I.1    Who Is Your Audience and What are Their Needs?


 

In planning any history of mathematics course, there is no more important question than who your audience will be. If you misjudge this question your course will be a disaster. Your students will be very unhappy. You will be distraught.

 

You should be able to determine your audience in advance. If the course is already on the books, then the syllabus will list some prerequisite. Perhaps the course is even required of some group of students. Knowing your audience settles the hardest question.

 

If you are teaching a course that has never been taught at your school, at least not in recent years, then you will have to drum up an audience. You will know some of these students and can safely assume that the friends they persuade to sign up too are somewhat like them.

 

Here are some questions that you should think carefully about:

 

·        What level are your students? Freshman, Junior-Senior, Graduate?

·        How good are your students? Are you at community college, a selective liberal arts college, an open enrollment state university, or a graduate university?

·        How much mathematics do they know? Calculus? Several abstract mathematics classes? Is it for liberal arts students?

·        What will they do after graduation? Will they become elementary teachers, secondary teachers, graduate students, or take a job? Is this a course for poets?

·        If they are prospective teachers, what history will benefit them?

·        Why are the students taking the course? Is it required of their major? Why is it required? Is it an elective class? Are they taking it because you will teach it? Are they seriously interested in history?

·        What do students need to get out of the course? How much “fact” do they need to know?

·        Is this a capstone course for mathematics majors that is intended to tie together what they have learned in other course?

 

No matter who your audience is, you need to be aware that they will not know enough mathematics and they will not know enough history (and neither will you). You have to teach history, you have to teach mathematics. This provides a considerable challenge.

 

A common audience is prospective secondary teachers. Their students will definitely benefit if they know something of the history of geometry, trigonometry, and algebra. Should you do something in the history course to review and expand their knowledge of this mathematics (where else in the standard undergraduate curriculum has their knowledge of these fields been expanded?). Certainly the prospective secondary teacher needs to know something of the history of quadratic equations. Why are they called “quadratic” equations? Doesn’t “quad” mean four? They may never have the need to solve a cubic equation, but learning how and learning something of their history will make it clear that complex numbers arose from solving cubic equations (everyone knows that x^2 = -1 has no solutions; why would mathematicians want to make up solutions for this equation?).

 

If your audience is prospective secondary teachers, you are almost forced into doing a survey of the history of mathematics. This limits your choice of textbooks.

 

If the class will consist of mathematics majors who intend to go to graduate school, then perhaps the best thing for them is to understand how modern abstract mathematics arose. A discussion of non-Euclidean geometry would benefit them (isn’t it interesting that this is the only undergraduate course that is customarily taught with a large historical component; the reason is clear --- the only motivation for the material is historical). How has the creation of non-Euclidean geometry changed the way we think about our world (contrast the Declaration of Independence with the Gettysberg Address; and how has the geometry of the forth dimension influenced abstract art --- aren’t these themes also important for the liberal arts student). So to would knowledge of the rise of abstract algebra benefit the prospective graduate student? Finally, an understanding of why the rigorization of mathematics took place in the nineteenth century took place is very important for a new graduate student to understand (for their teachers in graduate school almost certainly won’t --- should I say can’t --- explain). So if your audience is prospective graduate students, perhaps a topics course in nineteenth century mathematics is what they need.

 

If your class is for poets what do you want them to take away from it? Perhaps the Copernican revolution should be part of the course, for it certainly changed the way we understand the world. Shouldn’t they understand how statistics influences what we do today? This calls for a substantially different approach.

 

Should you be lucky enough to have a group of mathematically knowledgeable students who have a serious interest in history, then perhaps you want to include the careful reading of original sources. This approach will give all students a deep appreciation of what historians do, so perhaps this should be one of your aims in any course you teach.

 

Finally, the students may be taking the course because you are teaching it. They may just want to know what interests you. This allows considerable leeway in the design of your course.

 

 


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If you have comments, send email to V. Frederick Rickey at fred-rickey@usma.edu .
First posted  11 January 2003; revised June 2005.