42 



SCIENCE 



[N. S. Vol. XXX. No. 758 



paper, tables and blackboards should be 

 used all through the grades. Drawing and 

 paper folding should lead to intuitional 

 geometry and mechanical drawing, and 

 geometry be closely connected with numer- 

 ical and literal arithmetic.^" 



As phenomena are observed by the indi- 

 vidual, they should be described graphic- 

 ally and also in terms of number and meas- 

 ure. The graphical depiction serves to 

 illuminate the quantitative determination, 

 and vice versa. 



The following has been suggested as a 

 fairly complete equipment for a mathemat- 

 ical laboratory i^" 



1. Set of drawing instruments, board, T square, 

 triangles (for each pupil). 



2. India inks, paper, note-books, cross-section 

 paper. 



3. A large, well-lighted room, goo'd drawing 

 desks. 



4. Carpenter's tapes, surveyor's tapes, archi- 

 tect's scales. 



5. Three-, five-, seven-place logarithmic tables; 

 pupils to choose which to use from accuracy of 

 data. 



6. Logarithmic slide rules and computing ma- 

 chine. 



7. Surveyor's compass, transit, level, rod, poles. 



8. Surveyor's plane table and sextant. 



9. Steelyards, balances, pendulums, barometers, 

 thermometers. 



10. Force appliances such as pulleys and simple 

 machines. 



11. One hundred good texts on arithmetic, al- 

 gebra, geometry, trigonometry, physics, elemen- 

 tary mechanics and astronomy, including Crelle's 

 multiplication table. 



12. A dozen treatises on these subjects, and a 

 few good histories of mathematics and the mathe- 

 matical sciences. 



13. Spherical blackboards, concave and convex. 



14. Three plane blackboards for projective and 

 descriptive work in geometry. 



15. Mathematical models. 



16. Samples of actual engineering and architec- 

 tural drawings of machines and structures. 



" " On the Foundations of Mathematics," Moore, 

 School Review, 1903, pp. 521-38. 



'° " The Laboratory Method," C. W. Myers, 

 School Review, 1903, pp. 727-41. 



17. Gyroscopic tops. 



18. A set of Hanstein's models for projective 

 work. 



19. Stereopticon and slides. 



The laboratory method has been given a 

 thorough trial at the University School, 

 Chicago, and methods have been developed 

 and text-books prepared from the labora- 

 tory point of view. The aim or ideal of 

 the work for the first year has been formu- 

 lated by Professor Myers as follows:^' (1) 

 to generalize and extend arithmetical no- 

 tions; (2) to follow up the notions of 

 mensuration into their geometrical conse- 

 quences; (3) to reconnoiter a broadly in- 

 teresting and useful field of algebra; (4) 

 to treat, with sufficient completeness for 

 high schools, a large part of what is most 

 practical and useful in elementary algebra. 

 This means postponing the scientific and 

 purely logical aspects of algebra to a later 

 period. 



Problems are drawn from arithmetic, 

 mensuration, geometry, physics and ele- 

 mentary mechanics; and the equation is 

 made the starting point and agency for 

 developing the topics considered. The 

 text-book which represents this first year's 

 work is essentially an extensive and varied 

 body of mathematical ideas correlated 

 around an algebraic core.^^ The treatment 

 begins with the informal methods of in- 

 ductive arithmetic, passes to the uses of the 

 equation and its transformations, and by 

 degrees assumes a deductive character. 

 Practical problems of a constructional or 

 mensurational character have been found 

 to appeal to first-year pupils with greater 

 drawing force than any other problems of 

 the text. 



" " Year's Progress in the Mathematical Work 

 of the University High School," G. W. Myers, 

 School Review, 1907, pp. 576-93. 



^ " First-year Mathematics for Secondary 

 Schools," G. W. Myers and others. University of 

 Chicago Press. 



