**ERIC Number:**EJ915487

**Record Type:**Journal

**Publication Date:**2011-Feb

**Pages:**6

**Abstractor:**ERIC

**Reference Count:**9

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

When 95% Accurate Isn't: Exploring Bayes's Theorem

CadwalladerOlsker, Todd D.

Mathematics Teacher, v104 n6 p426-431 Feb 2011

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people are not naturally disposed to Bayesian reasoning. Gerd Gigerenzer and Ulrich Hoffrage's (1995) work suggests that human minds can solve Bayesian reasoning problems "naturally" when the relevant information is presented as frequencies rather than as probabilities. This article discusses an activity that allows students to explore the problem using simulated data and then expected frequencies and, finally, to connect these "natural" contexts to the "unnatural" context of working with probabilities. Through this progression, students develop an understanding of Bayes's theorem in a much more intuitive way. Further, the use of simulated data emphasizes the indeterminate nature of statistical inquiry and allows students to see an application of variance and the law of large numbers in a real-life context. (Contains 4 tables and 2 figures.)

Descriptors: Critical Thinking, Probability, Mathematical Logic, Mathematics Skills, Mathematical Formulas, Problem Sets, Problem Solving, Case Method (Teaching Technique), Teaching Methods, Educational Strategies, Simulation, Bayesian Statistics

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:**Higher Education

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A