Due by Friday, March 11. Turn in at the Math 421 dropbox. If you need an extension of a few days, just email me no later than March 11 saying when you will submit the paper. Extensions to the weekend or Monday, March 14, granted automatically; for longer extensions please ask for approval.
Format. Your paper should be about 4 to 6 pages (typed, single-spaced, with an extra line between paragraphs). Include reference information for all material or persons (books, websites, classmates, etc.) you consult in writing the paper. Give page or section numbers for specific ideas you use, and use quotation marks around direct quotations from any source, including from our text. (The purpose of such citations is to make it easy for a reader to find the original source, if she wishes to do so. Thus the exact format does not matter, as long as it includes enough information to make it simple to locate the information you are using or quoting without having to read through many pages in the source.)
Content. It's probably not an exaggeration to say that M421 is built around a single idea, the Round Trip Theorem, which is a way of tying together two operations by making them reciprocal to one another. After a brief mention in Chapter 1, it emerges at the beginning of Chapter 3 from the two different descriptions of the walk taken by two children in the 5th grade. Then it appears and reappears in many languages and many contexts, both naked and real.
Your job in this paper is to trace the development of this idea, of two operations and how they are tied together by a Round Trip Theorem, from its "humble beginnings in a 5th grade classroom" to the Fundamental Theorem of Calculus. What is the core idea here? Does this idea really stay the same, or does it keep changing, so that it is unrecognizable as you go from one situation to another? It certainly looks different as we move along. In what ways does it change, and in what ways does it stay the same? What is the purpose of having you, a future high school math teacher, consider it in all these different situations?
In the course of your paper, you should also say how this idea has been useful as we have moved from one situation, language, or context to another. You should be very specific here. Here are examples of topics you could address.
Writing should always be done with an intended readership in mind. You may imagine either of two audiences for your paper. (1) Students who have begun to take this course and, after the first week or so, are seriously wondering what it's all about. (2) A future instructor for the course who has glanced over the book, but is still seeing it as a bunch of different, only slightly related topics. How do the five chapters fit together, what concepts in each chapter are important to the course as a whole and should not be neglected?
You may find it useful to reread sections 3.1 and 5.1 of our text before starting your paper, or after writing an outline or first draft.
If you would like to write a paper on a different topic, you should write a proposal, between a half and one page in length, and get it approved by me. The proposal should state the theme you propose in one or two sentences, list several questions or topics you will address in your paper, and describe the intended audience. You should make clear how you will include and tie together ideas from several parts of the course. Submit your proposal to me by hard copy or email (in the text of the message or as an attachment) and I will aim to approve or deny your request within two workdays. The latest date you may submit a request is March 3.
Return to the
Math 421 Homepage.
Most recently updated on February 24, 2011.