Ethics in Mathematics Courses

Margie Hale, 31 October 2002

Stetson University has a clear statement about Academic Honesty, which is articulated in the Connections Handbook and administered by the Honor System. The nature of cheating and plagiarism in mathematics deserves special discussion. First, much of mathematics is by common consent in the public domain. Second, because mathematics depends on the careful use of technical terms with precise and limited definitions, it is sometimes difficult to put mathematical statements into "your own words." Different words could very well be incorrect in the language of mathematics.

This statement on ethics pertains to work done in a typical university math course. There are other considerations for those doing research, whether at the undergraduate, graduate, or professional level. My course description for MS 497-498 contains a statement of ethics in mathematics research.

Course Policies

The description for each course should have a statement of class policies regarding the types of work submitted for a grade. It is the student's responsibility to become familiar with these policies, and to ask for clarification when needed. Ignorance of course policies, or of the definition of "cheating" in whatever form, cannot be used to avoid a penalty.

It almost goes without saying that the notion of academic honesty extends to all interactions with professors and students. Tell the truth about your work and your reasons for late work or missed classes. Follow through on arrangements made for instructor meetings, group projects, and peer study sessions.

In-Class Tests and Quizzes

Unless otherwise instructed, all work is to be your own, without assistance from other students, books, or notes. If you are unsure whether calculators or computers are allowed, ask the professor.

Take-Home Tests

Policies vary widely from class to class. Ask the professor what resources you may use. Encourage him or her to place explicit instructions on the test.

Homework

In most classes, you are free to use your books and notes to do the homework. Usually working with other students is encouraged, if done in a spirit of learning together, not just copying. Most assignments can be taken to the Math Clinic for help. Some professors have specific restrictions on homework assistance: ask.

Papers and Projects

Many assignments involving papers and projects assume or encourage you to use outside references. In general, definitions and statements of theorems need not be quoted, though most should be referenced. For explanatory text, all direct copying of another's words is plagiarism, unless it is a short passage marked with quotation marks and referenced. Even then, as in all writing, such quotations should be used sparingly and for emphasis, not as a replacement for providing essential information in your own words. Some paraphrasing is considered plagiarism; be sure that you understand what you are writing and express it in your own way.

If you take an example from a source, reference the source, and explain it in your own words. If possible, modify the example so that the work is truly yours. You will learn better that way. But still reference the idea for the example.

Pictures and graphs spruce up a report, and you are encouraged to use them. Familiarize yourself with graphics programs such as Paint®, Excel®, Mathematica®, and Photoshop® so you can create custom pictures. Images from the internet, if not copyrighted, may be used if they are referenced. The same holds for images scanned from a book or journal.

Math Referencing Style

List all references at the end of the paper, by author, in alphabetical order. Number them with bracketed numbers [1]. Within the body of the text, use just the numbers. For example,

Within the paper:

The Fundamental Theorem of Calculus is well known (e.g., see [3]). The next example illustrates a generalization, called the Coarea Theorem [1], which allows evaluation of certain integrals in two dimensions.

In the Reference section:

[1] Bennett Eisenberg and Rosemary Sullivan, The fundamental theorem of calculus in two dimensions, American Mathematical Monthly 109 (2002) 806-817.

[2] Margie Hale, "Ethics in Mathematics Courses," Margie Hale's Home Page, 31 October 2002. 03 March 2003 <http://www.stetson.edu/~mhale/teach/ethiccrs.htm>.

[3] James Stewart, Calculus: Concepts and Contexts, Brooks/Cole, 2001.

Styles [1] (journal article) and [3] (book) are from the American Mathematical Monthly. The online style [2] is adapted from the MLA style from the Holt Handbook. The first date is from the web page. The second is the date accessed by the student doing the paper. Footnotes are not usually used in math articles.

What to Reference?

Contrary to writing in the humanities or social sciences, once a mathematical definition has been made or a theorem proved, it is essentially in the "public domain": anyone can use it. However, you should acknowledge many ideas with a reference.

The Pythagorean Theorem is ancient and so widely known that it need not be referenced at all. Most definitions and results are not so widely known, and whether you give a reference depends on the audience for the paper you are writing. A good rule of thumb is that you need not reference definitions or named theorems from textbooks. That is, state the definition or theorem and use it; list the source in the reference section; but don't put a reference number in the text. See the Math Referencing Style, above. Always reference definitions, results, and conjectures from journal articles.


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