{"id":14164,"date":"2023-01-30T15:25:53","date_gmt":"2023-01-30T20:25:53","guid":{"rendered":"https:\/\/notes.math.ca\/article\/catching-the-eye-using-images-to-bring-history-to-life-in-the-classroom\/"},"modified":"2024-09-12T13:29:38","modified_gmt":"2024-09-12T17:29:38","slug":"catching-the-eye-using-images-to-bring-history-to-life-in-the-classroom","status":"publish","type":"article","link":"https:\/\/notes.math.ca\/en\/article\/catching-the-eye-using-images-to-bring-history-to-life-in-the-classroom\/","title":{"rendered":"Catching the Eye: Using Images to Bring History to Life in the Classroom"},"content":{"rendered":"

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While it is always great when mathematics educators can include substantive studies of primary sources in their courses\u2014such as the projects described by the TRIUMPHS team<\/a> in the December 2018<\/a> issue of these Notes<\/em> [1]\u2014sometimes instructors may just be looking for a quick historical illustration, fact, or concept that illuminates a given day\u2019s lesson. One extensive and eye-catching resource for such glimpses of the past is the Mathematical Treasures collection found in Convergence<\/em><\/a>, the Mathematical Association of America\u2019s online, open-access journal devoted to the history of mathematics and its uses in teaching. The collection\u2019s over 1200 pages provide images of mathematical objects and of selected pages from mathematical manuscripts and texts housed in various libraries, museums, and private collections, all of which may be shared in your mathematics classroom. Below, I highlight some of my favorite Mathematical Treasures and explain what I think makes them engaging for students.<\/p>\n

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\n\t\tFigure 1.<\/strong> Autographed title page from De Morgan\u2019s copy of La Methode des Fluxions<\/em>. Convergence<\/em> Mathematical Treasures<\/a>.In 1750, the Comte de Buffon\u2014better known today as a naturalist\u2014translated into French Isaac Newton\u2019s Method of Fluxions<\/em> (written in 1671 but published posthumously in 1736) [Figure 1].\u00a0 But the confluence of great figures in the histories of mathematics and science doesn\u2019t end there, as this particular copy was purchased by Augustus De Morgan in 1852. Note that he added both his autograph and information about how he found the book near the place of publication on the title page [6].<\/p>\n

Another posthumous publication by a giant in the history of mathematics, the 1787 Institutiones Calculus Differentialis<\/em> by Leonhard Euler, catches our attention with both its mathematical content\u2014Euler wasted no time by bringing in differentials on the very first page\u2014and its typographical beauty [Figure 2]. As I\u2019ve written elsewhere, \u201cI can\u2019t get enough of the wonderful engraved artwork of texts of the sixteenth through the early nineteenth centuries. Don\u2018t you love the cherubs doing geometry in the \u2018E\u2019? Given that it is Euler and the letter e, I couldn\u2019t help imagining for a moment one of the little guys being Euler\u201d [3; 7].<\/p>\n

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\n\t\tFigure 2.<\/strong> First page of Euler\u2019s 1787 Institutiones Calculus Differentialis<\/em>.\u00a0Convergence<\/em>\u00a0Mathematical Treasures<\/a>.<\/p>\n

Historical books do not need to have made major theoretical contributions to be educational. For example, the next two Treasures help us encourage preservice teachers, liberal arts students, and others to think about how humans learn mathematics. Before mass-printed textbooks were readily available, children and teenagers typically wrote down what their teachers recited or copied from the class\u2019s single textbook in a \u201ccyphering book.\u201d These were carefully prepared, often lavishly decorated, and preserved within a family for generations. The pages shown here were prepared by 15-year-old Mary Serjant, who was born in England in 1673 [Figure 3]. On the first page, she was working on \u201cbroken addition,\u201d and on the second she showed an example of the Rule of Three, a proportion containing three known quantities and one unknown [4].<\/p>\n

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Figure 3.<\/strong> Two pages from Mary Serjant\u2019s 17th-century copybook. Convergence<\/em> Mathematical Treasures<\/a>.<\/p>\n

The cyphering-book tradition was especially associated with Christ\u2019s Hospital in London [2]. Another innovative type of teaching material from that institution is Johann Alexander\u2019s 1693 textbook, which is really a workbook with a blank page facing every page of text [5][Figure 4]. A student has attempted to solve this right-triangle problem for x<\/em>. Did they find the right answer?<\/p>\n

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Figure 4.<\/strong> Page 60 (and its facing blank page with student work) from Alexander\u2019s 1693 Synopsis Algebraica<\/em>. Convergence<\/em> Mathematical Treasures<\/a>.<\/p>\n

The full collection can be perused via an index organized alphabetically by author\/creator<\/a> as well as in several subindices by repository or form of material. Is there a historical document or object that you like to use in class which is not yet represented in Mathematical Treasures? Submissions can be sent to convergence@maa.org<\/a> and should include:<\/p>\n