48 



SCIENCE 



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



mathematicians, however, have always ac- 

 quired their disciplined powers while in 

 the pursuit of knowledge having intrinsic 

 worth, which indicates that mathematics 

 should be related to actually useful and 

 related things. 



The past decade has seen a revolution in 

 the schools. The old-time school with its 

 barrenness of resource has been abolished, 

 and the pupil has been placed in direct 

 contact with all the vital activities of his 

 time. To-day the child thinks through his 

 hands, and it is currently believed that 

 mathematics can play only a limited part 

 in the new education. Yet since the whole 

 universe is a manifestation of energy, 

 mathematics must find its place in every 

 subject. As a matter of fact, it is closely 

 identified with physics and has already 

 found its place in biology, botany, zoology, 

 etc. 



A radical change in the usual methods of 

 presenting the mathematical branches must 

 be made. Instead of taking them tandem 

 fashion, the subjects of arithmetic, geom- 

 etry and algebra must go hand in hand. 

 The child solves the question for himself 

 by introducing them all at once even before 

 he enters school. It becomes then simply a 

 question of assisting the pupil in the fur- 

 ther development of the mathematical 

 powers which he began to employ spon- 

 taneously before he came to school at aU. 



To illustrate the preceding principles 

 and methods an outline of some work done 

 in the eighth grade of the University Ele- 

 mentary School (Chicago) is given. The 

 subject was botany and the pupils were al- 

 lowed to take their time to work out the 

 problems, as their observations demanded. 

 In doing the work, the following principles 

 were observed: 



1. There must be a clear, general notion 

 of the image to be developed. 



2. There must be a careful selection of 

 appropriate units of measurement. 



3. The most expeditious methods of meas- 

 urement or of applying the units must be 

 chosen. Estimate first; then measure. 



4. There must be a careful selection of 

 processes by which the comparisons are 

 made. 



5. This must be followed by an objective 

 representation of the results in the form of 

 data obtained by observation. Gallons, 

 quarts, pints, feet, yards, square feet, 

 square yards, acres, miles, etc., must be 

 seen until they become a part of the mental 

 equipment. 



6. Using the results obtained as data, a 

 great nature picture must be constructed. 

 That is to say, through the original and 

 primary conception under which the pupil 

 has been working, the real magnitude of 

 world operations should be made to appear 

 in definite quantitative results. 



To illustrate these principles, the dis- 

 persal of seed was chosen as subject matter. 

 The observation material in this case was 

 found in a vacant city lot adjoining the 

 school, and by extending the calculations 

 to allied subjects, such as the amount of 

 solar radiation, and of annual rainfall, the 

 fundamental operations of arithmetic were 

 thoroughly covered. The details of the 

 work are fully explained in the last-men- 

 tioned article. S. E. Slocum 



University of Cincinnati 



WILLIAM EIMBECK, 1841-1909^ 

 Me. William Eimbeck, the subject of this 

 sketch, and myself were close friends for 

 many years. His ambitions were well known 

 to me, and I am very well aware that his fail- 

 ure to attain the final success he had hoped 

 for was due to an organic disease which slowly 

 crept upon him during the later years of his 

 life. 



' Memorial address before the Philosophical So- 

 ciety of Washington, May 22, 1909. 



