NEW USES OF THE ABSTRACT—BOEHM 323 
years [1e., through sophomore calculus] without learning anything 
that’s been done since the year 1800.” 
THE DARTMOUTH PLAN 
Some colleges are now making progress in modernizing their math- 
ematics curricula. Several no longer require a special course in trigo- 
nometry. “We really don’t have to train everybody to be a surveyor,” 
explains one department head. Under the leadership of Kemeny, 
Dartmouth in the last 5 years has almost completely revised its under- 
graduate course. There are now, in fact, three separate courses of 
study in mathematics: one for mathematics majors, another for engi- 
neers and others who must have mathematical training, and a third 
for the liberal-arts students who want to make mathematics part of 
their cultural background. 
The courses are amazingly popular. Ninety percent of all Dart- 
mouth students take at least one semester of mathematics, and more 
than 60 percent finish a year of it (mathematics is an elective for 
most of them). Kemeny and two associates have written for one of 
their courses a remarkable textbook entitled “Introduction to Finite 
Mathematics.” Within a year after its publication in January 1957, it 
was being used by about 100 colleges, in some cases just for math- 
ematics courses especially designed for social-science majors. And 
several New York high schools have adopted the book for special 
sections of exceptional students. 
MATHEMATICS FOR CHILDREN 
The movement to teach more mathematics and teach it sooner has 
filtered down to the secondary-school level. The College Entrance 
Examination Board, through its commission on mathematics, has 
drawn up a program for modernizing secondary-school mathematics 
courses. ‘The chief aim of the commission, according to its executive 
director, Albert E. Meder, is to give students an appreciation of the 
true meaning of mathematics and some idea of modern developments. 
Algebra, he points out, is no longer a “disconnected mass of memorized 
tricks but a study of mathematical structure; geometry no longer a 
body of theorems arranged in a precise order that can be memorized 
without understanding.” 
The College Board has the support of most leading mathematicians. 
About 20 of them are meeting with 20 high-school mathematics teach- 
ers this summer at Yale to write outlines of sample textbooks based 
partly on the College Board’s recommendations. This group, headed 
by E. G. Begle of Yale, plans to write the actual books within the next 
year so that teachers and commercial publishers will know how mathe- 
maticians think mathematics ought to be taught in high school. 
