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5 Intellectual Education only here treated of.
6 Not a complete scheme of Human Knowledge.
7 Permanent and Progressive Studies
8 Must unfold human faculties:
SECT. 2 Of Permanent Educational Studies
Art. 10 Human Faculties of Language and Reason.
11 Importance of Language.
12 Reflex attention to Language.
13 In Greek and Latin Literature.
SECT. 3 Of Progressive Educational Studies
Art. 19 Progressive Studies to be used in Education,
20 And modern Sciences.
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15
Art. 24 Ethnography and Geology.
25 Permanent Studies most essential.
SECT. 4 Of English Education
Art. 26 The above views applicable to it,
27 And to Cambridge.
28 Classical authors not to be superseded.
29 The authors themselves to be studied:
30 And Greek and Latin Grammar.
31 Geometry cannot be superseded.
32 Value of Geometry.
33 Arithmetic to be learnt.
34 Conic Sections.
35 Mechanics and Hydrostatics.
36 Newton's Principia.
37 Astronomy.
38 Optics.
39 The Higher Mathematics are Progressive Studies.
22
SECT. 5 Of Analytical Mathematics as an Educational Study 38
Art. 40 Meaning of Analysis.
41 Merits of Analysis.
42 Analysis compared with Geometry.
43 Is not an exercise of the Reason.
44 Does not exemplify the usual kind of reasoning.
45 Does not depend on the matter reasoned on.
46 Exemplified in Proportion.
47 In Trigonometry.
48 In Conic Sections.
49 In Statics.
50 In Dynamics.
51 In Astronomy.
52 Analysis not valuable in Education.
[52] As the Mathematical element.
53 Analysis evades difficulties.
54 Standard Geometrical Demonstrations to be used
55 With Questions,
56 And Problems.
57 Geometry necessary as introductory to Analysis.
58 Analysis ill understood disgusts students.
59 Faculties which Analysis cultivates.
60 Hence Analysis worthless as discipline.
Art. 61
Historical interest of Mathematics
62 Belongs to Geometry;
63 Is lost in Analysis.
64 Hence the educational value is lost.
65 Geometrical Mathematicians solve problems better.
66 Recapitulation.
Art. 67 Progressive Studies as well as Permanent Studies are necessary,
68 And Mathematical in particular.
69 List of such subjects.
70 Analysis here not objectionable:
71 But Analysis does not supersede Geometry.
72 Division of Mathematical writings.
73 Capital Works to be studied.
74 List of them restricted.
75 Original Investigations not to be required.
76 To be admitted in practical problems.
77 Systematic Treatises to be read.
78 Elementary Treatises.
79 Not to be rapidly changed.
80 To be selected by authority.
81 Not to supersede Geometry.
82 English and Foreign Mathematics.
83 The study of Newton not an evil.
84 Chance of a school of English Mathematicians.
85 We require Mathematics as an Education.
63
SECT. 7 Of Classical Educational Studies, Permanent and
Progressive
Art. 86 Necessity of Latin as a Permanent Study,
87 And of Greek.
88 Latin and Greek as Progressive Studies.
89 Progressive cannot supersede Permanent Studies.
90 Latin more necessary than Greek.
91 May translations supersede Latin and Greek?
92 Do Translations perplex Examinations?
93 Translations are valuable in Literature.
94 Capital works in Classical Literature.
95 Cannot be superseded by private teaching.
96 Writing Latin to be practised.
78
Art. 97
Latin long the language of literature,
98 As an accomplishment.
99 Writing Latin verse.
100 Writing Greek prose,
101 And Greek verse,
102 Not necessary for good scholarship. 103 Greek not to supersede Latin.
SECT. 8
Of the Value of Permanent Studies
Art. 104 Objections urged against Permanent Studies.
105 They do not narrow the mind,
106 On account of their excellence,
107 Though read with Commentators.
108 Are such like the Aristotelian Commentators?
109 The memory is to be used in cultivating the reason.
110 Schoolboy ridicule of cramming.
111
Common ridicule of technicalities.
112 Rules to be learnt before reasons.
113 Value of new methods of teaching.
114 Old methods to be respected.
115 Mathematics and Classics both necessary.
116 Have been united generally :
117 And naturally:
118 And usefully.
95
CHAPTER II.
OF THE METHOD OF TEACHING IN CLASSICS
AND MATHEMATICS.
SECT. 1 Of College Lectures and Professorial Lectures 110
Art. 119 First, of Classical Teaching.
120 Teaching at School.
121 College Lectures.
122 Their difference from Professorial Lectures.
123 Previous knowledge required.
124 Difference of students' capacity
125 Size of Classes.
126 Professorial Lectures necessary.
127 Their advantages and disadvantages.
SECT. 2 Of Mr Lyell's Remarks on the English Univer-
Art. 128
sities
They occur in his Travels in America.
129 Ascribed to me opinions opposite to what I have
expressed;
130 Pretending to seek my views.
131 Our College system agrees with Mr Lyell's Pro-
fessorial.
132 He does not condemn our peculiarities.
133 He condemns me for recommending respect.
134 What will Mr Lyell do with unwilling students?
Lectures will not secure attention.
135
136
137
Hence Examinations instituted.
Mr Lyell's confusion about a critical spirit.
138 Mode of teaching the Philosophy of Science.
139 How do men learn to think for themselves?
140 Progressive Sciences may be introduced at Cam-
bridge.
141 Is the College System new in our Universities?
142 It is as old as the Reformation.
143 It is established by the Statutes.
144 Is it desirable to have only a few College Tutors?
145 Present faults of the College System.
146 Mr Lyell's remedies not effective.
SECT. 3 Of Examinations
Art. 147 Examinations are means of teaching.
148 May be separated from Lectures.
149 But are then not a good Education.
150 Examinations and Lectures must agree.
151 College Examinations.
152 Difference of Examinations and Lectures may
occur.
153 Examinations will then govern all,
154 And Private Tutors will be sought.
155 Evil consequences of this,
156 Incurred in mere Paper Examinations:
157 And with changing Examiners.
158 These evils to be avoided.
159 A Standard course requisite.
160
Case when the Lecturers are the Examiners.
161 Cannot be general in the University.
162 Advantages of Oral Examinations.
117
. 132