Faculty: Keith Howard, Assistant Professor, Mathematics
Librarian: Minyu Zhou, Librarian and Technology Consultant
Course: Math 230 - Euclidean and Non-Euclidean Geometry
PROJECT DESCRIPTION:
Euclidean and Non-Euclidean Geometry, in addition to being an interesting course for students in mathematics is also a recommended course for those students interested in pursuing a career in teaching. This will be my first time teaching this course, which has not been offered at Kenyon within recent memory (at least about ten years). An important pedagogical objective of this course will be to teach students how to develop a coherent theoretical structure using various resources and to develop the ability to search for, read, and interpret primary scientific literature. Achieving this goal will be helped significantly through the infusion of information literacy. Gaining such experience should prove a valuable resource for students interested in higher pursuits in mathematics and for students interested in teaching.
Active learning strategies will be central to the approach of this course. Students will develop and present theoretical results that form the foundations of Euclidean and Non-Euclidean geometries. Students will also search and retrieve journal articles for the purpose of interpreting the results and presenting them before their colleagues. This mid-level course will introduce students to the processes of mathematical research that include article searches, individual and collaborative theoretical development and the collegial process of disseminating information. By providing students the opportunity to explore first-hand the different types of informational resources available to them it is hoped that they will develop skills that will extend far beyond the theoretical focus of the course.
Pedagogically, information literacy will impact this course in two forms. The first form deals with the manner in which students prepare for day-to-day classes. It will be expected that students research, analyze, and present course topics. Students are also expected to consult a suggested listing of texts to derive solutions to specific problems for presentation. I plan to work with Minyo Zhou to make the suggested text listing available on the LBIS web page.
The second more significant manner in with information literacy will be integrated into the course will be through the requirement that student research a topic of interest using primary sources. Students will work on this requirement throughout the course. Early in the course, through workshops with Minyu Zhou, students will learn how to conduct and refine an article search. Students will also learn how to evaluate primary papers in terms of the topics of interest and the prerequisite knowledge assumed by the work.
IMPLEMENTATION:
Prior to the start of the course a web page will be developed linking information on various geometric topics of interest and their applications. The web page will also contain a detailed outline of axioms, definitions, theorems, and larger question meant to provide perspective to the theoretical results that are to be developed in the course. The website will also list selective primary resources that students will be encouraged to consult as we develop the theoretical structures of several geometries. This web page will be linked to a second web page, created by Minyu Zhou, which list specific resources available though our library system.
On the first day of class students will be encouraged to peruse the links of geometric topics to discover areas of personal interest. Ultimately students will select a particular area of interest, that they will research and present papers on. Students will also be given a course outline of specific theorems and questions to be developed. The next couple of class meetings will be devoted to the establishment of foundational axioms and theorems. Beyond this point students will immediately begin to construct and present results by developing the ideas included in the course outline. This will be accomplished through independent efforts of analysis and information searches of various texts of interest. Students will claim certain results for presentation to the class in the Moore Method.
Certain days will be set-aside as resource development days. In collaboration with Minyu Zhou, Librarian and Technology Consultant, we will cover
In preparation for these efforts Minyu Zhou and I will meet several times over the summer to discuss the listing of particular journals of interest for student projects. We will also conduct a sample article search that will serve as a case study for students in conducting and refining there article search. In addition, we will set up specific criteria to assist students in the evaluation of journal articles using abstracts, keywords and the AMS' Mathematical Subject Index.
Students will have ongoing meetings with the instructor during the course of the semester reporting on the progress of their independent project. During these meeting students will receive guidance on the article choices they have retrieved and feed back on the depth breath and progress of their research. The project will conclude with the development of a power point or html display of project results, a classroom presentation before their peers and the submission of mathematical paper detailing the result of their research experience. Students will provide a written abstract to the class prior to the classroom presentation. The paper will have the format of a research paper including an abstract and a conclusions section. The paper will be expected to adhere to proper protocol for citing sources. Each student will read the paper submission of one other student and provide a detailed review of the paper. Exercises will be developed in advance to educate students in such issues as understanding citations and the proper protocol for citing sources and communicating research results in writing.
PRODUCTS:
It is anticipated that this project will result in the creation of an informative course webpage, a selective listing of accessible resources, and an extensive outline of specific course topics to be researched and/or developed by students. The web page will initially serve as a guide for students, pointing them in the directions of interesting topics of research in Geometry. Part of the goal of the website will be to pique student's interest in areas of worthy ongoing research for them to investigate and present before the class. The webpage will evolve over the course of the semester to include a showcase of the results of students' efforts. The listing of resource on the LBIS resource web site will serve as a starting point for students in doing independent investigations in learning to seek out, process and report upon ongoing research. The course will be taught in the style of the Moore Method, where students research and present ideas on an ongoing basis guided by a selective listing of questions and topics provided in the form of the extensive outline.
TIMELINE:
Preliminary planning of the web page and the course outline has begun in the spring of 2003, however, most of the preliminary work will be completed during the summer of 2003. By early August, specific topics of interest and related accessible journals will be compiled. The course web page along with the LBIS recourse web page should be ready by mid August. Students will begin to investigate topics of interest on the first day of class and will have their first information literacy "workshop" session during the second week of class. Sessions to help students revise and refine their search will be conducted throughout the course. By the third week of class students will have identified a specific topic of interest, and must identify several primary research articles for consideration. By mid term, students will be required to submit a general review of the article(s) that will serve as the basis for their project. Final papers will be submitted just after Thanksgiving break with the final week of class reserved for presentations. A fellow student will review each student paper. The results of individual research experiences will be showcased on the course web page.
ASSESSMENT:
An evaluation will be administered at the end of the course. The evaluation will address the effectiveness of specific elements related to information resources including the use of secondary resources for course materials and the use of primary resources for the research topic. Questions will be designed by Keith Howard and Minyu Zhou to assess the value and success of the integration of information literacy in the course.