AU2003100397A4 - Apparatus for teaching arithmetic - Google Patents

Description

AUSTRALIA

PATENTS ACT 1990 COMPLETE SPECIFICATION INNOVATION PATENT APPARATUS FOR TEACHING ARITHMETIC The following statement is a full description of this invention including the best method of performing it known to me: APPARATUS FOR TEACHING ARITHMETIC FIELD OF THE INVENTION The present invention relates to an apparatus for teaching arithmetic.

BACKGROUND TO THE INVENTION Mechanical apparatus for teaching arithmetic calculations to children are well known in the prior art. For example, in Australia sets of Cusineaire rods were used in primary schools during the 1960's and '70's as an aid to help children understand and visualise arithmetical operations such as addition and subtraction.

Other mechanical apparatus have involved sets of scales or balances with weights corresponding to various integer values however such devices have not met with widespread adoption.

It is well known that counting frames or abacus, having a number of straight rods loaded with beads representing numbers, have been used in Chinese culture for centuries as an aid to arithmetic. There are problems associated with using a traditional abacus as an aid to teaching addition and subtraction to children. One problem is that children tend to have difficulties in remembering the numerical values that the beads on a particular rod are associated with. Furthermore, use of a conventional abacus involves sliding beads back and forth along the rods from one end to another. Children typically find it difficult to comprehend the significance of the different positioning of the beads.

It is an object of the present invention to provide an aid for the teaching of arithmetic. More particularly, it is an object of the present invention to provide an aid for the teaching of arithmetic that is a useful alternative to the devices described previously and which ameliorates at least some of the problems discussed above.

SUMMARY OF THE INVENTION According to a first aspect of the present invention there is provided an aid for teaching arithmetic including: a support; a plurality of counters; a number of means for conveying counters mounted to the support and arranged to convey the counters from a first position, wherein the counters are visible to a second position wherein they are obscured; and indicia adjacent the number of means for conveying counters indicating numerical values to be associated with the counters.

Preferably the means for conveying counters comprises a number of runners.

Preferably the counters comprise beads which are located about each of the runners.

In a preferred a partition is mounted to the support.

Preferably the runners are arranged so that they straddle the partition.

Preferably the aid includes a number of pairs of runners and indicia corresponding with each pair indicating that counters conveyed by a particular pair of runners are to be associated with a particular power of ten.

The indicia may include depictions of houses.

The apparatus may be provided in a virtual format as a display generated by means of a suitably programmed computer.

Further preferred features of the present invention will be described in the following detailed description which will refer to a number of figures as follows.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a perspective view of a front side of a teaching aid according to a first embodiment of the invention.

Figure 2 is a side plan view of the teaching aid of Figure 1.

Figure 3 is a further perspective view of the teaching aid of Figure 1 wherein all beads of the apparatus have been moved to an obscured position.

Figure 4 is a view of the rear side of the teaching aid relative to Figure 3.

Figures 5 to 12 depict various states of the teaching aid of Figure 1 for purposes of explaining its use.

Figure 13 depicts a teaching aid according to a further embodiment of the present invention.

Figures 14 to 26 depict various states of the teaching aid of Figure 13 for purposes of explaining its use.

Detailed Description of Exemplary Embodiments Figures 1 and 2 depict an aid 2 for teaching arithmetic, according to a first embodiment of the present invention, in perspective and right plan views respectively. The aid has a support in the form of base 4 along which eleven rigid runners in the form of wire arches 6a-6k are arrayed. In the presently described embodiment each of the arches 6a-6k is composed of a corresponding one of front legs 8a-8k and a corresponding one of rear legs 10a-10k joined by an intermediate arc 14a-14k. Mounted along a midline of base 4, and straddled by arches 6a-6k, is a partition 12. In use, partition 12 provides an optical barrier between front legs 8a-8k.

and rear legs 10Oa-10Ok as will be discussed further shortly.

Mounted on each arch are a number of counters in the form of beads 16. Ten beads are mounted about each of arches 6a-6j, whereas nine beads are mounted about arch 6k so that there are a total of 10x10+1x9=109 beads in the presently described embodiment.

Beads 16 may be manually conveyed along their respective arches from front to rear leg and back again.

Figure 3 shows aid 2 in a configuration where all of beads 16 have been slid onto rear legs 10a-10k. In this configuration partition 12 prevents viewing of the beads as shown. In the configuration depicted in Figure 3 it is also possible to more clearly see that partition 12 bears various indicia. In particular, behind front legs 8j and 8k there appears a drawing of a house 18 bearing the label "Ones House" and behind front legs 8a-8i there is a drawing of a wide house 20 bearing the label "Tens House". Behind each of front legs 8a-8b there is drawn a corresponding number "10" leading to a door of the Ten's House. Figure 4 shows a rear view of the aid.

Apparatus according to the present invention may be constructed of any practical materials. For example the base and partition might be wooden.

Alternatively an extruded plastic could be used. The loops will typically be made of metal wire though they could also be plastic or any other suitable material.

Furthermore, the aid could be provided as a "virtual" rather than a physical apparatus. In that case a suitably programmed computer would generate a display of the apparatus and manipulation of the beads would be accomplished by using an input device, such as a mouse or keyboard, attached to the computer.

An example of the use of the aid to teach the process of subtraction to a group of children will now be given.

The following example involves the sliding of beads from a visible first position, on front legs 8a-8k to a second position on rear legs 10a-10k where they are obscured from sight. It will be realised that as a bead is taken out of sight a child tends to remove it from consideration which is advantageous as it assists in understanding arithmetical operations that the aid is used to demonstrate. It is preferably that during each of the demonstrations the demonstrator also shows corresponding calculations on paper or, for group demonstrations, chalkboard or whiteboard.

Example I Subtraction of 38 from 63 The teaching aid is initially set up as shown in Figure 5 so that the children see six full columns of ten beads in the "tens house" and a column of three beads on the extreme right wire in the "ones house". At this point the demonstrator would write on paper: 6 3 38 It is immediately apparent to the children that it is not possible to take eight beads from the column in front of the "ones house", so there needs to be some "trading" or "regrouping".

The "ten" to be traded should be taken from the extreme left column of those carrying beads in front of partition, (thus illustrating that with one ten gone, five remain) The "ten" should be placed on the left wire in the "ones house" illustrating that there are now thirteen beads in the "ones house" as shown in Figure 6.

At this point the demonstrator would write on paper: 13 38 At this point it assists in the children's understanding if it is emphasised to them that the sixty-three beads have merely been regrouped. This can be done, for example by counting the columns off with the children so that they see that 63 beads are still visible, just regrouped to five in the "tens house" and one ten with the original three in the "ones".

Eight beads can now be subtracted ("taken away") from the "ones house" of Figure 6 by sliding the three beads on the front leg of the rightmost arch over the partition and then sliding five beads from the front leg of the second rightmost arch over the partition so that the configuration shown in Figure 7 is attained. It is advantageous (at least initially) to count the beads away as they are removed. It will be noted that five beads remain in the "ones house". At this point the demonstrator would write on paper: 13 38 3 8 Three columns of ten beads can now be removed ("taken away") from the "tens house". The three columns of ten beads each are removed from the leftward arches so that the counting down of visible beads is obvious to the children. Five beads are left in the "ones house" as shown in Figure 8.

6 At this point the demonstrator would write on paper: 13 -4-a 3 8 2 It is preferable that while sliding the columns of beads over the arches it is explained to the children "we have fifty now forty thirty twenty", in order to emphasise that "three from five leaves two".

Example 2 Addition of 37 and 27 The teaching aid initially needs to be set up so that the children see three full columns of ten beads in the "tens house" and a column of seven beads on the left hand wire of the "ones house" as shown in Figure 9. At this point the demonstrator would write on paper: 3 7 2 7 The seven to be added in the ones house should be counted on first filling the left wire with and then placing the remaining beads on the extreme right wire in the "ones house" as shown in Figure 10. At this point the demonstrator would write on paper: 3 7 2 7 14 Children will readily comprehend that there are too many beads in the "ones house" and that the full column of ten on the leftward wire of the "ones house" should be "traded" or "regrouped", to remove the extra beads. The visible beads should be counted out loud again at this point "ten, twenty, thirty, forty, forty-seven" to establish for the children the number of beads after this "ones house" operation.

Remove the column of ten beads from the "ones house" and "trade" or "regroup" the teaching aid by placing a full column of ten beads on the next right wire in the "tens house" as shown in Figure 11. At this point the demonstrator would write on paper: 1 3 7 27 4 At this stage, the beads should be counted out loud again "ten, twenty, thirty, forty, forty-seven" to emphasize that they have simply been "regrouped" or re-arranged.

Two full columns of ten beads should now be added to the next left wires in the "tens house" as shown in Figure 12. At this point the demonstrator would write on paper: 1 3 7 27 6 4 It is a simple and very visible explanation to show that the "extra" ten that was in the "ones house" was "carried" into the "tens house" and totalled with the original thirty and twenty in the exercise.

The aid may also be readily used to explain simple addition and subtraction where no trading is involved.

The inventor has found that few children need to see these demonstrations more than twice to master the use of the aid. Those not grasping the process immediately will require only two or three "hands on" exercises (while simultaneously completing each step on paper) to have control of subtraction from numbers up to 100, and additions with sums up to 100.

Figure 13 shows a teaching aid according to a further embodiment of the present invention. In the embodiment of Figure 13, eight arches are arranged in four pairs 18-18D. Indicia signifying the value of beads carried by each of the arches are provided in the form of four houses 20-20D marked on the partition. The houses are each located adjacent a corresponding one of the four pairs of arches. The houses are labelled, from left to right, "1000's House "100's House" "10's House" and "l's House". Ten beads are carried on the left arch of each pair and nine beads on the right arch.

The use of the apparatus of Figure 13 will now be described with reference to a number of examples.

Example Subtraction of 2976 from 7342 The teaching aid is initially set up as shown in Figure 14. That is, so that the children see a column of seven beads on the right hand wire in the "thousands house", three beads on the right hand wire in the "hundreds" house, four beads on the right hand wire in the "tens" house, and two beads on the right hand wire in the "ones house". At this point the demonstrator would write on paper: 7 3 4 2 2976 Upon viewing the aid in the state shown in Figure 14, most children will immediately comprehend that it is not possible to take six beads from the column in the "ones house", and that there will have to be some "trading" or "regrouping" of beads.

Because six beads cannot be removed from the "ones" house, one bead must be "traded borrowed" from the "tens" house. Accordingly one bead is removed from the "tens" house but its equivalent (a full column of ten beads) is inserted on the left wire in the "ones" house as shown in Figure 15. At this point the demonstrator would write on paper: 3 12 7 3 -4--2 -2976 -2 9 7 6 Six beads can now be removed from the "ones" house the original two on the right hand wire and the necessary four from the left hand wire. Six beads remain in the "ones" house.

The "regrouping" operation is now repeated because seven beads cannot be removed from the three now available in the "tens" house. One bead is removed from the "hundreds" house and its equivalent (ten tens) is inserted as a full column of beads on the left hand wire on the "tens" house as shown in Figure 16. At this point the demonstrator would write on paper: 2 3 12 7 7 -3--4-2 -2976 2 9 7 6 6 Now seven beads can be removed from the thirteen available in the "tens" house the three of the right hand wire and the necessary four from the left hand wire.

Nine beads cannot be removed from the available two in the "hundreds" house of Figure 16 so the "regrouping" operation is repeated by removing one bead from the "thousands" house and inserting the equivalent (ten hundreds) on the left wire in the hundreds house as shown in Figure 17. At this point the demonstrator would write on paper: 6 12 13 12 S3 4-2976 2 9 7 6 6 6 Now nine beads can be removed from the available twelve beads of the hundreds house the two on the right and the necessary seven from the left.

The subtraction is completed by removing two beads from the available six in the "thousands" house as shown in Figure 18. At this point the demonstrator would write the final result on paper as: 6 12 13 12 7342 -2976 4366 :7 3 4 2 9 7 6 4 3 66 Example: Addition of 2976 and 3347 The apparatus is loaded with the first addend (3347) so that three beads are visible on the left hand wire in the "thousands" house, three on the left hand wire in the "hundreds" house, four on the left hand wire in the "tens" house, and seven on the left hand wire of the "ones" house as shown in Figure 19. At this point the demonstrator would write on paper: 3347 3 3 4 7 2 9 7 6 Six additional beads must be added in the "ones" house. The first four fill the left hand wire and three are placed on the right hand wire as shown in Figure 20. At this point the demonstrator would write on paper: 334? +2976 133 3 4 7 2 9 7 6 13 The full column of ten is "traded" from the "ones" house and its equivalent (one bead in the "tens" house) is added to the existing column of four beads there as shown in Figure 21. At this point the demonstrator would write the corresponding paper calculation: 1 3 3 4 7 2 9 7 6

III

3347 +2976 3 The addition process is repeated in the "tens" house. Seven additional beads fill the left hand wire and "overflow" to put two beads on the right hand wire. The column of ten is traded over as one equivalent bead in the "hundreds" house to bring the apparatus, via Figure 21 and Figure 22 to the configuration shown in Figure 23. The paper calculation corresponding to Figure 22 is: 1 3347 3 3 4 7 2 9 7 6 12 3 The paper calculation corresponding to Figure 23 is: 1 1 3347 3 3 4 7 2 9 7 6 23 The addition process is repeated in the "hundreds" house. Nine additional beads fill the left hand wire and "overflow" to put three beads on the right hand wire. The column of ten is traded over as one equivalent bead in the "hundreds" house to bring the apparatus, via Figure 24, to the configuration shown in Figure 25. The paper calculation corresponding to Figure 24 is: 1 1 3 3 4 7 2 9 7 6 13 2 3 The paper calculation corresponding to Figure 25 is: 111 3347 3 3 4 7 2 9 7 6 323 3 2 3 The addition process is repeated in the "thousands" house with the two from the second addend placed to bring the apparatus to the final configuration shown in Figure 26 which represents 6323 being the sum of 3347 2976. The paper calculation corresponding to Figure 26 is: 111 3 3 4 7 2 9 7 6 6 3 2 3 13 Although the present invention has been described in terms of preferred embodiments, it is not intended that the invention be limited merely to these embodiments.

Equivalent methods, structures, arrangements, processes, steps and other modifications apparent to those skilled in the art will fall within the scope of the following claims.

Claims (4)

1. An aid for teaching arithmetic including: a support; a plurality of counters; a number of means for conveying counters mounted to the support and arranged to convey the counters from a first position, wherein the counters are visible to a second position wherein they are obscured; and indicia adjacent the number of means for conveying counters indicating numerical values to be associated with the counters.

2. An aid for teaching arithmetic according to claim 1 wherein the counters are obscured in the second position by means of a partition mounted to the support and wherein the runners are arranged so that they straddle the partition.

3. An aid for teaching arithmetic according to any of the preceding claims wherein the runners are paired and including indicia corresponding with each pair of runners indicating that counters conveyed by a particular pair of runners are to be associated with a particular numerical power of ten.

4. An aid for teaching arithmetic according to any of the preceding claims wherein the apparatus is provided in a virtual format as a display generated by means of a suitably programmed computer. An aid for teaching arithmetic substantially as described herein with reference to the Figures. Dated this 27th Day of May 2003 PRIAMUS EDUCATION CO PTY LTD By my attorneys Eagar Newcomb Buck Patent and Trade Mark Attorneys