**ERIC Number:**EJ879354

**Record Type:**Journal

**Publication Date:**2010-Apr

**Pages:**5

**Abstractor:**ERIC

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

The Pascal-Fermat Correspondence: How Mathematics Is Really Done

Devlin, Keith

Mathematics Teacher, v103 n8 p578-582 Apr 2010

The mathematics that students see in their textbooks is highly polished. The steps required to solve a problem are all clearly laid out. Thus, students are denied what could be a valuable learning experience. Often when students meet a problem that differs only slightly from the ones in the book, they are unable to proceed and afraid to "play with" the problem to see whether they can find a way to do it. If students could see examples of the false starts and the erroneous attempts of the experts, they might be more inclined to persevere themselves. This article shows how the August 24, 1654 letter from Blaise Pascal (of Pascal's triangle) to Pierre de Fermat (of Fermat's last theorem) is particularly well suited for exposing high school and college-level students to the process of actual mathematical discovery and problem solving. The letter records how two of the greatest mathematicians of all time struggled for several weeks to solve a probability problem. The Pascal-Fermat correspondence is an excellent teaching resource. It shows students that mathematics does not come easily, even to the world's best mathematicians; that it can take time and effort even to understand a problem, let alone solve it; that the experts make mistakes; and that the principal requirement for doing mathematics is perseverance. (Contains a bibliography.)

Descriptors: Textbooks, Error Patterns, Probability, Learning Experience, Secondary School Mathematics, College Mathematics, High Schools, Problem Solving, Mathematics Instruction, Teaching Methods, Letters (Correspondence), Professional Personnel

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**High Schools; Higher Education

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A