INTRODUCTION TO SEQUENCED WRITING ASSIGNMENTS
MTH 222T/331T Linear Algebra and Discrete Mathematics Introduction to Long Writing Assignment Tom Farmer Linear algebra is an area of mathematics that has applications and connections in many other fields, both inside and outside mathematics. Although the shortage of time prevents us from discussing these fields as regular parts of the course, this assignment will encourage students to explore such a connection in some depth. This is an opportunity for independent study in an area of a student’s own choosing. And it may be one of the first times and one of the rare times for mathematics students to go through a process of writing and revising mathematical exposition. There is a hidden difficulty in designing this assignment. I have listed a number of mathematical areas that students may read about, but I have not verified that an interesting 5-page paper, of the sort described, can be written in each of these areas. I need to obtain appropriate sources for the topics and I need to see if I can come up with reasonable problems that are suitable as the focus of a paper. I expect to have about 15 students—I would like to be prepared with at least 5 different topics with suitable sources and problems. I know some students will be able to come up with their own ideas. Also, if I can find 5 ideas then surely there will be any number of variations on the problems to make for sufficiently many different ideas for papers. I have chosen to have the paper written in phases for several reasons. Of course, the main one is that some students tend to leave the writing of a paper until the last possible moment, and I want to get them to spread the work out over several weeks. More importantly, I do not want these papers to merely duplicate an encyclopedic treatment that can be found in undergraduate texts. As suggested in Bean’s Engaging Ideas, it will be more interesting and effective to use a problem as the focal element for these papers. The discussion of an interesting problem seems to be a reasonable way to organize the presentation of needed concepts and theorems. This presentation should find the shortest distance from “zero,” where the reader may know nothing about the topic, to where the problem can be discussed. By handing in the Phase 1 and Phase 2 papers, I hope the students will find themselves with the time and the motivation to reflect on how best to organize, integrate, expand and revise as they put together the final product. I thought of having a peer review not so much for the usual purpose of giving feedback to the writer. Rather, I think that the prospect of giving your paper to other students in the class will motivate the writers to do more careful work. Most importantly, I wanted the students to read at least a couple of other papers to see other topics and to see how other students handled the assignment. TOM FARMER SEQUENCED WRITING ASSIGNMENTS FOR STUDENTS
MTH 222T/331T Linear Algebra and Discrete Mathematics Long Writing Assignment
Goal. Become an independent learner of mathematics. Work on problem-solving, organization, and communication skills. Plan. In this assignment, I ask you to read from several sources on a mathematical topic of your choice (with my input). The end result is to have a polished 5-page paper that focuses on two or three carefully selected problems that serve to illustrate the topic. The paper is completed in phases that are described below. Topics. Please see me to discuss possible topics and sources. I want every student to find a topic that interests and suits them. Topics that I have in mind are ones that make significant use of linear algebra concept, but will not be covered in our course. Some possibilities are: Topics in Graph Theory Markov Chains Game Theory Topics in Dynamical Systems Topics in Computer Graphics Image Processing I encourage you to investigate some of these subjects to see whether you can find useful sources and to see if the subject grabs you. In any case, I can help you find good sources of information. Phase 1. After an initial meeting with me to discuss topics and sources and after reading and digesting some of the introductory material on your topic, your task in this phase is to select two or more problems that can be used as good illustrations of the topic. One problem can be elementary and the other should be substantive and more intriguing. It may be open-ended and impossible to solve in this paper. Write a 2-3 page paper solving the elementary problem and solving or discussing the intriguing problem. Assume your reader already knows the needed definitions and theorems. This can be a rough draft but should be done on a word processor. (I suggest you use Word along with its Equation Editor.) Eventually, this paper will be revised and incorporated into the Phase 3 paper. This paper is due on Monday of Week 8. Phase 2. Write a development of the definitions, concepts and theorems that are necessary in order to prepare readers for the problems posed in Phase 1. Be economical—do not include discussion of unnecessary concepts or results. Once again, this can be a rough draft done on a word processor and is expected to be 2 or 3 pages in length. Due on Monday of Week 10. Phase 3. Combine your Phase 1 and Phase 2 efforts and add what is needed to make a lively and interesting introductory paper on your topic. It is likely that you will need to do much more than simply string your two preliminary papers together. Your audience consists of your professor and the other students in our class. This time the paper is to be carefully revised and edited. Five pages, double spaced would be a good length. Bring 3 copies of the paper to class on Tuesday of Week 12. That day we will form groups of three and each student will take home copies of the papers of two group members. We will spend the class period Wednesday meeting in these groups to discuss the papers. The purpose is partly for the benefit of the writers and partly for the benefit of the readers—everyone will be able to see what two other students have done with a topic. As a result of the peer review discussions, some final editing may take place before the final paper is handed in on that Friday. Evaluation. This project constitutes 10% of your grade in the course. But I hope you will give it more weight because the work product will be shared with other students. Phase 1 and Phase 2 papers must be handed in on time (or face penalties for each day late) but they won’t be scored. I will write some comments and ask some questions. The final Phase 3 paper will be scored in the manner described in the rubric below.
Grading Rubric. Mathematical Writing assignments involve mathematical skills and writing skills, so the evaluation criteria include both. The criteria for this assignment are
·all aspects of the assignment are covered ·explanations are thorough ·supporting arguments are included
·appropriate mathematical or computer methods are used ·mathematical steps are correct ·mathematical logic is clear
·organization is logical and includes an introduction and conclusion ·transitions from one idea to the next are smooth ·mathematical and computer work are smoothly integrated with the text ·mathematical statements are presented with complete sentences ·figures or computer output are described in the exposition ·grammar and spelling are correct.
·the overall impact is positive ·creativity and innovation are apparent |