Educational aids to simplify the process of abstraction and generalisation in the initial stages of teaching arithmetic

AUSTRALIA PIooloo17 " jl ' , " " Section ..................... a enls Act 1990 R= ! Patent Request : Standar," "-'---" .... .. • . u r en[ # patent of Add,hen t/We' be ng the pers°n(s) enti 1 ied bel°w as the ApPlkmnt request the grent of a patent to 4,a n i Pe n, reran invention described in the accompanying standard complete specirmatJon Full application details follow :_ Applicant Address ...................................... Nominated Person - ........... Address "--' 7. .... .-, ........ i---, ....... . ................ k{cLc{a-I/ r''- v,- [/" O-S'{- _ Invention Title State 5/1 rPostcode 5-1C: ! e"J "n70 -44 0 ,, ' "lt., -{ h t { i{- -q*s. o- {e<:t (-c.; .-, ! {721 Name(s) of actual inventor(s) j ._ ................................ PIAP.tA /VA A,'oiv i ,., ........................................... I ]"q Cf Oi-! IkJol, v <l,,c..ol,,m u t • - ....................... [741 Address forservica in Australta State Postcode :-- Contact -- -; • - Phone No. Attorney F--- ----- Code . Associated 15r 0 visi 0 na 1 App 11 cati 0 n(s)-Detai 1 s' Application Number(s) and Date(s) 1 ";-)t "1 r- - " V O g f V i-...LY i Application Number PUp_ 6i - -- / I Basic Convention Application(s) Details . ___U " Application Number Country Country Code [32J Date of Application : - ! I .. _ 1 / Olvlslonal Application Details 2] Original application number l Patent invention Details (Patent of Addition r4uests only) ._ Application number Patentnumbor [-- - ----7., i i l _._ i I Drawing number recommenr.;ed to .accompany the abstract 1 1 (12) PATENTABSTRACT (19) AUSTRALIAN PATENT (1 1) DocumentNo. AU-A-62043/96 OFFICE (54) Title EDUCATIONAL AIDS TO SIMPLIFY THE PROCESS OF ABSTRACTION AND GENERALISATION IN THE INITIAL STAGES OF TEACHING ARITHMETIC International Patent CI assification(s) (51)6 G09B 001 !06 G09B 023/02 (21) Application No. : 62043/96(?2) Application Date : 13/08,'96 (43) Publication Date : 19,,'02/98 (71) Applicant(s) MARIANNA NOWAKOWSKA (72) Inventor(s) MARIANNANOWAKOWSKA; WOJCIECH NOWAKOWSKI (70) Nominated Person(s) WOJCIECH NOWAKOWSKI (57) Educational Aids to simplify the process of abstraction and generalisation in the initial stages of teaching arithmetic. The be!ow mentioned invention is a teaching aid for arithmetic. It is uti!ised in the initial stages of teaching (especially in showing positive integers and illustrating the four concepts of mathematics: addition, subtraction. multiplication anl division). This teaching aid, according co the invention consists of a geometrical shape eg. cylindrical or rectangular (the outside walls being different eg. colourful) which have raised edges so that round objects do not roll off and grooves to enable cardboard cut-outs to be placed in them. P IO0/O °AIPO AUSTRALIA Regulation Patents Act 1990 Original Complete Specification Standard Patent invention iUe The following statement is a full description of ihis invention, including the best method of performing known to me:- Educational Aids to simplify the process of abstraction and generalisation in the initial stages of teaching arithmetic. The present invention relates to a method and a teaching aid for arithmetic. is utilised in the initial stages of teaching (especiallyin showing positive integers and illustrating the four concepts of mathematics: addition, subtraction, multiplication and division). In one form the invention issaid to reside in an educational aid comprising a set of Stands, each stand having means to retain an object to be counted on the stand, and at least tw o visually discernible faces of the stand, each face being coioured or patterned so as to be:¢isually distinguished from other of the faces. There may.be two, three or four separate faces which may be made in different colours. The shape of the stands may be cylindrical•or rectangular -and the retaining means may be a slot or recess. In a further form the invention is said to reside in_ a method of teaching numeracy skills using a set of stands as defined in any oneprevious claim, comprising the steps of; setting upa line of stands each_stand having an object retained thereon, at least two of the visually discernible faces being exposed on one side of the line of stands; counting the number of objects retained on the set of stands to give a total; counting the number of different visually discernib 1 e faces of each type; and comparing the number of different visually discernible faces with the total. Hence the teaching aid according to the invention consists of a geometrical shape eg. cylindrical or rectangular (the outside walls being different eg. colourful) which may have raised edges so that round objects do not roll off or grooves to enable cardboard cut-outs to be placed in them or both. The stands can be made either of wood or plastic. This then generally describes the invention but to assiSt with understanding preferred embodiments will be discussed with reference to the drawings. In the drawings: FIG 1 shows a first embodiment of a stand; FIG 2 shows an alternative embodiment of a stand; FIGS 3 to 6 show examples of using the stands to teach numeracy skills. In embodiments of the invention the set of stands may comprise: 10 cylindrical stands 2 as shown_in FIG 1 or 20 rectangular stands 1 as shown in FIG 2. The measurements of the stands may be as follows: the cylinders - 70 mm in diameter, 70 mm in height; the rectangular - 50 x 50 x 60 mm. The grooves 3 On the tops of the stands may be cut 25 mm deep and 3 mm wide. The rectangular stands 1 have two grooves 3 at right angles to each other through the centre Of the walls; the cylinders 2 have only one groove. The cylindrical stand.2 may be painted as:follows: half lengthwise in green, the other - red. The grooves Outlined above form the borders of the two colours. The walls of the rectangular stand 1 may-be painted yellow, blue, red and green. It is best to have the stands on a shelf extending from the blackboard. On the front of the shelf are placed cylinders or rectangles totalling the number being taught to the children. When beginning toteach children the concepts of numbers it is best to use the simplest form of stand ie. the cylinder. On these stands are placed groups of objects which thechildren have to cou-nt. One object is placed on one stand. These objects may be: fruit, toys, cut-outs of animals, ships or characters from fairy tales. Using different objects to demonstrate the concepts of numbers simplifies the abstract process - rninimising the association of numbers With certain objects. For example: Place six cat cut-outs on 6 stands, telling a story_ about them. The cats are then taken off. The 6 stands are the material-evidence of the number of cats, the number in a given set, ie. 6 which is the number ofchildren are required to leam and to disassociate from the material, to abstractly and to remember. Next we place 6 mice on the same 6 stands. After taking the 6 mice off, we place six other objects eg. trees. The stands are not only the material evidence to remember the numbers being taught but also a way of demonstrating the number by having it represented in different forms. The stands therefore are an aid to teaching the process of abstraction and the process of generalisation, that is they help these two processes which are vital in teaching any concept which is in any way in the form of abstract. Numbers which are learnt in detail and also the concepts of addition, -subtraction, multiplication and division are illustrate-d-thus: 1. Showing the number by using colours of the stands - FIG 3. 2. Objects are placed on the stands - FIG 4. 3. Spacing between the stands - FIG 4. Using all three methods in conjunction - FIG 6. Subtraction - eg. 7 - 3, is illustrated thus: Seven cars are placed on seven stands. Three cars then "drive-off":_ The empty stands are the material evidence of the cars which have driven off - the number of the set which was taken away. The remaining four cars illustrate the result of the subtraction. All the seven stands showing the initial number of cars. The stands are able to be used to demonstrate addition and subtraction involving numbersgreater than ten as also to demonstrate fractions of given numbers. They can also be used as stands for letters of the alphabet and to analyse t-he formation of words. The stands can be used in con)unction with other educational aids eg. figures or sets Of numbers. They require a higher degree of abstraction than numbers and help the children to imagine a certain number, eg. the number four or seven. When using these aids, the teacher should also try to bring in some elements of play to awaken the child's activity. The objects being used on the stands should be ones that will be of interest to the given group. The stand are brightly coloured and therefore attractive to the children• The shape of the stands al!ows the child to become familiar with geometrical shapes which will be taught in the future. Beside these, the ease of manipulation of the stands allow for quick illustrating without time wasting on drawings or preparation time for the teaching of the subject_ _ - ....... How these stands are used to work with children is dependent on the inncJvative nature of the teacher• It has been proved that the stands: 1. Instructive (didactic) values 2. A wide range of usage 3. To a large extent ensure the methodical nature of teaching basic arithmetic.