method. And while the mathematical subjects of the quadrivium were
taught as science and for their own sakes, the new mathematics is a
sort of supplement to language, affording a means of thought about form
and quantity and a means of expression, more exact, compact, and ready
than ordinary language. The great body of physical science, a great
deal of the essential fact of financial science, and endless social and
political problems are only accessible and only thinkable to those who
have had a sound training in mathematical analysis, and the time may
not be very remote when it will be understood that for complete
initiation as an efficient citizen of one of the new great complex
world-wide states that are now developing, it is as necessary to be
able to compute, to think in averages and maxima and minima, as it is
now to be able to read and write. This development of mathematical
teaching is only another aspect of the necessity that is bringing the
teaching of drawing into schools, the necessity that is so widely, if
not always very intelligently perceived, of clearheadedness about
quantity, relative quantity, and form, that our highly mechanical,
widely extended, and still rapidly extending environments involve.

Arithmetic and geometry were taught in the mediaeval school as
sciences, in addition the quadrivium involved the science of astronomy,
and now that the necessary fertilizing inundation of our general
education by the classical languages and their literatures subsides,
science of a new sort reappears in our schools. I must confess that a
lot of the science teaching that appears in schools nowadays impresses
me as being a very undesirable encumbrance of the curriculum. The
schoolman's science came after the training in language and expression,
late in the educational scheme, and it aimed, it pretended--whatever
its final effect was--to strengthen and enlarge the mind by a noble and
spacious sort of knowledge. But the science of the modern school