I.2 What are the Aims of Your Course?

What are your goals in your history of mathematics class? This is, of course, an idiosyncratic question, but I do think that you should have specific goals and that you should state them explicitly to the students. In the history of mathematics course that I teach, I state the Aims of the [i.e., my] Course right in the syllabus:

To give life to your knowledge of mathematics.
To provide an overview of mathematics---so you can see how your various courses fit together and to see where they come from.
To teach you how to use the library and internet (important tools for life).
To show you that mathematics is part of our culture.
To indicate how you might use the history of mathematics in your future teaching.
To improve your written communication skills in a technical setting.

Now you may well have different goals, but I do encourage you to think about this in advance and to explicitly state some goals to your students. This will help you in designing the course, in justifying it to your colleagues.

Counteract negative views in your department.

Among some mathematicians the history of mathematics is not regarded as a serious pursuit. They believe it is something that people do when they can no longer do research in mathematics. You may encounter this view in your department, or it may be present but your colleagues don't express it.

It is worth you while to spend some time talking to your colleagues about your course. Point out to them that you are doing significant amounts of mathematics in your course (give some illustrations). Point out that it is not a course in anecdotes. Yes, you do relate this information, but you are really involved in a serious intellectual pursuit. You have high demands on the work that the students do. They must master a great deal of material and they are required to write about mathematics in a way that shows that they have mastered the details.

Aims of there people.

If you examine the syllabi which are on the web, you will find a great number of aims in teaching history of mathematics courses. Here are some of them:

To explain the use of historical material in the classroom.
Considerable emphasis on how to find out information and how to present it.
Get students reading original sources.
Critical analysis of factual materials.
To deal with methodological and philosophical controversies.
The art of communication.
To impart the view of mathematics as a continually developing human activity.
To understand different ideas of mathematics held at different times.
To give students a chance to reflect on their chosen field.
To get you interested in a particular mathematical topic.
To look at some of the great unsolved problems of mathematics.
To examine in detail some aspects of modern mathematics.
This course is a supplement to a course on Galois Theory.
To see the strands of mathematics which fused into modern statistics.
To enable students to widen, deepen and transform their views of the nature of mathematics, keeping in mind their future teacher objectives.

You should look at other peoples syllabi and borrow their good ideas.

Now before the course begins, it is probably impossible to talk to the students to see why they are taking the course. Their aims could be quite different than yours. At the beginning of the term and then again several weeks later, ask the students what they want to get out of the course, what their aims are. Since the history of mathematics is not a course with a fixed syllabus, it may be possible to accommodate some of their aims. To do so would gain you lots of points.

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If you have comments, send email to fred-rickey@usma.edu .
Posted December 30, 1996. Last revised July 2005.