An Improved Instrument or Device for Teaching Arithmetic.
Year: 1894

page_text: Date of Application, 26th June, 1894-Accepted, 12th Jan., 1895
COMPLETE SPECIFICATION.
An Improved Instrument or Device for Teaching Arithmetic.
I, FRIEDRICH Adolf Görtsch, of 31, Eckernförder Chaussee, Kiel, in the
German Empire, Schoolmaster, 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:-
The subject of this invention is an instrument or device for propounding
arithmetical problems, the purpose it is intended to serve being to place before
school children a more or less wide range or series of problems to be solved,
appertaining to all departments of elementary arithmetic, and to enable such
problems to be more diversified than they are in any of the existing books or
manuals, however rich and varied the collection of exercises they contain may be
deemed to be. It is not proposed, however, in introducing this improved instrument
or device to offer a substitute for the usual exercise book, no more than to replace
the customary method of propounding problems for solution orally and of
encouraging mental calculation.
This device is merely intended to place a series of problems at the disposal of
the master in certain cases and for a predetermined object; namely, where it is
desirable for him to be temporarily relieved from the necessity of propounding
problems by word of mouth, and where, owing to the greater number and variety
of the problems which, by the employment of this device, are brought under the
notice of his pupils in a given time, the lesson is likely to become no. e beneficial
to them.
The invention will be best understood by reference to the accompanying
drawings, in which
Figure 1 is a front view,
Figure 2 a section on linear, Fig. 1, and
Figures 3 to 13 detail views, partly in section, and partly in elevation.
A is a disc of cardboard, wood or any other suitable material, whereon the
improved calculating device is mounted.
This disc is provided in its centre with a pin or spindle a, on which two other
discs B and C are revolvably arranged. The two letter dises are of an unequal
radius and have a series of numbers inscribed both on their upper and lower surfaces.
The numbers appearing on the upper surface represent integers, while those on the
lower ince, serve to form fractions, either simple or compound. The disc B carries
a spring D on either side, and such spring, being guided by eyes formed of wire,
are capable of being slipped over the edge of the disc C with slight friction. The
object of this spring is to connect the two discs B and C in their various relative
positions. Over the discs B and C are placed two segment-shaped strips of
coloured cardboard, E E', capable of revolving upon the pin or spindle a, and
arranged to be guided by the ring G situated near their edges on the lower side,
which arrangement enables them to be moved as cl se together as may be necessary.
Each of the said cardboard strips E E' consists of two super-posed sheets, so connected
with each other as to leave openings corresponding to the circles of figures in
position. Into these openings or slots, are-shaped cardboard slips Cº C₁CC",
carrying the required numbers, are inserted to enable numbers of sums to be formed
having a 1 in the highest place and a 0 in the lowest place. The lower sheet of
each of the cardboard slips has extensions of projecting parts dd, intended to
cover over those numbers which, having no connection with the problem to be dealt
with, should not appear.

page_text: By means of a clamp or clasp H H', either the larger or the smaller disc may be
fastened to the cardboard strip while the other disc is turned by itself. Over the
cardboard strip E E there is placed an auxiliary disc 1.
It consists of two sheets
of cardboard, fastened one over the other in such a manner that there form slots or
apertures KK K' into which, according to the nature of the problem to be
propounded, a small sheet or slip may be inserted, bearing the corresponding sign
indicating addition, subtraction, multiplication or division. The auxiliary disc also
serves for fastening in position the slip bearing the comma or decimal stop (Fig. 13).
To prevent the dise from slipping off the pin or spindle a, they are retained in place
by a nut. The method of employment and operation of the improved arithmetical
device may be best illustrated by a few examples.
When it is desired to make use of the device it is first of all hung on to the usual
blackboard or a well lighted wall of the classroom, when it is set to suit the
particular kind of arithmetical problems which it is desired to present to the
children for solution. The disc is then set in rotary motion. When it is desired
to give elementary problems with single numbers only the cardboard strips E
and E' should be so adjusted that their inner edges coincide with the mark 1 on
the scale provided at the upper edge of the device. The children may then be
allowed to work out one problem after the other, the dise being in each case turned
from one figure to the next.
In the case of some problems it is necessary to turn only one of two dises B
and C, and to keep the other stationary. Supposing, for example, that it is desired
to practise the simple multiplication table with the number 7. Then the cardboard
strips are moved to the mark 1, and the disc C is turned in such a manner tha
there appears between the strips E and E the required Figure 7. The disc is now
fastened in position against E by means of the clasp !!', and the discs B and C are
disconnected by means of the spring D, whereupon 13 is set in rotary motion. The
mode of operation is much the same when a series of different numbers have to he
added in succession to any given number which is not to be varied—or to be
subtracted from such number.
When it is required to form problems with numbers consisting of more than a
figure ench, the cardboard strips E E are in the first place brought into coincidence
with the marks 2, and 4. In the last mentioned position, where there appear
numbers consisting of as many as four figures, it will in most cases be advisable to
terminate the operation of the device, at any rate in those cases where it is used to
set up problems for mental calculation.
The number of problems which this apparatus enables to be formed is unlimited;
ench revolution of either dise producing sixteen problems, which, by the repeated
displacement of the discs may be multiplied sixteenfold, or form sixteen times that
number of combinations, it follows that 16 x 16 = 256 arithmetical problems of
each class may be formed. A list of problems accompanying the device, to
acilitate its employment, though by no means exhaustive, should contain at least
1,500 series or groups of figures, by the aid of which it will be possible, by going
through all the different positions to which the device may be moved, to obtain an
aggregate number of 250 x 500 = 125,000 different problems, the whole of which
will be found all the more valuable in practice because they supply excellent
material for mental computation. As regards the auxiliary disc J, sufficient has
been said about to explain its function; but whether, or to what extent, the
signs +,
and should netually be used in practice, it will rest with the teacher
himself to decide. In many cases it will probably be deemed superfluous to use
any of these signs at all, as it is not customary, now, to write them.
however, there is any reason for preferring to make these signs appear in visible
shape, by means of the slips above referred to, these slips may be arranged to be
serviceable for other purposes as well as for exhibiting the signs in question. For
instance, in the case of sums such as these: 84, 65 the disc having the "plus"
+9+8
When,
slip attached to it may be turned to such a position, that the said slip comes to

page_text: cover over the tens of the lower number, whereby the necessity is avoided of using
an extra wide slip for this purpose.
Having w 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:-
1. A device or instrument for teaching arithmetic, consisting of discs such as B
and C. mounted concentrically upon a common pin or spindle and having series of
numbers inscribed on both their faces or sides: such discs being capable by means
of a spring D of being moved to, or adjusted in, a variety of positions in relation
to each other, according to the class of arithmetical problems it is desired to
propose for solution; the numbers used for cach problem being separable from the
remaining numbers of the discs by means of radial segment-shaped cardboard strips
such as Ed and E' d.
2. In combination with the number-carrying discs or dials (such as B and C), an
auxiliary disc, such as I, which when it is slipped on to the spindle a over the said
numbered discs or dials, serves for the reception of slips bearing signs such
as +, -, xor, or the decimal stop or comuma (Fig. 13).
Datel his wechla