Proposal for minicourse

This is the proposal that was submitted in January 1996 and approved in May 1996 by the MAA Minicourse Committee which is chaired by L. Carl Leinbach (leinbach@cs.gettysburg.edu) and Marvin Brubaker. We intend to follow this proposal in the actual minicourse, but, undoubtedly, there will be some changes.

Title:

Teaching a Course in the History of Mathematics

Abstract:

Many colleges and universities are introducing courses in the history of mathematics and asking mathematicians without a strong background in history to teach them. This minicourse will assist those teaching history by introducing participants to numerous resources, discussing differing approaches and sample syllabi, providing suggestions for student projects, and, in general, giving those teaching such courses for the first time the confidence to master the subject themselves and to present the material to their students.

Description of the Course:

This minicourse aims to give faculty members guidance in teaching a course in the history of mathematics. There are more and more colleges and universities offering such courses, partly because such courses are often required by certification requirements for secondary school teachers. Thus many faculty members are being asked to teach these courses, often without having had much preparation themselves. Although mathematicians are generally qualified to teach any undergraduate mathematics course, even those in subjects in which they did not do graduate work, the history of mathematics is different. While mathematicians assigned to teach this course usually have an interest in the area and have done some reading in history, they often lack the broad knowledge of the field that is necessary for a successful course. Moreover, a professor without some experience in the history of mathematics will have a hard time just "following the textbook."

The proposed minicourse aims to alleviate this situation for many faculty members. Naturally, in the space of four hours it will not make faculty experts in the history of mathematics. But it will provide faculty with a knowledge of resources from which to develop their expertise and it will provide them with many ideas from which to construct their own course in the history of mathematics.

Topics to be covered:

Resources in the history of mathematics (40 minutes).
- Books, bibliographies, encyclopedias.
- Journals and indexes.
- Web pages.
- Electronic discussion groups.
- Library catalogues and databases on the internet.
How to organize a course in the history of mathematics (100 minutes).
- Who is the audience?
- What are the aims of the course?
- Questions to ask of oneself about the nature of mathematics and its history, the answers to which will impact on the choice of text and the construction of the syllabus.
- Choice of textbook (or not having a textbook).
- Choice of readings.
- How can one choose material which will fit into the time alloted.
Student projects (60 minutes).
- What library resources are available, either on campus or in the area?
- What resources are available electronically?
- What projects are suitable for students preparing to be secondary teachers?
- Joint or individual projects?
- Written projects and/or oral reports?
How to prepare yourself (20 minutes)
- Start a reading program now.
- collect material for overhead transparencies.
- Outline the semester day by day and prepare a few specific classes to test the reasonableness of your plan.
Evaluation of a history of mathematics course (20 minutes).
- Evaluation by the instructor.
- Evaluation by the students.
- Evaluation by outside "experts."

Part 1 of the course will consist of a guided discussion of resource material which will have been distributed to the participants beforehand. Through the use of some examples of mathematical topics, we will guide the participants through a search of available material on the history of the topic. We will show examples of some of the web pages that are available and present some examples of discussion that have been going on in at least one of the electronic discussion groups on history (but we will not actually use the web online at the minicourse).

If the minicourse has more than thirty participants, it will be divided into two groups for part 2, each led by one of the presenters. We will have distributed beforehand a collection of sample syllabi. We will concentrate our discussions first on the practical aspects of constructing a course by looking at the strengths and weaknesses of those syllabi, taking into account questions a. and b. We will then take up some more philosophical discussions as indicated in c. These questions come from articles by William Anglin in The Mathematical Intelligencer (1992) and an article by Frank Swetz in PRIMUS (1995). It is these questions which any instructor of a course in the history of mathematics needs to think through for him or herself. Among the questions are the following:

Should the history of mathematics be presented as though mathematics were always a "good thing"?
Should the course idolize "rigor"?
Do cultural factors influence mathematical achievement?
How should the history of mathematics relate to the history of science?

Our experience in conducting the Institute in the History of Mathematics and Its Use in Teaching shows that these and similar questions will provoke a good deal of discussion. Many of the participants, even if they have taught a history course already, will not have considered these questions much and will be forced to think about them. At the end of these discussions, participants will be in a better position to make decisions about whether or not to use a textbook and/or collection of readings and how to choose from the wealth of available material.

For part 3, we will have distributed lists of student projects, especially those associated to the various syllabi discussed in part 2. Given that many colleges are teaching the history of mathematics to meet a requirement for prospective secondary teachers, most of the time in this part will be devoted to the nature of project suitable and desirable for those prospective teachers. Namely, since we believe that a knowledge of history is necessary for secondary teachers, we will suggest and give examples of projects in which students consider how the history of a particular topic can be used in teaching that topic.

In part 4, we will help the participants outline a personal program which will help them prepare to teach the course. With their knowledge of the resources available and having thought out a suitable syllabus, they can choose types of materials which will best prepare them to teach the course that they have chosen to teach.

For part 5, we will discuss the types of evaluation instruments which might be used for such a course and see how these can fit in with general university evaluation procedures. We intend that the discussions in part 4 and 5 will continue after the formal minicourse ends. Thus we intend that the participants join in an electronic discussion group. In that group, in which the presenters and other "experts" in the history of mathematics will also participate, further guidance can be given on preparation to teach and informal "evaluations" of courses in progress can be performed and suggestions for improvement made.

Logistics

We will use the standard two-hour + two-hour format on consecutive days, but will also request that two rooms be made available (assuming that there are more than thirty participants) so that some of the discussions can take place in smaller groups.

Biographical Sketches:

Victor J. Katz is a Professor of Mathematics at the University of the District of Columbia. He has regularly taught courses in the History of Mathematics since 1971 and is the author of the textbook A History of Mathematics: An Introduction (HarperCollins, 1993). He is the co-director, with Fred Rickey of the NSF-funded Institute in the History of Mathematics and Its Use in Teaching (1995-1998) and is the editor of the Newsletter of the International Study Group on the Relations between History and Pedagogy of Mathematics. He has written many articles and given numerous presentations on the history of mathematics and on the use of history in the teaching of mathematics.

V. Frederick Rickey is Distinguished Teaching Professor at Bowling Green State University in Ohio. He has been teaching history of mathematics courses since 1970 and has conducted several MAA Minicourses on "Using History in Teaching Calculus." He has written several articles on the history of mathematics (one on Newton won a Polya Prize) and is perhaps best known as a speaker on a wide variety of topics in the history of mathematics. He has also been Editor of Electronic Services for the MAA.

Return to the minicourse home page.
If you have comments, send email to V. Frederick Rickey at fred-rickey@usma.edu

Posted 2 December 1996.