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The Educational Times Database: Using the Database in Mathematics Research and Pedagogy

Robert M. Manzo (University of North Carolina at Chapel Hill)

The ET database is intended to be helpful to researchers and teachers of the history of mathematics. There are many ways the database can aid teaching and research. To start with, researchers could leverage the database’s typology of questions in order to chart patterns in the timing and authorship of ET/MQ questions. For example, a search for all “Mechanics/Forces” questions published in 1876 yields eleven results, while a search for that year’s total “Conics” questions yields thirty-seven results. One could compare the relative popularity of specific question types among ET/MQ readers in specific years, and even compare what was discussed in the ET to topics addressed in peer journals. Such a comparison could reveal general historical trends in mathematics research, or, on the other hand, it could reveal how different mathematics journals appealed to different sub-disciplinary audiences.

Arithmetic (Mixture / Rate) 1 Triangle & Circle Geometry (Trilinear Coordinates) 41
Algebra 2 Projective Geometry / Vanishing Points 43
Trigonometry 3 Non-Conic Curves & Loci/Envelopes 44
Plane Geometry & Analytic Geometry 4 Conics (General) 45
Calculus 5 3-Dimensional Geometry / Surfaces / Tetrahedra / Spheres 46
Analysis (Real & Complex) 6 Geometric Constructions 47
Logic 7 Conic Sections (Parabolas, Ellipses, Hyperbolas) 48
Probability and Expectation 8 Differential Equations / Orthogonal Trajectories 51
Number Theory 9 Calculus (Maxima / Minima) 52
Combinatorics 10 Calculus (Integrals) 53
Applied Mathematics / Physics 11 Analysis (Sequences & Series) 61
Recreational Mathematics (Magic Squares, Chess) 12 Analysis (Inequalities) 62
Geometric Probability, Average value 13 Analysis (Approximation) 63
Average Value / Average Distance 14 Difference Equations 64
Optics 15 Knot Theory 71
Electricity & Magnetism 16 Statistics 81
Mechanics (Forces) / Statics / Equilibrium / Velocity / Acceleration 17 Philosophy 91
Hydrostatics / Hydrodynamics / Gas Dynamics 18 Astronomy 92
Thermodynamics 19 Glottochronology 93
Linear Algebra 21 Calendar Problems 94
Equations & Solving Equations 22 Partitions 95
Abstract Algebra (Group Theory) 23 Continued Fractions / Convergents 96
Polynomials / Invariants / Forms 24 Voting 97
Matrices & Determinants 25 Set Theory / Topology / Graph Theory 98
Quaternions 26 Music Theory 99
Spherical Trigonometry 31    

Table 1. The database’s typology of mathematical questions, created by Dr. James Tattersall.
All questions from the ET/MQ have been assigned to one of these categories.
Each category has its own numerical code, to ease processing of searches by the database.

The database also lends itself to analysis of historical patterns of authorship, revealing which individuals or classes of people contributed to the ET. In a 2004 article, for example, Tattersall used his then-unpublished data tables (now the backbone of the ET database) to create a profile of the ET’s female contributors. Several findings emerged, including the fact that women were most active in the ET from the 1870s to the 1890s. Women’s increased engagement with mathematics (as detailed in the “Women Contributors” section below) was precipitated by the 1860s education reforms that brought more women into secondary and higher education in Britain. The three most frequent female contributors to the ETChristine Ladd (1847–1930), Sarah Marks (1854–1923), and Belle Easton (dates unknown)—together submitted a total of 359 questions and solutions. Tattersall’s data tables allowed him to compile statistics that served as evidence to support broader historical claims. “The number of mathematical contributions made by women to pedagogical journals such as ET,” claimed Tattersall and co-author Shawnee McMurran, “increased dramatically in the late nineteenth century, indicating that women were taking advantage of educational opportunities, becoming more mathematically active, and establishing themselves as intelligent and competent analytical thinkers. In giving women credit for their mathematical contributions, ET helped promote an emancipated view of women” [Tattersall and McMurran 2004, 107]. Future researchers could use the database to explore patterns of participation by other categories of people and then connect those patterns to broader historical contexts, as Tattersall and McMurran have done. The potential for creative uses of the database in research thus is boundless.

Name Solutions Submitted Problems Posed Total Active ET Period
Christine Ladd 82 53 135 1872–1899
Sarah Marks 95 22 117 1881–1899
Belle Easton 81 26 107 1874–1893
Elizabeth Blackwood 23 76 99 1872–1897

Table 2. A table that compares the contributions of the most frequent female contributors to the Educational Times.
Excerpted from a pre-publication typescript of the article [Tattersall and McMurran 2004].

In the classroom, the ET database can be used as a tool to “integrate” or “permeate” the history of mathematics into conventional instruction [Siu and Tzanakis 2004, viii]. “Appropriate integration of mathematics history into the curriculum,” according to Tattersall and McMurran, “can lead students to make connections between various mathematical ideas; it can help students appreciate the integral role that mathematics has always played in society; and it can guide students to reach for a more meaningful understanding of major mathematical concepts” [Tattersall and McMurran 2004, 103]. For example, through exposure to mathematics history, students can gain an appreciation of the careers of famous mathematicians and learn the value of publishing in small venues such as the ET/MQ. Ivor Grattan-Guinness noted that the MQ contains “the first publication of Bertrand Russell” and that “at least twice Lord Kelvin put in an appearance, once on properties of determinants … and once on determining latitude” [Grattan-Guinness 1992, 77–78]. With the use of the ET database, other early publications by well-known mathematicians might be found, and qualifiers such as “at least” could be discarded and replaced by exact statistics on a particular author’s ET/MQ submissions. Besides famous names, numerous under-celebrated or otherwise unknown mathematicians contributed to the ET/MQ, and their presence is equally a part of mathematics history. Through contact with the work of people such as the lesser-known ET contributors Sarah Marks and S. Narayana Aiyar (whose biographies are sketched in the “Women Contributors” and “International Contributors” sections, respectively), students can gain a deeper appreciation of the appeal and vitality of mathematics beyond the lives of “great men” such as Bertrand Russell (1872–1970). Additionally, instructors can use the database to search for problems on specific topics, in order to extract example problems and have students compare the kinds of questions asked on those topics now versus then. This can shed light on the historical emergence, transformation, and/or disappearance of particular lines of mathematical inquiry. Beyond the few ideas mentioned here, use of the database for pedagogical purposes is open to myriad possibilities.

Robert M. Manzo (University of North Carolina at Chapel Hill), "The Educational Times Database: Using the Database in Mathematics Research and Pedagogy," Convergence (March 2021)