Notes on the History of Graph Paper

Just re-ordered graph paper for next year for my department. We don't use nearly as much these days as five or ten years ago... calculators have made them much less common in schools. It reminded me that I hadn't actually put anything here about my notes on the history of graph paper, so for those who are interested...

Graph paper, a math class staple, was developed between 1890 and 1910. During this period the number of high school students in the U.S. quadrupled, and by 1920, according to E.L Thorndike, one of every three teenagers in America “enters High School”, compared to one in ten in 1890. The population of “high school age” people had also grown so that the total number of people entering HS was six times as great as only three decades before. Research mathematicians and educators took an active interest in improving high school education. E. H. Moore, a distinguished mathematician at the University of Chicago, served on mathematics education panels and wrote at length on the advantages of teaching students to graph curves using paper with “squared lines.” When the University of Chicago opened in 1892 E.H. Moore was the acting head of the mathematics department. “Moore was born in Marietta, Ohio, in 1862, and graduated from Woodward High School in Cincinnati. “(from Milestones in (Ohio) Mathematics, by David E. Kullman) Moore was President of the American Mathematical Society in 1902. The Fourth Yearbook of the NCTM, Significant Changes and Trends in the Teaching of Mathematics Throughout the World Since 1910, published in 1929, has on page 159, “The graph, of great and growing importance, began to receive the attention of mathematics teachers during the first decade of the present century (20th)” . Later on page 160 they continue, “The graph appeared somewhat prior to 108, and although used to excess for a time, has held its position about as long and as successfully as any proposed reform. Owing to the prominence of the statistical graph, and the increased interest in educational statistics, graphic work is assured a permanent place in our courses in mathematics.” [emphasis added]
Hall and Stevens “A school Arithmetic”, printed in 1919, has a chapter on graphing on “squared paper”.

John Bibby has written (August,2012) to advise me that John Perry, who was at the time President of the Institution of Electrical Engineers, has a section on "Use of Squared Paper" in an article in Nature in 1900 (The teaching of mathematics, Nature Aug 1900 pp.317-320.) They wanted $19 to see the article, so I take John at his word. I did find another similar endorsement of "squared paper" by Perry in "Englands Neglect of Science" published in 1900 also. On page 18 after several lamentations about trained engineers who had no ability/understanding of the mathematics applying to their field, he writes: "I tell you, gentlemen, that there is only one remedy for this sort of thing. Just as the antiquated method of studying arithmetic has been given up, so the antiquated method of
studying other parts of mathematics must be given up. The practical engineer needs to use squared paper."

The actual first commercially published “coordinate paper” is usually attributed to Dr. Buxton of England in 1795 (if you know more about this man, let me know). The earliest record I know of the use of coordinate paper in published research was in 1800. Luke Howard (who is remembered for creating the names of clouds.. cumulus, nimbus, and such) included a graph of barometric variations. [On a periodical variation of the barometer, apparently due to the influence of the sun and moon on the atmosphere. Philosophical Magazine, 7 :355-363. ] The increased use of graphs and graph paper around the turn of the century is supported by a Preface to the “New Edition” of Algebra for Beginners by Hall and Knight. The book, which was reprinted yearly between the original edition and 1904 had no graphs appearing anywhere. When the “New Edition” appeared in 1906 it had an appendix on “Easy Graphs”, and the cover had been changed to include the subhead, “Including Easy Graphs”. The preface includes a strong statement that “the squared paper should be of good quality and accurately ruled to inches and tenths of an inch. Experience shews that anything on a smaller scale (such as ‘millimeter’ paper) is practically worthless in the hands of beginners.” He finishes with the admonition that, “The growing fashion of introducing graphs into all kinds of elementary work, where they are not wanted, and where they serve no purpose – either in illustration of guiding principles or in curtailing calculation – cannot be too strongly deprecated. (H. S. Hall, 1906)” The appendix continued to be the only place where graphs appeared as late as the 1928 edition. The term “graph paper seems not to have caught on quickly. I have a Hall (the same H S Hall as before) and Stevens, A school Arithmetic, printed in 1919 that has a chapter on graphing on “squared paper”. Even later is a 1937 D. C. Heath text, Analytic Geometry by W. A. Wilson and J. A. Tracey, that uses the phrase “coordinate paper” (page 223, topic 153). Even in 1919 Practical mathematics for Home Study by Claude Irwin Palmer introduced a section on “Area Found by the Use of Squared Paper” and then defined “paper accurately ruled into small squares” (pg 183). It may be that the term squared paper hung on much longer in England than in the US. I have a 1961 copy of Public School Arithmetic (“Thirty-sixth impression, First published in 1910) by Baker and Bourne published in London that still uses the term “squared paper” but uses graphs extensively.