GB2296596A

GB2296596A - Arithmetic teaching aid

Info

Publication number: GB2296596A
Application number: GB9526400A
Authority: GB
Inventors: David Benjamin Barker; Joanne Stagg; Bevan Davies; Rebecca Lago; Shama Choudry
Original assignee: Individual
Current assignee: Individual
Priority date: 1994-12-23
Filing date: 1995-12-22
Publication date: 1996-07-03
Anticipated expiration: 2015-12-22
Also published as: GB9426184D0; GB2296596B; GB9526400D0

Abstract

An arithmetic teaching aid is described, with a units display and a tens display, the units display having an auxiliary ("carry") display of the points; preferably there is a hundreds column also. There is further a transfer button to replace ten points in the units display by one point in the tens display, or vice versa, and similarly for tens and hundreds. The teaching aid can be used to teach the concept of carrying a number in addition or subtraction. The teaching aid can be used to teach arithmetic in a number of different base-valve number systems. <IMAGE>

Description

Arithmetic Teaching aid Children between the age cf 5 and 13 often experience difficulty in carry; a number when being taught to aid and subtract. The transition from adding or substracting in units to such Operations in tens and units is frequently traumatic and a variety of methods have been adapted over the years to cope with these learning difficulties. The problem seems to centre around the transition from thought to paper exercise.

What is needed is a device which will make concrete the concept of carrying tens to the units column and vice versa.

According to the invention triera is provided a teaching aid for arithmetic to base n, comprising a housing, a display for units, a display for the first power of n and means for performing arithmetic operations on the ns and/or units, the ns display and the units display each including a main set of at least n-l display points, in whi=h at least the units display also includes an auxiliary set of n points, and transfer means are provided for repiacing one point in the ns display by n points in the units display, andcr vice versa.

This device enables the pupil to visualise what is happening when the "carrying" operation is performed for the purpose of subtractlon: the use of an auxiliary or shadow display for the units, which is preferably placed clcsci alongsIde the main units display and spaced fro the ns display, shows clearly the equivalence of a single point in the ns display and n points in the units display.

In the sirnplest case there are displays only for units and the first power of n; however, for practical purposes a display and transfer means at least for the seccnd power of n would be useful. The lower powers of n wouid all have an auxiliary set of points, while the highest power needs only t:.e main set.

The displays could be mechanical but are preferably formed by rows or columns of lights such as LEDs; in ore advantageous form the main column is brighter ci of a stronger cclour than the shadow column. The means for performing arithmetic operations can consist, externally at least, of simple keys for raising and lowering the contents of the units and ns displays, and keys for performing the transfer operation fro the ns column to the units column; the transfer keys can also be used to transfer n points in the units column to one point in the ns column when addition is performed.

Of course the device will b used many for demonstrating arithmetic in base ten, but it is conceivable that a device could be made to another base or, preferably, to a base which can be varied by the user; the columns might te have sixteen points, perhaps with a cover for obscuring the upper part of the columns when working to a base lower than sixteen.

To illustrate the invention a specific example will n be described. referring to the attached drawing which shows the display face of one type of teaching aid in accordance with the invention The teaching and consists of an easily portable plastic vacuum-formes case approximately A4 landscape in area anc 50 millimetres thick. The device is operated by a series of push-to-make switches and 50 display points in the form of LEDs which are small bright lights, in five columns of ten to rate the numbers being counted. The device is powered by battery, is very light and contains a series of counter circuits which control the number of lights displayed in response to the pressing of the switches.

For each of the lower two number columns (tens and units) there are two parallel display columns of LEDs; the units are in red and the tens green. Each of these sections has a main working column and a shadow or carry column which does not light up quite so brightly.

Nevertheless, it is generally the same colour. The two columns of a pair are close together and the twd Fairs spaced relatively far from each other. The top column, for the hurdreds, Is yellow and there is no shadow column. There are ten display points in the main columns as weli as the shadow columns, though for normal numerical purposes only nine wculd be needed in the former.

The device is operated by pressing keys. These are of two kinds: counting or data-entry keys and transfer keys. for example, tc carry out 16 minus 9 first illuminate one LED in the (main) tens cclumn and six LEDs ir the (man) units section. To carry out the substraction use will have to be made of the fact that one in the tens column actually means 10 units.

Pressing t.e transfer button demonstras this equivalence, and the students will be able to watch as the number can be switched eah way. Thus the one in the tens column is transferred by means of one push-to- make transfer switch which immediately illuminates ten LEDs in the shadow area of the units column and extinguishes one LED in the tens column. Thus the student car. now deduct the 4 from the 16 LEDs illuminated in the units area and is left with 7 illuminated LEDs.

In order to calculate 9 plus 16, 1 and 6 are entered in the tens and units columns, Then the units 'count up' button is pressed to count up to +1+2+3+4.

At this point the column becomes full and ten units must be tr.nsferred to the tens column. The device may emit an auclible signal to indicate this. Once the transfer is performed, the student must remember that there are still 5 more counts to go before the ful l9 have been counted. Thus a further count cf 1+2+3+4+5 gives a totai rending of 2 tens and 5 units, i.e. 25.

the required answer. For addition the shadow column is not needed.

In an example using the hundreds column, the number 174 is entered in the three main columns using the count keys. 97 is to be subtracted from this, starting i the units column. Since 7 cannot be substracted from 4 the "minus" transfer button "tens to units" is pressed, the ten LEDs in the units carry column are then illuminated, and 7 units caT be deducted. Meanwhile the tens digit is reduced by 1.

The tens substraction is then carried out, and similarly @ cannot be subtracted from. 6; the student therefore presses the "hundreds to tens" transfer button, whereupon the 1 disappears from the hundreds column and the ten LEDS in the tens carry column light up. The final subtraction cf 9 from 16 can then be done using the count button, giving the answer 77. The student is encouraged to follow these operations on paper whilE. sing the teaching aid.

In the example shown there are two transfer buttons representing the transfer means, but a single button could be used which recognises which way a transfer is possible and carries it out. It would in principle .e possible to do away with a transfer button altogether and have the apparatus carry out the transfer or carry operation automatically as required, though this 1 rduce the didactic benetit. There might be some value in a device whose transfer means worked only one way, say from units to tens (for addition) or tens to units (for substraction@.

Although the indicator lights are most naturally arranged in columns this i3 not strictly necessary.

Nor need the transfer to the units columns be only to the auxiliary or shadow column: as an alternative the main column might be filled up first. The Internal electronics can be arranged to recognise when the moin units column is empty and then to fill it with the units from the shadow column.

Claims

claims

1. A teaching aid for arithmetic to base n, comprising a housing, a display for units a display for the first power of n and means for performing arithmetic operations on the ns and/or units, the ns display and the units display each including a main set of at least n-1 display points, in which at least the units display also includes an auxiliary set of n points7 and transfer means are provided fcr rerlacing one point in the ns display by n points in the units dIsplay, and/or vice versa.

2. A teaching aid according to claim 1, in which the n points In the units display are the auxiliary set of points.

3. A teaching aid according to claim 1 or 2 and further comprising a display cf the second power of n, including a main set of n-1 display points, the ns display further comprising an auxiliary set of n paints.

4. A teaching aid according to claim 3 further comprising a display of at least one higher power of n, including a main set of n-1 display points, in which each display of a power of n except the highest comprises an auxiliary set of n points.

5. A teaching aid according to any preceding claim, which the displays are formed of rows or columns of lights.

6 A teaciling aid according to claim 5, in which the lights are LEDs.

7. A teaching aid according to claim 5 or 6, in which the lights of the main columns are different to those of tbe auxiliary column or columns.

8. A teaching aid according to claim. 7, in which the lights of the main columns are brighter than those of the auxiliary column or columns but of the same colour.

9. A teaching aid according to any preceding flair, further comprising keys for lowering and rising the contents of each maIn display.

10. A teaching aid according to any preceding claim, in which the bse n is 10.

11. A teaching aid acccrding to any preceding claim, in which the transfer means comprises two keys, for transfer respectively from the units to the ns display and vice versa.

12. A teaching aid substantially as described herein before with reference to the accompanying drawing.