★ Keep up to date with the latest news  subscribe to the Transcribe Bentham newsletter; Find a new page to transcribe in our list of Untranscribed Manuscripts
1830: For Posolgy
Quere whence received? From MacLaren?
Process of Teaching Arithmetic & Algebra to Children.
Stage. I.
(For Young Children)
The four first rules of
Arithmetic performed
on numbers under ten:
1. with actual and
familiar objects, as
stones, conters & c.
2. with the Swan pan
or arithmetical toy;
& with marks on slate
as III, or , or ooo.
3. Without objects, —
abstract questions being
asked, as How many
legs have two chairs?
How many are two and
three?
4. With Arabic
numerals, the sum or
product not to exceed
ten: the nature of
Multiplication and
Division partly
explained, and the
convenience of the
signs +  × ÷, and
of the names sum,
difference, product &c.
gradually insinuated.
Stage II.
Numeration and first
four simple rules.
By Numeration we add
units, one by one, and
name them. The names
of numbers beyond ten
should be taught, and
the meaning of the
name explained; as,
thirteen means threeten
or three and ten: twenty
means twainten or twice
ten: hundred means
tenty or ten tens &c..
The reason for building
up names of numbers in
this manner instead of
giving a perfectly distinct
name to each; and instead
of repeating the word "one"
for each unit which a
number contains &c. &c.
should be discovered by the
pupil. He should also
invent marks for numbers
First: dots or strokes .... or III
each
Stage II continued.
each representing a
unit; next size may
distinguish units as
for 1
for 2
or 4
or 10 &c.
for 4
or 10
or 20
or 100 &c.
or 3 circles of increasing size
colors may represent
numbers — as white for 1
blue for 2 or 5 or 10 &c.
a separate simple mark
for each number may
be tried: also the Roman
numeration II I or C &c.
& then position in
columns as 100s
—
Tens
—
Units
—
& with these columns
any of the above marks
may be used. The separating
lines may then
be dispensed with, and
the ordinary mode adopted.
Exercises on the different
scales, as, the five scale,
the three scale, as well
as the ten scale should
follow. the descending
scale, or decimals, will
then be clear as
│tens │units ││tenths │hundredths│
& the same with other scales
as:
twenty │fives │units ││fifths│twenty
fives │fifths
Addition.
The pupil should first
add numbers in his own
way, & discover the difficulty
of adding large numbers
at once; then discover that
by adding the corresponding
parts of large numbers
the difficulty will vanish.
A little assistance from,
and leading questions
by, the tutor will suffice.
By Addition (which is
compendious Numeration)
we add clusters of units
together, having previously
learnt the number to which
they are equivalent.
Addition by Roman & Grecian
method, & by various scales
also shewn.
Multiplication is abridged
Addition. The different
modes of it to be found by
experiment, & the best
retained.
Subtraction & Division
being the reverse of Addition
& Multiplication, present
no new difficulties.
Stage III.
The pupil should again go
over the same ground;
addition, and variations
being made, and the
first four rules in
Decimal Fractions
being included.
Compound Addition
Subtraction, Multiplication
and Division
will now be discovered
by the pupil without
much difficulty.
Vulgar Fractions and
Proportion may be
next found out, if
questions be proposed
for solution, of proper
form, and of gradually
encreasing difficulty.
Stage IV.
The previous ground again
gone over. The numeration
of different nations expounded,
and defects & advantages
pointed out. Examples of
the notation of music &
other sciences given.
Algebra commenced.
Arithmetical & Algebraical
rules done at the same time
that both may be compared.
A variety of modes of
Algebraical notation shewn
or invented. The Metaphysics
of Mathematics or what
it has in common with
other sciences, and peculiar
to itself unfolded; and
it's value and station
among Sciences shewn.
Striking cases, and cases
that frequently occur, of
their use & abuse, shewn.
A learner so taught
would, if he proceeded,
improve his science.
This stage is within
the powers of a boy of
12 years of age. After
every stage an interval
should intervene.
With some pupils a
stage must be gone
through several times.
If the above plan were
worked out and taught
by a competent person
it is thought that less
of the pupil's time would
be required than is at
present occupied at
School in Arithmetic.
Identifier:  JB/135/090/002 "JB/" can not be assigned to a declared number type with value 135.



1830 

135 
posology 

090 
for posology 

002 
stage i / stage ii 

collectanea 
2 

recto 

j whatman 1821 

admiral pavel chichagov 

1821 

"quere whence received? from maclure?" 
46208 
