Science & Education

, Volume 20, Issue 1, pp 1–35 | Cite as

Using History to Teach Mathematics: The Case of Logarithms

  • Evangelos N. Panagiotou


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.


Natural Logarithm Seventeenth Century Logarithmic Function Arithmetic Progression Geometric Progression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I wish to thank Professor Michael R. Matthews for great support and encouragement. I also wish to thank the four anonymous reviewers for their generous help in greatly improving the English in an early version of this paper and for their numerous suggestions and constructive criticism for improving both the style and content.


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Authors and Affiliations

  1. 1.School Advisor in MathematicsEviaGreece

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