In the author there lives the perfectly purified conviction (such as he expects too from every thoughtful reader) that by the elucidation of this subject one of the most important and brilliant contributions has been made to the real victory of knowledge, to the education of the intelligence, and consequently to the uplifting of the fortunes of men.

J. Bolyai (1802-1860)


Reflections of My Work

After viewing all of my work from this quarter, I found it rather difficult to pick any one write-up that met each of the specified criteria. Each write-up offered something rather unique whether it was learning mathematics or learning how to use a particular piece of software. After much deliberation, here are the answers to the four reflection questions.

I learned the most mathematics...


To answer questions A and B, I cannot pick one write-up. I can however choose Write-ups 4-9 as being the assignments that I learned the most mathematics. These six writeups focused on the learning of geometry, a topic that I thought I knew alot about. Well, I was proven wrong with this course and these assignments. I learned more geometry from these six write-ups than I could have ever learned by picking up a book and reading about them. I have taught these geometrical concepts for several years, not realizing all of the extensions that are possible especially using GSP. In several of the write-ups I have commented on how useful and interesting these concepts are when taught from an interactive approach using GSP. GSP is the key to learning and understanding more about Geometry than I thought possible. Write-ups 8 and 9 were the most interesting write-ups of 4-9. I never knew what a Pedal Triangle was until this course and how so many concepts are related to that one particular triangle. My favorite discovery was the Nine-Point Circle. Once again, never heard of this circle until this course. It was so exciting to uncover so many of its neat and interesting properties and characteristics. Another neat discovery was how a parabola can be traced from the construction of the orthocenter of a triangle. Each of the six write-ups 4-9 opened up new doors that I had not known were shut. By that I mean, I thought I knew quite alot about Geometry and I have been mistaken. But I do know much more from this course and from working on these six GSP write-ups than before I walked into the computer laboratory. In fact, these write-ups have taught me how very little I do know and how much more I have to learn and discover, something that GSP and this course has at it's main goal.

Click here to return to my home page to view Write-Ups 4-9.

I am most satisfied and happy about...

Once again, it is very difficult to pick just one of the twelve write-ups that I am most happy about. I am pleased about each write-up. If I had to pick just one that would be Write-up 12. It proved to be the most satisfying because I launched the m&m idea myself. I am also proud of the finished write-up. If I had my own classroom, write-up 12 would be a great teaching tool to use to discuss exponential equations. I am proud however of each write-up and the progress that I have made this quarter, not just in terms of learning new mathematics but in regards to new software and how to use a computer. The first two weeks were very difficult for me. At times, I thought I would not learn quickly enough and thought I could never learn all that I needed to run the computer. Well I did. I am proud of myself for breaching the sharp learning curve at the beginning of the course and hanging in there. I have learned so much. I feel confident that I am abreast of the current software and technology that is available in the mathematics classroom. I do realize that I still have a long way to go and much more to learn.

Click here to view Write-Up 12.


My best, most creative, most thorough, more useful work is...

How can I pick? After viewing all of my work, I enjoyed each write-up in of itself. Each write-up is unique and interesting and offers mathematical insight. But if I had to pick, my best work is reflected in the Final Project. Each Part, 1 and 2, reflects an overall conglomeration of mathematics learned along with use of various software such as GSP, Excel, and Algebra Xpresser. I am proud of my Final Project in the sense that it reflects how much I have learned along the way in this course. I am intriqued by the very fact that the cardboard box problem could be demonstrated using several different approaches and computer software. I cannot begin to tell you how many times I have taught that same problem in a mathematics class and the students thought the problem to be boring, uninteresting, dull, and non-realistic. Using the three different approaches has shown me a new perspective: How all of what we have learned is connected. I would love to teach this problem now knowing what I know and using the available technology. My students would be much more awake and interested. I am sure of that.

Click here to view Final Project.

Final Thoughts


I am leaving this course much more aware of the mathematics education technology that is available. Furthermore, I feel much more comfortable around a computer. I do not feel computer anxious anymore. This course has helped to alleviate past stress that I incurred as a result of being around computers and not knowing how to use them. I truly loved this course. It was ALOT OF WORK. But I learned much more than I thought possible.

One final note, Thank you for your willingness to always answer my questions, many they were. I am also very appreciative of your letting me use your Power Mac over the weekends. It was very thoughtful . THANK YOU!!!

Euclid's work will live long after all the text-books of the present day are superseded and forgotten. It is one of the noblest monuments of antiquity.

Sir Thomas Heath (1861-1940)


Return to Final Project Page