Teaching with Original Historical Sources in Mathematics

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2022-01-13 21:30:04

Our journey towards utilizing original texts as the primary object of study in undergraduate and graduate courses began at the  senior undergraduate level.  In 1987 we read William Dunham's article A "Great Theorems" Course in Mathematics (American Mathematical Monthly 93 (1986), 808-811), in which he describes a course based on mathematical masterpieces from the past, viewed as works of art.  His ideas and materials went on to become the well known best-seller Journey Through Genius: Great Theorems of Mathematics.  We were inspired to develop a similar course, at the senior level, but with one crucial difference: Whereas Dunham presents his students with his own modern rendition of these masterpieces, our idea was to use the original texts themselves.  With assistance from New Mexico State University's honors program, dean, and mathematics department, we developed and team taught the course Great Theorems: The Art of Mathematics, and it has now found a successful and permanent niche in the university's curriculum, serving as a lively capstone course for students majoring in a number of diverse disciplines.  It is the only mathematics course certified to meet the university's "Viewing a Wider World" upper division general education requirement. Our experiences with this senior level  course convinced us that teaching with original sources could be both successful and inspiring for us and our students.  The course is described in detail in  Mathematical Masterpieces: Teaching With Original Sources (html) (or dvi or ps) (in Vita Mathematica: Historical Research and Integration with Teaching, R. Calinger (ed.), MAA, Washington, 1996, pp. 257-260). We also involved other faculty in teaching and contributing material for this course. Our four author second book Mathematical Masterpieces: Chronicles by the Explorers has emerged from this course, written with two of these colleagues at New Mexico State University, Arthur Knoebel and Jerry Lodder. 

We came to believe that this approach to teaching and learning could also help provide the motivation, perspective, and overview so lacking in typical lower division courses, since it is being increasingly recognized that an historical point of view can address these deficiencies.  As Niels Henrik Abel observed: "It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils."  We have written an article Recovering Motivation in Mathematics: Teaching with Original Sources (html)  (or dvi or ps) (UME Trends 6, September 1994) espousing our reasons and philosophy for this teaching approach. We were  inspired to try to use the study of original texts as a teaching pedagogy introducing lower division students to important currents of mathematical thought.

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