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ERIC Number: EJ858575
Record Type: Journal
Publication Date: 2009-Oct
Pages: 6
Abstractor: ERIC
Reference Count: 3
ISSN: ISSN-0025-5769
Want to Play Geometry?
Kaufmann, Matthew L.; Bomer, Megan A.; Powell, Nancy Norem
Mathematics Teacher, v103 n3 p190-195 Oct 2009
Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical understanding, nurtured through years of game playing. Students understand that playing by the rules implies an agreement that rules are true and unchangeable and that a game is not fair if the rules contradict one another. Furthermore, every student knows how to prove whether a play is fair or not. Much axiomatic reasoning, the basis of proof, takes place while students play games. This article discusses the "Axiomatic Game," a two-day activity suitable for middle or high school classrooms. This activity helps students understand and appreciate axiomatic systems. Students develop their own postulates and theorems and use them to derive proof in a nonmathematical context. For teachers who wish to encourage deductive reasoning within an axiomatic structure, the "Axiomatic Game" is a motivating, inexpensive, and quick way to accomplish this goal. At the same time, the game stimulates creativity, verbal communication, writing, and the higher-level thinking skills of analysis, synthesis, and evaluation. It draws on students' previous game-playing expertise to unveil the mystery and wonder of axiomatic systems. (Contains 2 figures.)
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A