Improved Set of Apparatus for Teaching the First Steps in Arithmetic.
Year: 1893

page_text: Date of Application, 18th July, 1893-Accepted, 28th Oct., 1893
UUMI LEID
Improved Set of Apparatus for Teaching the First Steps in
Arithmetic.
I, HENRY FINCH RIX, of No. 32 Great Davis Street South Yarra, near
Melbourne in the Colony of Victoria, Inspector of Schools, do hereby declare the
nature of this invention and in what manner the same is to be performed to be
particularly described and ascertained in and by the following statement:-
This invention has been designed for the purpose of providing a set of apparatus
whereby the first steps in arithmetic may be taught to children by the concrete
method more rationally and with greater facility than hitherto.
According to this invention, I employ a number of objects, separated from each
other by a narrow space so as to make counting easy, and divide them into pairs of
fives by wider spaces, because, five and ten being the natural number groups, this
arrangement by forming number pictures will enable the number of the objects to
be recognised by the children at a glance, and so obviate the necessity of counting
these objects at each step.
I also use on some parts of the apparatus reversible discs and pegs, coloured
differently on opposite sides and ends respectively, so that it may be readily shown
what pairs of numbers make up the number pictures formed by the groups of these
objects, and in other parts of the said apparatus the same numerical facts are
illustrated by contrivances which admit of the balls forming the separate number
groups being rapidly thrown together so as to form recognisable number pictures.
I employ different contrivances or devices for demonstrating the same facts in
order that the children may unconsciously learn to abstract ideas of number from
the objects numbered, that is, to generalise from different representations of the
same numerical fact.
The apparatus comprises a frame upon which the various devices above referred
to may be conveniently supported and shown.
On top of this frame in front is what I term the "notator," that is, a set of
shelves formed with two compartments on the right, one above the other and each
adapted to contain five pegs. There are also two compartments in the centre, each
of which is adapted to contain five groups, each consisting of ten pegs in one
piece symmetrically arranged in two rows of five each, and there are also two
compartments on the left, each adapted to contain five groups each made up of ten
tens in one piece, arranged symmetrically in two rows of five each. I also provide
ten separate pegs adapted to be bound together in one group, and I also provide a
group of one hundred consisting of ten separate tens similarly bound together, in
order that the rule of subtraction may be demonstrated, for which purpose
provide a shelf on top of the notator in order to place the number of pegs which
may have to be borrowed from the tens or hundreds compartment, as the case
may be.
I
Below this "notator" is what is termed a "ball frame" which, according to my
invention, is formed with ten wires, each of which is fitted with ten balls, separated
from each other and divided into groups of five, as above described.
single wire
Upon one side of the frame are supported what I term a
calculator" and a "double wire calculator," the former consisting merely of a wire
bent at right angles so as to project from the side of the apparatus, and adapted to
carry twenty balls (separated into groups of five) of similar construction to the
ones used on the ball frame, whilst the double wire calculator is formed of two
wires bent in a similar manner and each carrying ten similar balls also divided into
groups of five.
Underneath the ball frame I also provide two other calculators, one called the

page_text: $6 peg calculator
formed of a board provided with two rows of ten holes divided
by wider spaces into groups of five, and adapted to receive pegs having their ends
painted two different colours, whilst the other is called a "disc calculator" and is
provided with pins similarly arranged to the holes in the peg calculator, and
adapted to support discs of leather or other material having holes in the centre and
their opposite sides coloured differently.
Below this again is arranged what I term a "subtractor" consisting of a wooden
frame across which are arranged two pairs of parallel wires, the front of each of
which pairs carries ten counters, which are separated from each other as well as
from the frame, and are also divided into groups of five, and are so constructed that
they can be turned over forwards so as to display a different colour to either of the
front colours.
At the back of the apparatus is what I term a table board" for tabulating the
results that have been demonstrated step by step with the various calculators above
referred to. It consists of a rectangular board studded with parallel rows of pins
adapted to support similar discs to those used in the disc calculator, so that by
using the different colours of the discs, and by arranging them to form number
pictures any of the addition or subtraction tables may be presented in concrete
form.
I have devised very simple and efficient contrivances for securing the different
apparatus upon the supporting frame, as will be well understood on reference to the
accompanying drawings, wherein
Figure 1 is a front elevation and
Figure 2 a rear elevation of my improved set of apparatus for teaching the first
steps in arithmetic.
Figure 3 a front elevation, and
Figure 4 a side elevation of the frame upon which the various contrivances
constituting such set of apparatus can be supported.
Figures 5 to 26 are various detail views illustrating such contrivances removed
from the frame.
The same letters of reference indicate the same parts in all the figures.
A represents the frame upon which the various contrivances above described are
supported, and B (Figures 1 and 5) represents the "notator" having two com-
partments 6-6 on the right, one above the other; two 62-63 in the centre and two
larger compartments 6 6 on the left. Above the compartments 6-6 are other
small ones in which to place the objects borrowed from the tens or hundreds
compartments. The two compartments b-b' are adapted each to contain five pegs,
made as illustrated in Figure 8, and the compartments 62-63 are adapted each to
contain five groups of ten pegs, cach group being in one piece, as illustrated in
Figures 1 and 7, except one group which consists of ten separate pegs bound
together by an elastic band or otherwise, whilst the other two compartments 6-1,
are adapted each to contain five groups of ten tens, each of such groups being made
in one piece (as illustrated in Figures 1 and 6) except one of them, which is by
preference built up of ten of the tens groups secured together by an elastic band
or otherwise (as illustrated in Figure 9).
The manner of employing this part of the apparatus will be well understood by
those who have had experience in teaching children by concrete methods, it being
merely necessary to place a certain number of pegs in the hundreds, tens or units
compartments and then to remove any given number, when the remainder can be
seen and counted or read off by the children without difficulty.
C represents the "ball frame" above referred to, which is according to my
invention, formed with ten wires c arranged parallel to each other and extending
across from side to side of said frame. Upon each of these wires is arranged two
groups of five balls c¹, said balls being made (as illustrated in Figure 11) with
projections on each side to keep them separate from each other so as to admit of
their being readily counted or read off. Each group of five is kept distinct
from the other group by a piece of small tube c² placed, as shown in Figure 1,

page_text: between such groups, and the balls e¹ are also kept away from the sides of the
frame C by other short lengths of tube c³ in order to admit of the objects being
accurately counted from the sides of the apparatus, as well as straight in frout, and
further, the upper five wires are separated from the lower five wires by a
wider space.
D represents the "single wire calculator" and E the "double wire calculator,"
which are secured upon the side of the frame A and project outwardly therefrom
(as illustrated in Figures 1 and 2). The first mentioned is formed of a wire d bent
outwardly at right angles, as illustrated at d', and having a loop bent upwardly at
its lower end and adapted to fit into a groove or over a projection d³, formed on a
bracket or block of wood projecting from the sides of the frame A, such groove or
projection being made around said block of wood (as illustrated in Figure 22) and
said loop upon the lower end of the wire d being made as illustrated in Figure 21.
Upon the "single wire calculator" D, I arrange four groups of five balls each,
as shown in Figure 1, spaces being left between each group and a larger one in the
centre to separate the two tens from each other in order to facilitate counting and
reading off, the balls also having projections at their sides to keep them distinct
from one another.
The "double wire calculator" E, as its name implies, is made of a double wire
or wire bent back upon itself (as illustrated in Figures 1 and 23) so as to form a
double support for two rows of the balls, each row consisting of two groups of five
(as shown in Figure 1). If preferred, this bent wire can be secured to the frame A
by means of a button é (as illustrated in Figure 1) in which case it is fitted over a
projection e¹, upon a wooden block or bracket (as illustrated in Figure 24). The
spaces between the groups in both the single and double wire calculators are kept
by short lengths of tube as in the ball frame (c2). In both of these calculators the
numbers can be shown apart and can then rapidly be thrown together, so as to
make a number picture representing the number of the whole of the balls, and as
only the balls required for each step to be demonstrated are placed upon the
horizontal parts of the wires, the attention of the children will be concentrated
upon them, and will not be drawn off by the objects not in use.
Below the ball frame" C is a peg calculator" consisting of a board F
drilled with two rows of ten holes (as shown in Figures 1 and 13) such rows being
separated into two fives by wider spaces. Pegs f having their two ends painted in
different colours (as indicated in Figure 14) are inserted in these holes.
By this means any required number of pegs may be inserted in the holes with the
same colour showing in all of them so as to make a number picture, and then one
or more of the pegs can be reversed, and thus the different pairs of numbers
making up the sum total of the original number of pegs can be shown.
The "disc calculator" (illustrated in Figure 16) is for the same purpose, but the
object is effected by means of discs coloured differently at the two sides and
adapted to be supported on pins g' projecting from the board G and arranged in
the same way as the holes in the peg calculator. With this contrivance also the
composition and analysis of numbers can be shown in the same way as in the peg
calculator.
H represents the "subtractor" above referred to, consisting of a rectangular
frame h having two pairs of wires h², extending across it from end to end, the
wires in each pair being parallel to each other.
Ten counters in groups of five are supported upon the front bars h³ and are
separated from each other by short lengths of tubing (as illustrated in Figures 1
and 17). Each group is coloured differently to the adjacent one, and each counter
can be turned down forwards so as to show a third colour on the side which will
then be presented to view. By arranging the counters so as to form a number
picture, and then turning down some of them, the number subtracted as well as the
number left, and the original number of objects are all seen at the same time, and
thus the children are impressed with the fundamental operation of subtraction.

page_text: "
I represents the "table board for tabulating the results that have been
demonstrated step by step with the calculators above described. It consists merely
of a board studded with parallel rows of pins i adapted to support discs of similar
construction to those above described (as shown in Figure 15) and are also
coloured differently at the two sides so as with the help of number pictures to
present any of the addition or subtraction tables in concrete form. Between the
pins are formed perforations in which separators consisting of pieces of wire
bent as illustrated in Figure 25 can be placed so as to divide into two groups any
number of discs of one colour so arranged as to form a number picture and thus
show concretely any step of the above-mentioned tables.
This table board I is secured upon the frame A by resting it in a bracket and
securing its upper edge by means of a sliding bolt 3, or if preferred it can be placed
as indicated by dotted lines in Figure 2 by resting it upon the two brackets &
instead of upon the lower one 3. The frames C and of the ball frame and
subtraction frame are conveniently secured each upon the main frame A of the
apparatus by means of bolts arranged as shown in Figures 1 and 3.
Having now particularly described and ascertained the nature of my said
invention and in what manner the same is to be performed I declare that what I
claim is :-
First. The herein described set of apparatus for teaching the first steps in
arithmetic consisting of the various parts constructed arranged and operating
substantially as and for the purposes herein described and explained and as
illustrated in the accompanying drawings.
Second. In a set of apparatus for teaching the first steps in arithmetic, a notator
consisting of shelves divided into two rows of compartments for containing the
units, tens and hundreds to be arranged in groups not exceeding five, substantially
as and for the purposes herein described and explained and as illustrated in the
accompanying drawings.
Third. In a set of apparatus for teaching the first steps in arithmetic, a set of
blocks formed in groups of hundreds, tens and units, the former being divided into
ten distinct groups of ten each 'in two rows of five each, by means of thick and thin
lines, the whole being constructed and arranged substantially as and for the
purposes herein described and explained and as illustrated in the accompanying
drawings.
Fourth. In a set of apparatus for teaching the first steps in arithmetic, a ball
frame wherein the balls are arranged in rows of ten each upon two sets of five
wires each said balls being divided into groups of five and separated from the frame
by means of distance pieces ensuring a space being left between them, whilst the
upper five rows are divided from the lower five by a wider space, and the balls are
kept distinct from each other by projections on each side, the whole being
constructed and arranged substantially as and for the purposes herein described and
explained and as illustrated in the accompanying drawings.
Fifth. In a set of apparatus for teaching the first steps in arithmetic, a single
wire calculator projecting from the side of the main frame, and fitted with twenty
balls divided into groups of five and by a wider space into groups of ten, and kept
distinct from each other by projections at the sides, the whole being constructed
and arranged substantially as and for the purposes herein described and explained
and as illustrated in the accompanying drawings.
Sixth. In a set of apparatus for teaching the first steps of arithmetic, a double
wire calculator formed of two wires, each fitted with ten balls similar to those in
the single wire calculator, and similarly divided into groups of five, said wires being
arranged to project from the sides of the main frame, substantially as and for the
purposes herein described and explained and as illustrated in the accompanying
drawings.
Seventh. In a set of apparatus for teaching the first steps in arithmetic, the 5
means herein described for securing the single and double wire calculators to the

page_text: main frame consisting in forming a loop upon the lower end thereof and fitting it
over a projection or groove in a block or bracket (such as d³) and securing it by
means of a button or otherwise, substantially as and for the purposes herein
described and explained and as illustrated in the accompanying drawings.
Eighth. In a set of apparatus for teaching the first steps in arithmetic a peg or
disc calculator, the sides or ends of said pegs or discs being coloured differently,
and the holes or pins provided upon said calculator to receive pegs or discs being
arranged in rows of ten and groups of five each, substantially as and for the
purposes herein described and explained and as illustrated in the accompanying
drawings.
Ninth. In a set of apparatus for teaching the first steps in arithmetic, a
subtractor consisting of a series of counters in two rows of ten each coloured
differently in groups of five and separated from each other and also coloured
differently at the back, so that when turned over forwards they will expose the
third colour to view, said counters being supported upon one of a pair of wires and
retained in their raised or lowered positions by the other one, substantially as and
for the purposes herein described and explained and as illustrated in the
accompanying drawings.
Tenth. In a set of apparatus for teaching the first steps in arithmetic, a table
board fitted with rows of pegs to receive discs which may either be coloured
differently on opposite sides or may be separated into groups by other means, such
for instance as stop pieces formed of copper or other wire inserted in holes provided
for the purpose, the whole being constructed and arranged substantially as and for
the purposes herein described and explained and as illustrated in the accompanying
drawings.
Dated this Tenth day of June One thousand eight hundred and ninety-three.