USING THE EDUCATIONAL TIMES IN THE CLASSROOM Jim Tattersall Shawnee McMurran Department of Mathematics Department of Mathematics Providence College California State University Providence, RI 02918 San Bernardino, CA 92407 [email protected] [email protected] The Educational Times (ET) was first published in the fall of 1847. In 1861 it was adopted by the College of Preceptors as their official publication. The College had been established in London by Royal Charter in 1849. The organization endeavored to promote sound learning, advance interest in education among the middle class, and provide means to raise the status and qualifications of teachers. Training was offered to those entering the teaching profession and periodic examinations for certification were administered to both teachers and students. A union was formed to make provisions for the families of deceased, aged, or poor members. In addition, the organization strove to facilitate better communication between teachers and the public. At monthly meetings of the College, held at Bloomsbury Square and open to the public, announcements and summaries of important educational movements were promulgated and papers were read by members concerning the theory and practice of education. ET contains notices of available scholarships, lists of successful candidates on examinations given by the College, notices of vacancies for teachers and governesses, book reviews, and textbook advertisements. Undoubtedly, the most important feature of this monthly journal was a section devoted to mathematical problems and their solutions. From 1864 to 1918 problems and solutions which had appeared in the journal were republished semiannually in Mathematical Problems and Their Solutions from the `Educational Times'. W.J.C. Miller, the first editor, served from 1847 until illness forced him to retire in 1897. Miller was mathematical master and vice-principle of Huddersfield College in Yorkshire until 1876 when he became Registrar, Secretary and Statistician to the General Medical Council. He was a Fellow of the Royal Statistical Society and a member of the London Mathematical Society. Miller's directions were few in number: "Make your answers as short as possible, write each question and answer on a separate sheet of paper with your name at the top of each, and remember to pay the postage in full!". Miller was succeeded by Daniel Biddle, a member of the Royal College of Surgeons and Fellow of the Royal Statistical Society. Constance Marks, of West Kensington, the third and last editor, served from 1902 to 1918. In 1906 she added subject and author indices to each volume. A century ago mathematical textbooks as a rule did not contain pages of diverse exercises. It was customary for teachers and students to seek out applications of the theory they learned. Hence ET proved to be an invaluable source of practice problems to anyone interested in mathematics. The first publications of G.H. Hardy and of Bertrand Russell were solutions to problems from ET. The Oxford mathematician William Clifford claimed that the journal did more to encourage original mathematical research than any other European periodical. Eminent British contributors included William Burnside, Arthur Cayley, Charles Dodgson, G.H. Hardy, Thomas Kirkman, W.W. Rouse Ball, J.J. Sylvester, Peter Tait, and William Thompson (Lord Kelvin). European contributors included were Eugene Catalan, Gaston Darboux, Jacques Hadamard, and Edouard Lucas. Americans who contributed include Raymond Clare Archibald, Asher B. Evans, Benjamin Finkel, Asaph Hall, Artemas Martin, and Frank Morley. Prominent subscribers included John Couch Adams, Emile Borel, Ernest Césaro, James Challis, Augustus De Morgan, Henry Dudeney, Francis Galton, Charles Hermite, Felix Klein, Joseph Larmor, Magnus Mittag-Leffler, James Clerk Maxwell, L.J. Mordell, Simon Newcomb, and Benjamin Pierce. Of the 18702 problems posed in ET from 1847 to 1915, approximately 1.3 percent were submitted by women and more than 3 percent of the solutions were by women. THE TOP WOMEN PROBLEM SOLVERS FROM THE EDUCATIONAL TIMES SOLUTIONS PROBLEMS TOTAL ACTIVE ET SUBMITTED POSED 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 ALICE GORDON 41 36 77 1885-1905 CONSTANCE MARKS 50 9 59 1899-1918 CHARLOTTE SCOTT 25 9 36 1880-1888 EMILY PERRIN 24 4 28 1885-1892 KATE GALE 21 0 21 1881-1891 MARGARET MEYER 20 0 20 1882-1885 FRANCES E. CAVE 15 0 15 1903-1908 ISABEL MADDISON 13 1 14 1886-1899 LIZZIE KITTREDGE 10 4 14 1873-1892 GERTRUDE POOLE 10 0 10 1887-1888 FANNIE JACKSON 7 1 8 1889-1897 Solutions to the problems required a good understanding of algebra, trigonometry, calculus, triangle and circle geometry, and basic concepts in mechanics. Careful examination of the problems and solutions indicates that women contributors were acquiring solid mathematical backgrounds and were capable of applying geometric methods and both algebraic and analytical reasoning. The accomplishments of the women who contributed to ET confirmed the view that they were capable of competing on the same mathematical playing field as the men. The most prolific female mathematical contributor, Christine Ladd, studied mathematics under the supervision of J.J. Sylvester at Johns Hopkins. Ladd's analytical skills came to Sylvester's attention through her solutions published in ET. Before attending Johns Hopkins, Ladd studied at Vassar College and taught in secondary schools in upstate New York and Pennsylvania. At Vassar, under the influence of astronomer Maria Mitchell, Ladd concentrated her studies on physics. Under Sylvester's tutilidge at Johns Hopkins, she became a diligent student of mathematics and was influenced by the work of Charles S. Pierce and Bertrand Russell in symbolic logic. Ladd completed her course work and dissertation in 1882. Unfortunately, Johns Hopkins did not recognize degrees for women at the time. Ladd was awarded her Ph.D. from Hopkins in 1926. She authored more than ninety articles in mathematics, symbolic logic, the psychological aspects of color and vision and she received the only honorary degree ever awarded by Vassar College. Prior to the last century the notion that intellectual capability is independent of gender was a rather revolutionary idea. By the last quarter of the nineteenth century women were making important strides toward both social and intellectual independence. This progress can be attributed in part to the inception of women's colleges which offered women higher educational opportunities previously inaccessible to them. The number of mathematical contributions made by women to pedagogical journals such as ET 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. Their clever solutions and some of the ingenious problems they posed clearly indicate that they were persistent, logical thinkers with solid foundations in algebraic, geometric, and analytic reasoning. The dedication of these pioneering women undoubtedly both inspired, and gave a greater appreciation for mathematical thought to their own students and to the women of Girton who followed in their footsteps. Approximately thirty-seven percent of all solutions to problems by women in ET were the work of seven women from Girton College, Cambridge: Sarah Marks, Charlotte Scott, Ada Isabel Maddison, Kate Gale, Margaret Meyer, Emily Perrin, and Frances E. Cave-Brown-Cave. Sarah Marks was the most productive woman problem solver in ET. As was customary for a typical Victorian woman, Marks managed family responsibilities, nursed ill friends and family members, and was concerned with social issues. However, her passion for science set her apart from most of the women of her era. While a student at Girton, she organized a woman's fire brigade, invented a device for measuring one's pulse, and designed and patented a draftsman's device that could be used for dividing a line into equal parts and for enlarging and reducing geometric figures. After taking a third class on the 1881 tripos, Marks received her B.Sc. degree from the University of London. Before 1948, women could not receive a degree from Cambridge University even if they had completed their education at Girton or Newnham and passed the formidable Cambridge mathematical tripos - the Cambridge examination for a degree with honors. To obtain a college degree, women had to pass an external examination from a school that granted such degrees to women. After receiving her degree, Marks referred to Cambridge as her alma "step"-mater. In 1884, Marks began attending a physics course offered by Professor William Ayrton, F.R.S., at Finsbury Technical College. Ayrton and Marks were married in 1885. In addition to taking her husband's name, Marks changed her first name Hertha. The name was suggested by some of her friends who compared her to the Teutonic goddess Erda and to the heroine in Swinburne's poem ‘Hertha'. Ayrton began experimenting with electric arcs, which, at the time, were widely used for lighting. Her work generated significant industrial and commercial interest. Ayrton's research led to the production of more reliable searchlights and to improvements in the performance of movie projectors. She was the acclaimed European expert of the electric arc and commissioned to write a series of papers for The Electrician that formed the basis for her book, The Electric Arc. Ayrton was the first woman elected to a British electrical engineering society. She authored the first paper written by a woman to be read before the Royal Society of London. In 1901 Ayrton began investigating wavelike motions and the development of ripple marks on the sea floor. Her discoveries showed how sand ripple formation applied to coastal erosion and sandbank formation. In 1902 she became the first woman to be nominated as Fellow of the Royal Society.