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The Early Republic

The World Stage

Between 1890 and 1910, the number of U.S. high school students quadrupled. Research mathematicians 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.”

At the turn of the century, some educators believed that models should be used to give a physical sense of mathematical theorems.

 GRAPH PAPER

 MODEL ILLUSTRATING PYTHAGOREAN THEOREM

 TOP OF PAGE Mathematicians had known from ancient times that there is a simple relationship between the length of the sides of a triangle with a right angle. As in the above (right) model, squares erected on the two shorter sides of a right triangle may be rearranged to form a square equal in area to a square constructed on the longest side. W.W. Ross, a local school superintendent, designed and sold several models to teach about surfaces and solids.

A few Americans pursued advanced mathematics after high school, but many more were needed by businesses to keep accurate accounts. Hence teachers drilled students in arithmetic and bought apparatus to assist them. Teachers rotated the slats of this instrument to produce new problems for students to work. It was very popular in Catholic schools in New York State.

 ARITHMETICAL FRAME

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