GB2417602A

GB2417602A - Numeracy teaching aid for multiplying and dividing by ten

Info

Publication number: GB2417602A
Application number: GB0424454A
Authority: GB
Inventors: Tanya Eaton
Original assignee: De Montfort University
Current assignee: De Montfort University
Priority date: 2004-11-05
Filing date: 2004-11-05
Publication date: 2006-03-01
Anticipated expiration: 2024-11-05
Also published as: GB0424454D0; GB2417602B

Abstract

A teaching aid for the assisting in teaching of numeracy concepts comprises a display panel 1 with a plurality of windows 3a-3e therein, the panel displaying in fixed positions adjacent the windows labels 2a-2e bearing the terms "hundredths", "tenths", "units", "tens", "hundreds" etc., a support 4 for receiving a variable sequence of digits and displaying the digits through the windows, and means for moving the support laterally with respect to the display panel in two opposite directions, so that individual digits forming the sequence are displayed through different windows in the panel and therefore adjacent to different labels. The individual digits may be placed on a backing plate and releasably retained on the support, may be written directly on the support using a wipe-clean marker pen, or may be disposed on a backing plate receivable in a recess 7 on the support. The labels may be disposed on backing sheets which are removably securable to the display panel. A decimal point 5 may be provided between two of the windows.

Description

24 1 7602 TITLE: Teaching Aid

DESCRIPTION

Field of the Invention

This invention relates to a teaching aid for assisting in the teaching of numeracy concepts for example to young children.

Background of the Invention

It can sometimes be difficult to teach young children the concept of the decimal numbering system in which a succession of digits represents, in reverse sequence, units, tens, hundreds, thousands, and so on in increasing powers of ten. If the number is a non-integer, then the components of the sequence of digits to the right of the decimal point represent, successively, tenths, hundredths, thousandths, etc. Even before a child is introduced to the concept of non-integral numbers utilising the decimal point, it is necessary for them to understand how a digit sequence requires successive digits to indicate values decreasing as powers of ten. Teaching aids to assist in the teaching of such whole number concepts include number fans, hundred squares, Cuisenaire rods, Gettegno charts, arrow cards and number lines.

These teaching aids encourage the teache, to er ter into coriversation with the pupils about the concepts being demonstrated. Some also make good use of colour to stimulate the visual senses, and some, like the Cuisenaire rods, need to be handled by the pupils so that they also introduce tactile stimulation.

All of the known teaching aids are extremely limited in their ability to progress from the teaching of whole number concepts to the teaching of decimal fractions, and there is a great need for a teaching aid which can move seamlessly from the teaching of whole number concepts to the teaching of decimal fractions so that the same teaching aid can be used throughout the logical development of a child's learning. - 2

The Invention The invention provides a teaching aid as defined in claim 1. The discrete elements of information relating to numerical concepts are preferably place holders, namely the words "units", "tens", "hundreds", "thousands", etc for the teaching of whole number concepts, and "tenths", "hundredths", "thousandths", etc for the teaching of fractional decimal concepts. The discrete elements of information may be mounted on backing sheets that can be mounted on the display panel in the fixed positions in a user- selectable sequence. Thus a teacher can choose to put up on display only the place holders "tens" and "units" for very basic introductory teaching, or could display a nine place holder sequence "ten thousands" to "ten thousandths" for the demonstration of much more advanced numeracy concepts.

The user-variable sequence of digits may comprise a series of digits each on its own individual backing plate that can be selectively received on or removed from the convertor for example by being releasably retained in position by magnetic attraction or by a hook and pile fastening, or by being dropped into a holding recess in the conveyor. Alternatively the sequence of digits can simply be written on the surface of the conveyor using a wipe-clean marker pen.

Typically, if the uservqrlable sequer;ce of digits was a "1" and a "5" in, sequence, then the digit "1" would appear through a first window in the display panel immediately adjacent the place holder "tens" in the array of information relating to numerical concepts, and the digit "5" would appear through another window immediately adjacent to the place holder "units". The concepts of multiplication and division by ten can then be explained by moving the conveyor the left or to the right. If it is moved to the left then it has to be explained to the pupils being taught that one ought not to leave the "units" window empty, and that it is appropriate and correct to add digit "O" in the "units". Similarly if a number ending with a zero were divided by ten, movement of the conveyor to the right would show that the zero in the "units" window can be ignored, or can be removed prior to moving the conveyor, l - 3 leaving the conveyor free to move the digit sequence to the right to demonstrate the consequence of division by ten.

For decimal fractions less than one, the discrete elements of information relating to numerical concepts ought to include a decimal point, and one or more new place holder words taken from the sequence "tenths", "hundredths", "thousandths", etc. Always the discrete elements of information relating to the numerical concepts are displayed in discrete allocated positions on the display panel. The place holders are preferably (but not essentially) vertically above the windows so that the sequence of digits appear in the windows as if in labelled columns. The decimal point is always between the windows "units" and "tenths", and conveniently the decimal point may be an inseparable part of the element of variable information carrying the place holder word "units" and is positioned to the right of the word "units" so that its fixed position is between the windows associated with the place holder words "units" and " tenths". Alternatively, and using exactly the same concept, the decimal point might be an inseparable part of the element of variable information carrying the place holder word "tenths", in which case it is positioned to the left of the word "tenths" and at a level to be displayed between windows carrying the associated place holder words "units" and "tenths".

The teaching aid of the invention encourages and stimulates conversation with the pupils, enabling the teacher to demonstrate visually and orally the basis for the decimal system of numerical ascendancy in a digit sequence presenting a base ten number. Colour coding may be used for the discrete elements of information relating to numerical concepts, so that the place holders "hundreds", "tens", "units" etc may all have their own unique background colour. This gives a further level of stimulation for the child being taught. Tactile stimulation is also possible using the teaching aid of the invention. For example, if the user-variable sequence of digits is adhered to the conveyor by magnetic attraction or by a hook and pile fastening, or if the individual digits are slotted into place in an array of holding recesses in the conveyor, then tactile participation with the youngster being taught is made very easy. A further level of tactile stimulation can be obtained by having each individual digit being receivable in a holding recess in the conveyor, and removable from that holding recess, but additionally making it possible for the pupil to slide individual digits laterally of the conveyor, from one holding recess to an adjacent holding recess; and from one window to an adjacent window. For this a passageway or slot is needed between adjacent windows in the display panel, wide enough to allow a pupil's finger to trace a path from one window to the next while pushing an individual digit along the conveyor between adjacent recesses. This enables the pupil to observe the consequence of moving only one digit from the sequence of digits to the right or to the led, separately from the other digits in the array and therefore creating a significantly different pair of numbers expressed decimally. If the sequence of digits is "4,5,6" for example, representing the number four hundred and fifty six, then the "4" lies adjacent to (preferably beneath) the place holder "hundreds", the "5" lies adjacent to (preferably beneath) the place holder "tens" and the "6" lies adjacent to (preferably beneath) the place holder "units". Movement of the conveyor to the led moves the entire digit sequence to the led so that "4" is repositioned adjacent to the identifier "thousands", "5" is adjacent to the identifier "hundreds" and "6" is adjacent to the identifier "tens". The pupil can be encouraged to do the same thing manually. To illustrate the concept of multiplying the number 456 by 10, for example, the digit sequence 4,5,6 is inserted beneath the place holders 'hundreds', 'tens' and 'units' respectively. The pupil is then invited to move the digit sequence to the led and must start with the 'hundreds' digit, '4'. That is moved manually to the window adjacent to (preferably beneath) the place holder 'thousands', but that action leaves a space beneath the place horder 'hundreds'. The 'tens' digit, '5', is then moved into that vacated window which is identified by the place horder 'hundreds'. Finally the 'units'digit. '6', is moved to the vacated window identified by the place holder 'tens'. The pupil following this sequence manually has learned the technique of the sequential movement of digits into columns associated with higher value place holders, and in so doing has utilized auditory senses (listening to instructions), visual senses (seeing how the individual digits move, reinforced by the use of bright colours) and tactile senses (touching the individual digits to move them). The teacher using the teaching aid of the invention can then reinforce that learning process by - 5 repeating the movement of the digit sequence using the conveyor to move all the digits simultaneously.

DRAWINGS: Figure 1 is a front view of a first embodiment of a teaching aid according to the invention; Figure 2 is a front view of a second embodiment of a teaching aid according to the invention; Figure 3 is a front view of a sequence of five discrete elements of information as used in Figure 2; Figure 4 is a minor modification showing how five discrete elements of information from Figure 2 can be incorporated on a single removable panel securable to the display panel of Figure 2; Figure 5 is a front view of the conveyor only of Figure 2, modified slightly to include printed numbers "O" at every window position, printed in a tint of a single primary column; and Figure 6 is a front view of a teaching aid of the invention utilising the conveyor of Figure 5, and having transparent screens over the windows to the right of the decimal point, so that the printed digits "O" cannot be seen to the right of decimal point where the background and foreground as viewed through the tinted screens become indistinguishable.

Referring first to Figure 1, the teaching aid comprises a display panel 1 which displays, in fixed positions, discrete elements 2a, 2b, 2c, 2d and 2e of information relating to numerical concepts. The elements of information 2a to 2e are the place holder words "hundreds" to "hundredths", each printed on a differently coloured backing sheet that can be removably secured to the display panel 1, or alternatively each printed directly onto the display panel 1.

The means for removably securing removable backing sheets to the display panel 1 can be magnetic attraction, patches of hook and pile fastening material on the front of the display panel 1 and the back of the backing sheets for the discrete elements of place holder information 2a to 2e, or any other securing means such as, for example, a peelable adhesive. - 6

The fixed positions of the discrete place holder elements of information 2a to 2e are fixed relative to an array of windows 3a to Be in the display panel 1. In the embodiment shown each place holder is positioned immediately above its associated window. A conveyor 4 in the form of a laterally movable slide is positioned behind the windows 3a to Be, so that numbers carried by the conveyor 4 can be seen through the windows. Each number carried by the conveyor 4 is presented as a sequence of digits, one per window, so that in the illustrated digit sequence 2,1,3 the "2" appears in the "hundreds" window 3a; the "1" appears in the "tens" window 3b, and the "3" appears in the "units" window 3c. A decimal point 5 is shown between the "units" window 3c and the "tenths" window ad, and in itself represents a further discrete element of information. As one option the decimal point 5 may be removable from the display panel 1 together with one or more of the discrete elements of information 2a to 2e, so that the same teaching aid can be used to teach purely whole number concepts and decimal fractional concepts.

In the simplest form of the teaching aid illustrated in Figure 1, the user- variable sequence of digits "2,1,3" can be added simply by writing the digits directly on the surface of the conveyor through the windows by using a wipe- clean marker pen. One end of the conveyor 4 is a multiplication sign and an arrow head, indicating that movement of the conveyor in that direction performs the task of multiplicatlor.. At the other is a division, sign and an, opposing arrow head, indicating that movement of the conveyor in that direction performs the task of division.

Figure 2 shows a slightly more sophisticated version of essentially the same aid. The teaching aid of Figure 1 could be made from very thin materials such as durable cardboard. The teaching aid of Figure 2, however, is more substantial because the individual digits in the sequence of digits are each printed on individual backing plates which can be dropped into aligned slots 6 in the backing plate and 7 in the conveyor, to be ultimately receivable in a holding recess in the conveyor immediately behind the respective windows.

The same reference numerals are used in Figure 2 for the display panel, conveyor, discrete elements of place holder information and windows as have - 7 already been used and described in relation to Figure 1. The conveyor 4 of Figure 2, however, is a rigid tray which is slidable in a linear guide track within the display panel 1, immediately behind and in line with the row of windows 3a to Be.

Figure 3 illustrates the discrete elements of place holder information 2a to 2e and 5 of Figure 2. These may be provided as separate items of information in each of which the individual words "hundreds" to "hundredths" is printed on a separate tile or backing sheet 8 except for the decimal point which is shown as being integral with the backing sheet 8 carrying the word "tenths". The decimal point is to the left of the word "tenths", and at a lower level so that in Figure 2 it lies in a fixed position between the windows 3c and 3d.

Alternatively it could have been integrally connected to the tile 8 carrying the word "units", to the right of the word "units" but at the same vertical level.

Having the discrete elements of information 2a to 2e and 5 on separate tiles 8 makes it possible for the teacher to discuss with the pupils the correct sequence of the elements of variable information in a descending series of power ten. Each individual tile 8 can be connected to the display panel 1 by magnetic attraction, by the component parts of a loop and pile fastener, or by any other convenient mounting method.

As an alternative to having the discrete elements of Preformation provided on separate tiles 8 as illustrated in Figure 3, they could all be printed on a single backing sheet 9 as in Figure 4, with a choice of backing sheets 9 being available so that different place holders can be allocated to the different windows 3a to Be of the display panel 1.

For moving the conveyor 4 of Figure 2 to the right or to the left behind the windows 3, there are provided handle portions of the conveyor 4 accessible from opposite ends of the display panel 1. Each handle portion is shown in Figure 2 as being a flexible tape 9. That at the left hand end of the conveyor 4 carries the multiplication symbol x and that at the right hand end carries the division symbol.. Alternatively a slightly more costly but extremely effective - 8 teaching aid could be constructed in a variant of Figure 2 that is not illustrated, by providing a crank handle extending perpendicularly through the display panel 1, rotation of the crank handle causing engagement of teeth of a pinion associated with the crank handle. If the teeth of that pinion engage with rack teeth cut into the conveyor, then rotation of the crank handle in one sense will cause sliding movement of the conveyor in one direction, and rotation of the crank handle in the other sense will cause sliding movement of the conveyor in the opposite direction. This can have a more positive contribution to the teaching of multiplication and division concepts to the very young because the physical turning of the crank handle has greater visual impact as an applied process, indicating multiplication or division, than has the simple lateral pulling of the conveyor 4. A variant of the above 'crank handle' concept would be to have two crank handles, one labelled with the multiplication symbol x and the other with the division symbol.. The two crank handles should be each unidirectional, so that they can rotate in one direction only to drive the conveyor; and each should have an associated free-wheel or slippage mechanism so that turning the 'x ' handle in its permitted direction causes the conveyor to move to the left and turning the '.' handle in its permitted direction causes the conveyor to move to the right.

Figures 5 and 6 illustrate another variant of the invention. A sequence of digits "O" are printed on the conveyor, each "O" being positioned to lie behind an associated window 3a to Be. The "O"s are printed in the same tint of a single primary colour. For example, if that single primary colour is red, then all the "O"s are printed in very pale pink. The windows ad and Be to the right of the decimal point 5 are covered by transparent screens which are tinted with the same shade of pink. Therefore when the "O"s printed on the conveyor of Figure 5 pass behind the shaded windows 3d and Be in Figure 6, they become invisible because the background and foreground as viewed through the tinted screens become indistinguishable. When the conveyor is moved to the left so that the number 213 displayed in Figure 6 is transported to the left, a digit "O" printed on the conveyor to the right of the "3" becomes visible in the "units" window 3c. - 9 -

A variant of this automatic display of trailing zeros which become visible when a selected number as multiplied by ten is feasible. If transparent coloured screens are provided over the "hundreds". "tens" and "units" windows 3a to 3c, but coloured with tints of one or more of the other primary colours, then when the pink "O" number appears behind the tinted window 3c, the "O" will appear not as a pale pink digit but as a black or dark gray digit, depending on the purity of the colours used in the transparent screens and the printing.

Preferably the transparent screens are integrally secured to the individual tiles 2a to 2e carrying the individual identifiers of the orders of magnitude of the windows. Preferably the colour coding of the tiles matches the colour coding of the associated screens.

It will be appreciated that Figures 1 to 6 are illustrative to the extent they show only five windows in the sequence, and only three digits in the user-variable sequence of digits. Clearly any number of windows, and any number of digits in the sequence, can be accommodated according to the invention, although usually a sequence of nine windows, from ten thousands to ten thousandths, will be the maximum size that anyone may require in use. Figures 2 to 6 shows that the conveyor 4 is longer than the display panel 1. That too is a design choice, and in practice the conveyor 4 could be longer than, shorter than or the same length as, the display pa, ,el 1. - 10

Claims

CLAIMS.

1. A teaching aid for assisting in the teaching of numeracy concepts to young children, comprising: a display panel for displaying in fixed positions discrete elements of information relating to numerical concepts; a number of windows in the display panel; a conveyor for receiving a user-variable sequence of digits and displaying those digits through the windows in the display panel; and means for moving the conveyor laterally of the display panel in either of two mutually opposite directions so that the individual digits in the sequence of digits are displayed through different windows in the display panel and thus adjacent to different elements of the information relating to the numerical concepts, depending on the lateral position of the conveyor.

2. A teaching aid according to claim 1, wherein each individual digit in the user-variable sequence of digits is on a backing plate that can be selectively received on or removed from the conveyor and is releasably retained in position by magnetic attraction or by a hook and pile fastening.

3. A teaching aid according to claim 1, wherein each individual digit in the user-variable sequence of digits can be written directly on the surface of the conveyor using a wipe-clean marker pen.

4. A teaching aid according to claim 1, wherein each individual digit of the user-variable sequence of digits is on a backing plate which is receivable in a holding recess in the conveyor, and is removable from its holding recess and replaceable by another such digit to vary the digit sequence.

5. A teaching aid according to claim 4, wherein adjacent holding recesses for digits in the user-variable sequence of digits are mutually spaced apart by the same distance as the mutual spacing of the windows in the display panel.

6. A teaching aid according to any preceding claim, wherein the discrete elements of information to be displayed on the display panel are mounted on backing sheets that can be mounted on the display panel in fixed positions in a user-selectable sequence.

7. A teaching aid according to claim 6, wherein the backing sheets are removably securable to the display panel by magnetism or by a hook and pile fastening.

8. A teaching aid according to any preceding claim, wherein the conveyor is slidably movable in a linear guide track behind the windows in the display panel.

9. A teaching aid according to claim 8, wherein the conveyor sliding movement is controlled by handle portions of the conveyor accessible from opposite ends of the display panel.

10. A teaching aid according to claim any preceding claim, wherein the discrete elements of variable information identify the increase, in powers of ten, of successive digits of the user-variable sequence of digits when viewed as a decima! number, and are chosen as a subset Of t"VV'O Or more adjacent identifiers from the sequence tens of thousands, thousands, hundreds, tens, units, tenths, hundredths, thousandths, and ten-thousandths.

11. A teaching aid according to claim 10, wherein the discrete elements of variable information also include a decimal point.

12. A teaching aid according to claim 11, wherein the decimal point is a inseparable part of the element of variable information carrying the identifier "units" and is positioned to the right of the word "units" and at a level to be received between the window in the display panel associated with the word "units" and the window to the right thereof. 12

13. A teaching aid according to claim 11, wherein the decimal point is a inseparable part of the element of variable information carrying the identifier "tenths" and is positioned to the leg of the word "tenths" and at a level to be received between the window in the display panel associated with the word "tenths" and the window to the led thereof.

14. A teaching aid according to any of claims 10 to 13, wherein the different identifiers are colour-coded.

15. A teaching aid according to claim 14, wherein each colour coded identifier carries a coloured transparent screen for covering and colourcoding a window adjacent to which the identifier is placed when the discrete elements of information are received on the display panel.

16. A teaching aid according to claim 15, wherein the colours of the transparent screens associated with identifiers "tenths", "hundredths", "thousandths" and "ten-thousandths" are the same or different tints of a single primary colour, the colours of the screens associated with the identifiers "ten thousands" down to "units" are tints of one or more other primary colours, and the carriage carries a permanent printed "O" at every window position printed in a tint of the said single primary colour, so that those printed digits "O" can be seen to the left of the decimal point but not to the, ight of the decimal point where the background and foreground as viewed through the tinted screens become indistinguishable.