NATURE 
205 
THURSDAY, JULY 14, 1870 
THE UNION OF THE ELEMENTARY TEACH- 
ING OF SCIENCE AND MATHEMATICS 
A eae is being more and more given to the 
teaching of science as a means of education. 
The object of education may be regarded as being to 
help people to think for themselves ; and our duty in 
practically educating people is two-fold ; we must supply 
them both with the materials for thought and with the 
method of thinking. It is in this latter respect that the 
scientific education which has as yet chiefly been given 
appears to us to have been somewhat deficient. Yet this 
is the most important part ; for materials for thought are 
supplied by nature itself, whereas the method of scientific 
thought and reasoning is the result of the world’s progress, 
and to inculcate that method ought to be our chief aim. 
The excellence of science as a means of teaching people 
how to think, consists in two things: first, that the facts 
with which it has to deal are real tangible things, and 
secondly that the method of reasoning which it applies 
to these facts is accurate; for if, in any part of science, 
the accuracy of mathematical reasoning is not attained, 
at least we can always put down our finger distinctly 
on the places where it is and where it is not attained. 
Now the error which has been made, and which is con- 
stantly being made, in the teaching of science throughout 
the country, is that these accurate methods of reasoning, 
and these tangible facts, have been separated from one 
another. In our boys’ schools and elsewhere (with very 
few exceptions), mathematics are taught wholly as applied 
to hypothetical cases, if even so much as that. They are 
thus the driest bones of method, or like a mill grinding 
without any corn in it. A manwholearns method in this 
way is like a man who learns anatomy from diagrams and 
not from thehuman bodyitself. On the otherhand the facts 
with which science has to deal are, with very few excep- 
tions, almost everywhere brought forward as isolated facts, 
or their connection is treated in such a way that the true 
scientific accuracy of reasoning, by which that connection 
is demonstrated, is either omitted, or receives an altogether 
unimportant place. In the more advanced walks of science 
and mathematics the University of Cambridge is perhaps 
primarily to blame for this separation between the scientific 
method and the facts of science. But that University is 
rapidly making amends for its previous errors, and is, 
perhaps, pursuing as direct a course as possible towards 
the reunion of these two. Perhaps it may be that our 
teachers of schools and others, coming mostly from the 
University, have carried this unfair dichotomy into their 
own teaching. The fact is that we are only just beginning 
to awake all through the country to the immense benefit 
to be gained from scientific teaching, and we could not 
expect that, until this awakening had occurred, science 
should have been properly taught. At the University there 
are certainly the most unbounded facilities for the true 
teaching of science, in the maturer minds and more ad- 
vanced mathematical acquirements of our students; but at 
the same time, the problem of uniting at schools the study of 
mathematics with that of the facts of nature is exactly the 
same problem. It is often objected, both by those engaged 
VOL. II. 
in teaching and by others, that an extensive knowledge of 
mathematics is required before we can apply it to Physical 
Science, This belief is perhaps one of the things which 
stand most in the way of the true teaching of science ; but 
the belief is entirely erroneous. Of course a person must 
first acquire a knowledge of the technical forms of mathe- 
matical expressions which are to be used; but it has 
been found that at the very earliest stages of the learning 
of any mathematical subject, the application of it to the 
facts of nature may be taught. In this way a new life is 
given to the whole study, and a comprehension of it is 
attained, which is, at least in most cases, otherwise quite 
unattainable. Let us take an instance. 
The subject called “ Variation” in Algebra is exceed- 
ingly uninteresting as it is usually taught; a sharp 
boy or girl regards it as, for the most part, but a 
poor and unnecessary substitute for the rules of pro- 
portion, and the applications of the rules for varia- 
tion are learned from such cases and exercises as have 
no connection with any subject of interest. Yet, as 
every one knows, in every part of physical science the 
facts which are eventually to take the form of equations 
present themselves as problems in variation; as, for 
instance, ““Ohm’s laws.” It has been observed that where 
the subject of electricity is taught (and we are happy to say 
that it is now sometimes taught to boys and girls) such a 
matter as the establishment of Ohm’s laws is left out ; if 
taught they are taught as results which have been arrived 
at, as of immense importance of course, but, at the same 
time, the train of reasoning whereby they are demonstrated 
is omitted, just decawse it involves the use of the rules of 
variation. And so indeed it will always be, so long as the 
plan is adopted of teaching people these and similar rules 
as abstract things. For when rules so taught come to be 
applied, the mind has to fit itself first into quite a new 
way of looking at things, and waste o! both time and 
trouble is the result. On the contrary, it has been 
found that a child whose knowledge of algebra extends 
only to the elementary rules, may be successfully intro- 
duced to the subject of variation by an experimental de- 
monstration of Ohm’s laws. By this means both subjects 
are much better understood, and the child feels himself in 
possession of quite a new power, whereby not only the 
intellectual, but also the moral benefits resulting from 
education are intensified. This is only an individual 
example, but in all cases it seems clear that the teaching 
of the rules of mathematics and of the facts of nature 
should be, and can be, even in the most elementary 
instances, so adapted as to go hand in hand. An oppor- 
tune and careful assistance enables the pupil to elicit for 
himself these rules as the most distinct form of expression 
of the facts of nature, and these rules enable him to trace 
the connection between these facts. The elementary 
parts of physical science teem with opportunities for the 
elucidation and application of the elementary rules of 
mathematics, the full force of which is not rightly under- 
stood until they are applied. 
A question which continually arises in the mind of an 
intelligent pupil is: “How did this or that piece of 
mathematics come to be used?” This is a question the 
need of which ought not to exist; for the pupil should be 
introduced to each piece of mathematics by the process 
of, as it were, himself discovering that it is the proper 
M 
