William Whewell.

On the principles of English university education; online

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Prefatory Remarks 1

Chapter I. — Of the Subjects of University Teaching.

Sect, 1. Of tlie Distinction of Practical and Specula-
tive Teaching ..... 5

Sect. 2. Of the Effect of Practical Teaching on the

Intellectual Habits . . . .12

Sect, 3. Of the Effect of Practical and Speculative

Teaching on the Progress of Civilisation 17

Sect. 4. Of the Learned Languages as Subjects of

University Teaching . . . .31

Sect. 5, Of the Necessity of combining Classical and
Mathematical Subjects of University
Teaching 39

Sect. 6. Of the Sciences as Subjects of University

Teaching ...... 42

Sect. 7. Of the Moral Effect of Practical and Specu-
lative Teaching 4(3

Chapter II. — Of Direct and Indirect Teaching.

Sect. I. Of Examinations, and of College Teaching 54

Sect. 2. Of Professorial Lectures . ... 68

Sect, 3. Of Private Tutors 73

Sect. 4. Of the Combination of the University with

the College System ... 78

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CuAPTEH III. — Op Discipline.

Sect, 1. Of the Necessity of Discipline .

Sect, 2. Of Colleore Manners .

Sect. 3. Of College Punishments .

Sect. 4. Of Attendance at College Lectures

Sect, 5. Of Attendance at College Chapel

Sect, 6. Of Fellows of Colleges

Sect, 7. Of the Free System .

Sect, 8. Of Changes m the College System



Thoughts on the Study op Mathematics as a

PART OP A Liberal Education . . .141

A Letter to the Editor of the Edinburgh Review,

occasioned by the Review of the First Edition 183

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The conBiderations which I here offer to the public
on the subject of Education, have been suggested by a
long and somewhat laborious course of researches on
the principles and history of science, and by many
years^ experience as a tutor in a principal College of
the University of Cambridge, I trust, therefore, that
I shall stand absolved from all suspicion of approach-
ing so important a subject without due thought and
preparation. I have for some time intended, on the
first occasion of comparative leisure, to state my views
on the points here treated of; and I should have done
so, in the same manner, and probably nearly at the
same time as I have done, whether or not other
pamphlets on questions connected with the English
Universities had appeared. I request the reader,
therefore, not to mix me up in his thoughts with any
controversies which may happen to be going on at this
time. I mean not to express any disrespect to persons

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engaged in such controversies ; but I must take the
liberty of saying, that I have neither sought nor
shunned the discussion of any questions on which they
may happen to have touched.

There is another controversy, to which some part of
the following pages may appear to have reference ; —
the question of the comparative value of Mathematics^
and of certain other studies which have been termed
Philosophy, as instruments of Education. An Edin-
burgh reviewer, in a criticism upon a former publication
of mine, maintained that the study of mathematics is,
for such a purpose, useless or prejudicial ; and recom-
mended the cultivation of "philosophy''' in its place.
In a letter to the Editor of the Review, (which I pub-
lished,) I expressed my willingness to discuss the sub
ject at a future time ; and, referring to the mathematical
course of this University, as my example of mathemati-
cal education, I requested to be informed, by description,
or by reference to books, what that " philosophy**' was,
which the reviewer was prepared to* contend for, as a
better kind of education. I considered this as a pro-
ceeding, in the courtesy of literary combat, equivalent
to sending my opponent the measure of my weapon,
and begging to be furnished with the dimensions of his.
When, therefore, the reviewer, in reply, flatly refused*
" to perplex the question by a compliance with Mr.
WbewelFs misplaced request,'* I certainly considered
myself as freed from any call to continue the con-
troversy. No adherent of the reviewer coUld expect
me to refute a pd*oposition which the author himself

• Edin. Hev. No. CXXVII.

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did not venture to enunciate in an intelligible form.
And, therefore, in the present book, I do not at all
profess to discuss the question of the value of mathe-
matics, and other kinds of philosophy, with reference
to the reviewer^s assertions, but simply so far as it is
brought before me by the general course of my

I must also observe, that my remains, at present,
will be bounded within the limits of my title. I do
not undertake to examine the subject of education in
general, but the Education of Universities; nor again,
of Universities in general, but of English Universities.
Moreover, I am far from intending or hoping to treat
the subject, even thus limited, fully and completely ;
my purpose is merely to offer certain Considerations,
having reference to the general Principles on which
the work of English Universities is and must be con-
ducted, rather than to their actual condition and their
proceedings in detail. I trust, however, that the
Principles which I shall endeavour to establish, are so
far substantial and practical, that their application to
the real business of Universities will be obvious and

A formal division of my subject might appear as if
I intended to exhaust it, and might mislead the
reader, since, as I have said, such is not my purpose.
But it will, I think, add to the clearness of what I
have to say, to divide my Considerations into three
chapters ; of which, the^r*^ will refer to the matter
taught, and mainly to the question of what may be
termed Practical and Speculative Teaching: — ^the


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i&emd chapter will have reference to the manner of
teaching, and to the relative value of the Direct and
Indirect Methods of instruction i—'-the third chapter
¥rill treat of that superintendence and control, besides
the mere teaching of the understanding, whi<^, under
the name of Discipline^ has hitherto been considered
a part of the office of English Universities. On all
these subjects I trust I shall be able to point out
certain large and weighty alternatives of principle,
between which, in all our Universities, old or new,
we must necessarily choose ; and I hope I shall be able
to give satisfactory reasons in favour of that choice
which I venture to recommend. I now proceed to
my task.

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Chapter I.

Sect. 1. — Of the Distinction of Practical and
Speculative Teaching.

There are two modes of teaching, which, in a general
view, may be broadly distinguished from each other.
In the one mode the lecturer expounds to his audience
the doctrines or results of some branch of knowledge,
the speculations of antecedent philosophers, or his
own, while the office of the audience is only to attend
to him, to listen, to receive, think on, and treasure up
what the speaker delivers, without being called upon
themselves to take any active part; without being
required to produce, to test, or to apply the know-
ledge thus acquired. In another mode of teaching,
the learner has not merely to listen, but to do some-
thing himself; not merely to receive, but to produce
his knowledge : — as when the mathematical student
proves the proposition which is enunciated by his
teacher, or solves a problem proposed to him;— or
when the classical scholar renders Horace or Thucy*
dides into English. The former I call speculative^ the
latter, prcKtical teaching. And I must beg the reader
to recollect the manner in which I use these terms ;

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namely, with reference to the mode of teaching, not the
possible application of the subject taught. It is because
geometry is taught thus practicaUy^ and not because
it is what is commonly called " practical knowledge,''
that I designate the cultivation of geometry, in the
manner which prevails in English Universities, as
Practical Teaching. In their marked forms, these
two kinds of teaching are very clearly distinguished.
Lectures uncombined with any questions or practical
demands on the learner, are familiar to us in our
own Universities, in those of foreign lands, in the
metropolis, and in the provinces ; as modes of treating
of physics and metaphysics, geology and political
economy, taste and politics. All such lectures I speak
of as speculative teaching, since they are employed in
delivering to the hearer the doctrine adopted by the
teacher, in a speculative form. Practical teaching,
where the scholar, with voice, pen, or pencil, follows
the track pointed out to him, and is constantly brought
back into it when he deviates, are still more familiar ;
for by this method we learn everything that, in the
most peculiar sense, we learn at all. It is by such a
process that we become able to read, to write, to cast
accounts, to translate Latin and Greek, to speak
French and German, to solve equations, to obtain our
own results in the highest branches of mathematics.
The teaching of mothers and fathers, of schools, and a
great part of the teaching of our English Universities)
has hitherto been of this practical kind.

Now we may observe, that when we come to such
branches of literature and science as are likely to be

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selected for the matter of University teaching, some of
these branches naturally and almost inevitably require
to be taught practically, while others as clearly are
more fitted for the speculative mode of teaching.
Languages and mathematics are of the former kind ;
but many of the sciences, and those especially which
are wide and varied in their topics, which involve
doubtful or newly-established principles, of which the
foundations are constantly undergoing changes, can
hardly be taught otherwise than speculatively. Such
subjects are, for example, geology, political economy,
and, as appears to me, metaphysics. In such subjects
as these, the student may listen, and may acquire such
knowledge as the teacher possesses ; but he is not, and
cannot be called upon, as a part of the teaching, to do
something which depends on the knowledge thus
acquired. He may follow with the clearest appre-
hension, and it may be, with full and well-founded
conviction, the views which are presented to him by
the teacher ; but still he is passive only ; he is a spec-
tator, not an actor, in the intelleotual scene. He does
not interpret and employ a peculiar acquired language,
as he does in his classical reading, or his algebraical

What I have called practical teaching prevails in
the Colleges of our English Univerisities. A large
portion of the teaching, in those institutions, has
always consisted, as it still does, of exercises, in which
the pupil translates his Greek or Latin author, proves
hifi proposition, or solves his equation, in the hearing
or under the eye of his tutor ; or answers interroga-

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toriee, in which he has to produce the knowledge which
he has acquired. I believe this to have been the
mode (^ teaching employed among us from the earliest
times. In that Ck>llege, at least, of which I know
most, such a method is enjoined in the statutes.
Disputations are to be constantly held in the chapel ;
verses written and affixed in the hall ; and the lec-
turers are to employ half an hour in expounding their
author, but a whole hour in examining their class**
But besides these practical lectures, we have always
had lectures of the speculative kind, delivered by the
University professors. Such lectures on history,
morals, political economy, law, medicine, anatomy,
geology, botany, mineralogy, chemistry, the mechanical
sciences, and other subjects, have constantly been going
on in our Universities; and have, especially of late
years, often excited very great attention. We may,
therefore, distinguish our practical and speculative
teaching, as college lectures and profe$$orial lectures ; —
and such a distinction corresponds to the phraseology
commonly in use among us.

It may be said, that with professorial lectures exa-
minations may be combined, and that such lectures
may thus be converted into practical teaching. Nor
do I intend to deny that, under certain conditions,
which I shall afterwards endeavour to determine, this
effect may be produced. But without now entering

* Lectomin singuli horam in dies singulos quibus legere
tenentur in classe suit examlnandft consumant; dimidiatam vero
in authore interpretando. 5/a/. Trin. Coll, Cant, cap, 9^^, De
Lectorum Officio.

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into this subject, I trust that the main features of the
distinction, which I am trying to point out, of the two
kinds of teaching, are already sufficiently clear.

Now it must be observed that, though all branches
of science and speculation, old and new, fixed and
moveable, may be made the subjects of exposition in
lectures, practical teaching is applicable only to a
limited range of subjects ; — ^those, namely, in which
principles having clear evidence and stable certainty,
form the basis of our knowledge ; and in which, conse-
quently, a distinct possession of the fundamental ideas
enables a student to proceed to their applications, and
to acquire the habit of applying them in every case
with ease and rapidity. The idea of space, of number,
of the general relations of grammar and the force of
language, are necessary and immutable parts of the
furniture of the human mind. And mathematics and
languages, which are the developement and working
of these ideas, can be practically taught, for we can
appeal to these ideas, and familiarize the mind with a
series of vast and varied, yet certain consequences, to
which they lead. But when we come to the wider
j^ysieal sciences, we can only present the facts as a
matter of observation, and the speculation as dependent
on the facts. Here there is no room for acquiring
habits of interpretation which can be tested by the
teacher. And in sciences which are not physical, as
morals or metaphysics, the philosophy of history, or
of taste, the instruction is still more inevitably of the
speculative kind. The teacher must be content to
tell, and the learner to receive, what has been thought,


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or ought to be thought, on these subjects. He does
not, hj learning them, acquire a new faculty, which
he must practically exercise. Such subjects as I have
just described, may, perhaps, without impropriety, be
distinguished by the collective title of " philosophy ; ''
and if this be allowed, it will, I think, appear, that
philosophy is only fitted for speculative, as mathemoHcal
and classical studies are for practical, teaching. In
saying this, I do not at all profess to know, whether
I am employing the term '^ philosophy,^^ in the sense
attached to it by other persons, who may have written
on the subject ; but it may, I think, designate ap-
propriately a large class of studies, all of which admit
of the same mode of communication to the student.

In such studies, moreover, even if examinations be
added to lectures, they can hardly constitute a prac-
tical teaching ; for in such instances, the knowledge
which lectures convey, is either merely retained in
the memory, or is employed as material for further
speculation by the student, and is not assimilated and
converted into a practical habit of intellectual action.
Examinations, therefore, in these cases, may test the
goodness of the menM>ry, and the clearness of the appre-
hension or general faculties ; and we may also conceive
examinations of a higher kind, that call out the powers
of original thought, and detect the activity of talent
and genius. But the trial of mere memory and clear-
headedness is not practical teaching, in the same sense
as the acquisition of a power of interpretation or calcu-
lation; and the higher kind of examination which we
have mentioned, presupposes that practical teaching of

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which we here speak, and is not to be confounded
with it. And thus, even with the addition of exami-
nations on subjects of general philosophy, there
will still remain, between those studies and the
mathematical and classical pursuits of the English
Universities, that difference which I describe by
calling the former speculative teaching*

Thus the distinction of speculative and practical
instruction, which at first sight appears to be a
difference of the manner of teaching, is found, on
examination, to imply a difference of the subjects
taught. When we have determined that we will
teach practically, we have decided that we must
lecture, not on philosophy, not on metaphysics or
speculative morals, or political economy, but on
subjects of a different kind ; — on the works of Greek
and Latin authors; — ^the properties of space and
number ; — ^the laws of motion and force.

Of course, I mean only, that so far as we teach
practically, we must select such subjects. Nothing
prevents us, and as I have said, we have not been
prevented, from giving, in addition to our college
courses, professorial lectures on all the other subjects
which I have mentioned. But it is not on that
account the less important to my purpose, to keep
the consideration of the two kinds of study distinct.
It is obvious also, that, in many cases, the same
subject admits of being dealt with in both ways. We
may not only ascertain that our pupils can translate
Sophocles, but we may present to them the widest
speculative views at which critics have arrived,

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respecting the history and structure of the Greek
language, or the Greek drama. We may enter into
discussions respecting the metaphysical grounds of the
axioms of geometry, the processes of algebra, the
laws of motion. Such speculations and discussions
are of the hi^est interest and value ; but it is easy
to see that they are something in addition to the
teaching of Greek and mathematics. They add im-
mensely to the value of the practical acquisition of
language and mathematical habits, but they presiq)pose
the acquisition ; and when these philosophical views
are substituted for the practical instruction, they are
altogether empty and valueless as means of education.
But I do not here insist upon this point. In the
present section, my object was to distinguish the two
systems, before I compared them. Trusting that the dis-
tinction is now suflSciently clear, I proceed to the com-
parison. And this I shall consider with reference to
such points as these : — ^the effect on the intellectual
and on the moral character of those who are educated,
and on the general progress of national culture and

Sect, 2. — Op the Effect of Practical Teaching
ON THE Intellectual Habits.

The advantages which belong to the study of
mathematics, as an intellectual discipline, have been
often stated ,by various perscms. I may repeat
language which I have already used : — " In mathe-
matics, the student is rendered familiar with the

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most perfect examples of strict inference ; c<mipelled
habituidly to fix his attention on those conditions on
which the cogency of the demonstration depends;
and, in the mistaken or imperfect attempts at
demonstration made hj himself or others, he is
presented with examples of the most natural fallacies,
which he sees exposed and corrected/^ My Edin-
burgh reviewer* expressed a wish, that these latter
^' novel assertions had been explained and exemplified f''
and obviously, was really at a loss to understand them,
although they refer to the daily occurrences of the
lecture-room. This is a curious proof how entirely
practical teaching is lost sight of, amid the speculations
of his school. I may observe, too, as I have done
elsewhere f, that reasoning, as a practical habit, is
taught with peculiar advantage by mathematics,
because we are, in that study, concerned with long
chains of reasoning, in which each link hangs from
all the preceding. ^^The language contains a con-
stant succession of short and rapid references to what
has been proved already ; and it is justly assumed,
that each of these brief movements helps the reasoner
forwards in a course of infallible certainty and
security. Each of these hasty glances must possess
the clearness of intuitive evidence, and the certainty

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Online LibraryWilliam WhewellOn the principles of English university education; → online text (page 1 of 13)