An investigation into historic and contemporary presentations of logarithms in textbooks: Can historic presentations enhance the contemporary presentations of logarithms?

This dissertation explores the presentation of logarithms in current textbooks and historic texts. The aim of the research is to discover any past textual presentations of logarithms that could enhance modern presentations. Based on the theory of Multiple Perspectives, the scope of the historical text analysis includes not only foundational mathematics texts around logarithms, but also textbooks, dictionaries, and encyclopaedias. The theoretical construct of a Concept Image is discussed, focusing on a concept's need to connect to other mathematics for students to have a full view of the concept. To understand modern presentations of logarithms, a survey of modern textbooks is completed including an analysis of connections, or pathways, created between logarithms and other mathematical topics. This analysis shows that logarithms today are solely related to exponents, with all aspects of the concept coming through the students' understanding of exponents and exponential functions. To explore the historical presentation of logarithms, the foundations and early history of the logarithm is traced, gathered both from primary and secondary sources. Then the presentation of logarithms in historical texts between 1614 and 1750 is explored, focusing on how these texts introduce logarithms, define logarithms, justify the properties of logarithms, and use them in applications. Finally, the term logarithm, and how it is translated and then defined in texts from 1614 to 1850, is surveyed. This analysis demonstrates the connections between logarithms and mathematical concepts other than exponents, focusing mostly on those connections, such as sequences, ratios, and proportions, which were not apparent in modern textbooks. The result of the analysis produced in this dissertation is a set of recommendations for modern textbook authors or mathematics instructors. These recommendations do not argue against the modern presentation of logarithms and their overwhelming connection to exponents, but instead suggest bringing additional connections to other mathematical concepts into multiple levels of lessons around logarithms. These additional connections could strengthen any student's concept image of logarithms, but perhaps more importantly, they could help students who do not have a strong understanding of exponents still have a pathway to understanding logarithms.