Geometry__: Most know of Euclid as the father figure of geometry. He published his book Euclid’s Elements in 300 B.C. which contains many theories, as well as Euclid’s 5 postulates. Euclid was a Greek mathematician. Geometry was basically born in the Greek culture through Greek mathematicians, at least according to any type of record available. I enjoyed learning the past of geometry because I knew Euclid played a huge role in its evolution, but I didn’t realize the time frame or that he was even considered a Greek mathematician.

In studying the roots of geometry, I have enjoyed hearing ideas of how to incorporate the history into lesson plans. It is possible to use the history as a tool to meet a content goal, such as Egyptian symbols for place value, or to use the history to catch student interest. In class my group came up with a lesson plan to teach younger students how to tell time incorporating the history of the Babylonian’s number system. Babylonians recognized numbers in terms of powers of 60, or sexigesimal fractions.

This unit on Geometry has made me realize the importance of its history, which I would not have thought interesting before. I think that this part of mathematics, geometry, is one of the most important and involved the most discoveries and conventions. Without geometry calculus, as well as physics, would have been slower to develop if it would develop at all. Both subjects require a base of geometry.

Another important contribution that geometry had was the evolution of art from 2D to 3D. Originally artists were searching for ways to mirror reality on paper. They struggled with how to portray depth on a flat surface. Alberti proposed painting what the eye sees and thought of the paper as a screen through which the artist views the object to be painted. He also developed multiple mathematical rules to accomplish this idea of drawing “depth”. Then projective geometry was promoted even further when the question arose: If an object is viewed from two different locations, then the two screen images of that same object will be different. How are those images related, and can we describe their relationship mathematically?

__Algebra:__ The part that amazes me most about algebra is that when it originally was created and used, it was expressed in words and written out completely. This seems so hard to me. At this time equations were easily reducible or written as degree 1 or 2. Thinking about teaching algebra, it is very beneficial now that we have a uniform symbolic way of representing equations. I could not imagine teaching Algebra without the current system. It is said that mathematicians had hard times communicating their equations and solutions, imagine how hard it would be to communicate algebra to young students who are just being introduced to the subject without these uniform symbols.

A major creation that came out of Algebra is imaginary numbers, and then Calculus. If people had not explored these mathematical concepts I can not even imagine where our society would be today. Thinking on a smaller scale, if these issues such as imaginary numbers had not already been addressed, then while teaching them to a class of students questions would have come up about what to do with the square roots of negative numbers, etc. It is intriguing to think of math as an evolving topic.