Imaginary Numbers

I am in the sharing mood tonight....I offer up the introduction to a paper I am working on dealing with imaginary numbers...again, there is that unfortunate requirement to read more than just a couple of sentences....sorry... Due to health conditions, I was forced to retire from full time teaching. I taught high school math for five years but due to immense pain throughout my body due to the conditions of military service, I was forced to seek part time employment. During that time, I worked as a tutor at a tutoring company. We had all sorts of courses that just a few of us were tasked with helping students with. I was the math guy, but due to my disabilities and the institutional requirements that the employees maintain a part time status; some of the other tutors had to accommodate and ended up having a few sessions with advanced math students in AP courses and Calculus. On one occasion, a fellow tutor approached me and detailed the lengths he had gone through with a student involving imaginary numbers. His comfort level was about the second semester of the Texas curriculums first semester Algebra 2. He asked me, Why do we study imaginary numbers? I pointed out that in engineering and other fields these theories on the imaginary number help to solve certain types of problems. He continued to inquire of their relevance. I explained the typical definitions of the imaginary number and how to work with it and the varying theorems that are associated with it. But he still seemed confused at the concept. Why he asked, if the number itself is undefined, why is it relevant. I have to admit that I failed to explain the concept. I accredit this to the way in which I was taught math – rigorous explanations of theorems and facts with little explanation of the history and concepts that led to a type of mathematical thinking, that is—the way we teach math in America. This brings this treatise to a concept proposed by Eli Maor, in his book, e:The Story of a Number, He stated an all too common dilemma faced by an American math teacher. “As one who has taught mathematics at all levels of university instruction, I am well aware of the negative attitude of so many students toward the subject.” Maor points out that perhaps math instructors and professors… …tend to overwhelm students with formulas, definitions, theorems and proofs, but we seldom mention the historical evolution of these facts, leaving the impression that these facts were handed to us, like the Ten Commandments, by some divine authority. The history of mathematics is a good way to correct these impressions. (Maor, 1994, p xii) It is my continued contention that including math history in our curriculums is a valid premise for establishing a better math curriculum at all levels of the study – especially secondary education, and even in the elementary grades. ....

To see the entire paper, see http://johnrozean.wix.com/mysite under "Papers"