**ERIC Number:**EJ909336

**Record Type:**Journal

**Publication Date:**2011-Jan

**Pages:**35

**Abstractor:**As Provided

**Reference Count:**79

**ISBN:**N/A

**ISSN:**ISSN-0926-7220

Using History to Teach Mathematics: The Case of Logarithms

Panagiotou, Evangelos N.

Science & Education, v20 n1 p1-35 Jan 2011

Many authors have discussed the question "why" we should use the history of mathematics to mathematics education. For example, Fauvel ("For Learn Math," 11(2): 3-6, 1991) mentions at least fifteen arguments for applying the history of mathematics in teaching and learning mathematics. Knowing "how" to introduce history into mathematics lessons is a more difficult step. We found, however, that only a limited number of articles contain instructions on how to use the material, as opposed to numerous general articles suggesting the use of the history of mathematics as a didactical tool. The present article focuses on converting the history of logarithms into material appropriate for teaching students of 11th grade, without any knowledge of calculus. History uncovers that logarithms were invented prior of the exponential function and shows that the logarithms are not an arbitrary product, as is the case when we leap straight in the definition given in all modern textbooks, but they are a response to a problem. We describe step by step the historical evolution of the concept, in a way appropriate for use in class, until the definition of the logarithm as area under the hyperbola. Next, we present the formal development of the theory and define the exponential function. The teaching sequence has been successfully undertaken in two high school classrooms.

Descriptors: Mathematics Education, Textbooks, Classrooms, Grade 11, Calculus, Mathematics Instruction, History, Mathematics, High School Students, Secondary School Mathematics, Numbers, Mathematics Achievement, Mathematics Curriculum

Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com

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

**Education Level:**Grade 11; High Schools

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A