Analysis

W. Ted Mahavier, Fall 2011 - Spring 2012, Lamar University

Additional Resources

1. The Analysis I syllabus and the Analysis II syllabus contain the usual information on grading, office hours and content.

2. The course notes include an introduction for the students that delineates a bit about how the course is taught. It also includes the entire content of the course: the axioms, definitions, and problems. These notes have been freely available at the Journal of Inquiry-Based Learning in Mathematics (see Item 6 below) since 2009 and thus I do not know how many individuals have used them. Individuals have reported using them in various renditions at The Air Force Academy, Berry College, Chatham University, CSU Long Beach, Emory University, Evergreen State College, Gordon College, Illinois College, Lamar University, North Carolina State University, Plymouth State University, St. Joseph's College, SUNY New Paltz, University of Redlands and Xavier University.

3.The files Worksheet 1, Worksheet 2, Worksheet 3, Worksheet 4, and Worksheet 5 provide an example of what I do if classes are not producing as well as I want. When this happens, I focus the class carefully by giving very specific problems to work on. Optimally, if one passes out a few problems each class period and modifies or adds to them each subsequent day during the semester, the class remains focused for the entire semester. There are definite advantages to having a full package available from the start, as I do. One disadvantage of having the materials prepared in advanced, is that sometimes students branch off in different directions and then presentations don't benefit students who aren't working on that particular concept or problem. When this happens we lose the cross-fertilization of ideas and progress slows as each student is working in a vacuum. This is what happened here and I created these sheets to refocus the class on some easier material than that on which they were stuck. After the worksheets were successful in getting the class moving again, I opened up the number of things they could work on in the last worksheet and we made good progress from there until the end of the semester. These were needed for a very few weeks, passing one or two out a week over a three week period.

4. The blog is the web site that I maintained during Analysis I. It is in chronological order and shows the pictures and comments I posted. The second semester is missing because I created a Facebook group and the students photographed and posted the pictures on that page for the second semester.

5. The Analysis I midterm and final are just what you'd expect! There were no exams during the second semester, only an optional portfolio at the end of the term. The first semester exams are elementary for three reasons. First, we do absolutely no preparation for these exams. Second, these exams constitute very little of the final grade as my goal is to de-emphasize testing and emphasize what research mathematicians do -- working on unsolved problems until they are resolved! The student who is presenting regularly need not worry about grades on these exams. Third, all material on the midterm is new to them. I tell them not to memorize proofs, because nothing on the tests will be any problem they have seen. All problems will be new problems that can be resolved by understanding the techniques they have discovered but requiring only the use of the definitions and axioms.

6. The Analysis I evaluation and the Analysis II evaluation are the anonymous student responses to questions I penned. While the university requires on-line evaluations, I supplement the on-line evaluations with these questions using a time-tested procedure that maximizes participation. I print out enough copies for every student and then use fifteen minutes of one class during the last week of classes to administer them. I come to class, pass them out with a folder, and assign one student to collect them and return them to the secretary's office where I wait. The designated student returns the responses, passes them to the secretary and we return and conduct class. It wastes minimal class time, since by the time I return there are usually presentations on the board being discussed. The method is effective, as I get 100% completion and the students know that the secretary will type up the responses and email them to me after the semester ends. I tell the students that I will sit on my sloop with the beverage of my choice prior to the next semester, read them carefully, and modify next semester's class based on any recurring theme in the evaluations. The courses I teach are slowly refined based on this type of feedback until the evaluations come back like these, 90% positive and without recurring constructive suggestions. As a concrete example of change, students are allowed to resubmit the weekly written work one time and in the past, I always gave the best of the two grades. Students repeatedly told me that I should average the two grades to force them to think harder and do better work on the first writeup so that they would learn more. While this policy is not initially popular with my classes, I tell them that it is a result of the evaluations of previous students. Then at least they know that previous students believed that the policy is in their best interest.

7. The video diary may be best viewed in concert with my old-school attempt at illustrating the method, The Moore Method: A Pathway to Learner-Centered Instruction by Coppin, Mahavier, May and Parker which is the definitive "how-to" book for implementing the Moore Method. I coordinated the writing of this book, with support from the Educational Advancement Foundation, and if you really want a detailed perspective on how and why I teach using the method, this is the place to get it. In this book, the authors each give a perspective on the Moore Method. I talk in detail about syllabi, grading, developing course notes, the potential impact of such a class, the culture in the classroom, and many of the pedagogical tricks I have learned over the years. We devote an entire chapter to fourteen frequently asked questions including: "Does a Moore Method course cover less material", "Does the Moore Method work only for brighter students?" and "Do Moore Method instructors lecture?".

8. The Journal of Inquiry-Based Learning in Mathematics (JIBLM) publishes peer-reviewed, university-level course notes that adhere to an inquiry-based pedagogy, including those used in this course. I began collecting course notes in 1995 and over the years the project morphed into this journal. Please visit it and consider publishing your notes as you develop your IBL courses.

9. The Academy of Inquiry-Based Learning has small grants, mentors and speakers who can help put you on a path to IBL instruction.