CA2108333C - Coin learning method and apparatus - Google Patents
Coin learning method and apparatusInfo
- Publication number
- CA2108333C CA2108333C CA002108333A CA2108333A CA2108333C CA 2108333 C CA2108333 C CA 2108333C CA 002108333 A CA002108333 A CA 002108333A CA 2108333 A CA2108333 A CA 2108333A CA 2108333 C CA2108333 C CA 2108333C
- Authority
- CA
- Canada
- Prior art keywords
- notational
- coin
- coins
- amount
- graphics
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B3/00—Manually or mechanically operated teaching appliances working with questions and answers
- G09B3/02—Manually or mechanically operated teaching appliances working with questions and answers of the type wherein the student is expected to construct an answer to the question which is presented or wherein the machine gives an answer to the question presented by a student
Landscapes
- Engineering & Computer Science (AREA)
- Business, Economics & Management (AREA)
- Physics & Mathematics (AREA)
- Educational Administration (AREA)
- Educational Technology (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Credit Cards Or The Like (AREA)
- Electrically Operated Instructional Devices (AREA)
Abstract
A method and apparatus is described whereby a child or other person may learn to use two different notational systems for coins, such as cents and dollars, by following an ordered set of instructions that guide the matching of movable graphic symbols and coin-replicas onto identical graphics on a printed surface. In the example the user learns 1) to recognize and name a notational symbol corresponding to each of the two notational systems; 2) that the two different systems can be used to express the same amount of money; 3) to associate the physical manipulation of a coin or coin-replica simultaneously with both notational systems; 4) to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and 5) to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount. Additionally, a final evaluation step provides feedback and options relative to calculating the requested amount.
Description
- 210~333 INTRODUCTION AND DESCRIPTION OF THE PRIOR ART
The present invention relates to children leaming to use money and read money notation. This is an important ski]l in our society, and the recent trends towards more abstract handling of money business--such as banking by personal computer and pu~ asillg by charge-cards or electronic direct payments--indicate that even more of this skill will be required in future. Although it might appear, to some, that not using physical ;
money for transactions makes less need for touch-based learning, this is not the case. An abstract tertn can only be manipulated m~ningfully if it accurately l~,pl~iS~ t~ something which is understood very well. For example, a person who has an imperfect grasp of the meaning of dollars, quarters, dimes, nickels, and pennies, and who needs to make a I,lnchase, is more likely to make a reasonably accurate transaction while exrhqnf~in physical money with a real person (whom they can consult for advice, or whose satisfaction with the transaction they can judge by non-verbal body language) than while balancing their check-book or ordering an item from a catalogue.
Thus both physical money m~nipnlations and ~ cnra~ely knowing the names and notation systems of coinse are necessary to co~n~ ,hend and use the money system of the real world. No previous teaching system appears to exist that satisfies thisre4ui.~,.l,ent to the extent that the present invention will disclose, ~lthough several existing patents address some aspects and will be briefly reviewed below; several are for speciqli7çd sihl ~ioll~, such as for slow-learning children or retarded adults.
Of largelyh;~toli-~' interestarethetollowing: Fisher, 1877, U.S,~188,505, (in what may be the shortest patent on record,) specifies and claims cardboard coins; but ;
how to use them or name them is not addressed. Anderson in 1932 (C:~n ~ n #393,364) shows a cut-out form with numbers written on it; the answers are written into holes in the form and co~ a,bd with the reverse side of the form. No action similar to real-world 2108~33 money-exchanging is provided. Westzstein, Canadian #476, 827, in an ingenious disclosure that may still have relevance for certain situations, claims numbers that are made up of multi-coloured pieces, such that the number of pieces equals the digit being learned; for instance, the numeral "9" is constructed of 9 coloured pieces that iFit together, jig-saw like, to form the digit. While this may make the connection, as he says, of "concrete objects outside the number with the number itself," (by "number itself"
meaning the abstract concept of the number), it still fails to teach either naming or manipulating; in other words, counting and keeping track of counting.
Thomas, U.S. #3,768,177, speci~les "a co~ ,o~it~ a..l..s~ and educational instruction kit for both children and adults," which is largely directed towards the physical layout of the carrying case and drawing tools, coins are addressed only as pictorial rl,~.bsenl~lion of simple addition and subtraction, without hands-on irul~ ~ion or practice in naming or symbol--~cogllilion. Comeaux & Ritchie, U.S.#4,775,321, specify a "System For Teaching Money Values" which is shown as alinear method of ordering items and their money value from smallest to largest; the example is a series of envelopes housed in a box and separated by file-cards. This is s l ~ -lly more complex than is needed for initial recognition usage skills, entailing a record-keeping ''Idbo ~' y" on the file dividers, and would be more a~prt~p. for older children, perhaps, once the basic skills were .lla~t~,~.,d.
Of patents al F h.g to address these basic skills in a s~st~ atic way, two are co~c~ y similar enough that they may be di~cucsed together: H~' qllict~ U.S.
#3,690,017; "Coin Value Teaching Device," (1972) and Shank, C~~ ~ii ~~ #1,212,229, "System for Teaching Coin 12el ~~ion~, s," (1986), both show a 1~ lvulal board with numbers on it that can be covered by a form fitting overtop that bears one or more coins or coin symbols e~ ecWcd or g. r~ ly c..ll~laL ~ ~ In each case several forms are provided, of several sizes, and the child or other user (Holmquist suggests retarded 2 1 0 ~ ~ 3 3 ~ ~
children) learns how many digits are l~nderneath a form of a given size which has a given coin or coins on top. A major and insurmountable d~ l)ack of this al),UIUaCII iS its ~ :~
unreality: the child is being asked to conceptually accept that a (say) six-inch by four-inch pieee of plastic with a quarter glued into it (or drawn on it), or 25 pictures drawn on it, -each of 1¢, is a coin-replica now but is not one later in "real interactions." ;
Finally, Yamin, U.S. #4,752,227, discloses a board game that has recesses that eoins are slipped into. While actual eoins ean be manipulated in this invention, several d-~wl,acks appear: the most important of these is that eonceptually it's still a step ~ ;~
removed from the real-world situation. One face of the board shows gr~phir~lly defined areas that have coin-spaces both for a series of small deno~ -alion eoins and for a larger eoin or bill equivalent to their total. The user plaees eoins into the small series, and then ;
àn equivalent eoin or bill into the adjaeent single spaee. The ehild or other user is ~;
"efol~i being asked to plaee twiee the amount that a transaetion would take into the defined area, in order to "learn" that one part of the area is e~ui~ alc.~, in money terms, to the other part. Fu~ o~, there is no provision for naming in Yamin: the board is :
un~ ,nlil,gly, and col.rus...~ly, made up of a large number of similar sized l~lc~.gles -1~ - g round I~CS5l.J~S (or holes, in one ~ bod ). Scal~,llh~g among these to find, ~ ;
say, where to put 10 pennies (and a dime) eould be a rl~.Sl- t g eYp~ri~n(e7 and not one ~-that would be useful in real-world l, u..s. A separate section on the baek faee of the board, in one err~' o~' --- t, speeifies eards that show how to "build" an amount and place it into similar l~,c~ js - -s; the example given is making 92¢ from, as shown on an accompanying card, a half dollar, a quarter, a dime, a niekel, and a eent. No ehoiee is provided; whieh, again, means this is a '~ g" situation: for instance, how often have any of us been asked to pay 92¢ for an objeet in a store and reaehed into our poeket and pulled out--oh what good luek!--exactly a half-dollar, a quarter, a dime, a niekel, and a ~ ~
eent? ~ -,~ 210~3 :
In contrast, the present system will provide the child with a learning situationthat can be used with a teacher, alone, or with a group of children. The child can learn to recognize money notation ("$" and "¢"); read fhe words S'penny", "nickel", "dime" and "quarter"; and visually recognize the coins co~ .por.dillg to the names. With this invention the child can learn to define and explain the equivalence of only pennies to one dollar (i.e., 100), then nickels to one dollar (20,) dimes (10,) and finally quarters (4). And the child can learn to use any coll-b;nd~ion of coins to add up to one dollar or less. The situation is not competitive, and will be un~ s~..lll;d and enjoyable, and any child using it, either alone or with others, can work at their own pace. Sufficient latitude is provided for creative solutions--choice, in other words--while still providing a framework that defines what needs to be done and how to do it. The visual aspect of the child's need is cc. ~. ~d, and i~ltC.~,;.lif~g symbols, in various colours, such as clouds, boxes, triangles, circles, coloured text, and so on, are used liberally.
In sum, the present invention provides for a display such as a board-game (or single- or multi-leaved large book) showing words, numbers, graphic symbols, andinsl.u.,i - -- on the printed surface and having a resource pouch or box with I
coins and graphic symbols. Notation is taught by ~ ' g a desigr~d graphic resource, such as a plastic piece showing "$" inside a cloud, with the same graphic on the board; a VelcroTM or other ~ft- ~ may opfinqqlly be used. Coin-pieces are matched with labelled spaces on the printed surface to a ~S~ ~ the correct notation, words, and numbers with he coin-piece. Then ~.PIJIUPI'-'- numbers of coin-pieces are placed in graphics ûn the printed surface tû show the addition and equivalence of each coin to a dollar. The se~_ e of events is L~lpc)llallt~ and p~uceGds logically to give the child an integrated und~rstq~ of symbolic notation and the medium of physical ~ ipulq-fion.
Practice and self-testing of the kno~. Icdg., is also ~ as a series of matched cards, with an amount shown on a first card, such as 82¢ (optionally with an ~ ;~
' ~"'; "
2~0~33 instruction, such as "use two of each type of coin.") The child forms 82¢ by placing a~ l iate coin-pieces on the printed surface, and then evaluates by checking a second (matching) card showing how this amount can be achieved in coin-pieces. The graphic -make-up of these second (evaluation) cards indicate to the child that this isn't the only way of making up the answer, given a reasonable number of different coins. While the card gives guidance as to how to that answer could be achieved in one way, it simultaneously sets out the field that the child can use to choose other ways of achieving the same answer in future. -In this way a cooperative learning technique made available, and the children can read and follow instructions at an activity center with no teacher present, even inc!ll-lin~ the evaluation answer key just described. The child then is self-teaching, self-~sP~Sing and self-correcting, so that the method can be used at home or at school, with or without adults, and alone or with other children, in a supportive and interactive group.
An object of the present inven~ion is to provide for a method of learning to useand refer to coins in two n~"dtio.lal systems, the unit of the first notational system referring to a smaller amount of money than the unit of the second notational system; the learning to occur in the following order: to recogni~e and name a notational symbol colresponding to each of the two notational systems; that the two different systems can be ~;
used to express the same amount of money; to a~cocic~ç the physical manipulation of a coin or coin-replica sinlult~-neously with both notational systems; to calculate and physically as~ 'e the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and to calculate and physically ass.,.llblc the amount of coins or coin-replicas of a mixture of denominations that sum to a l~ue~ted amount. Optionally, the learning occurs by following se~luenti~lly l..ullb~ ,d text instructions given on the printed surface or on accompanying cards giving ~ -instructions to match movable pieces bearing graphics onto a printed surface bearing - ;
~; ~10~333 ~ ~
approximately identical graphics. There may be additional final step of checking that the ~ ~ -calculation and assembly of the requested amount has been performed correctly. The method may be used for cases in which the first system is the cent system and the second :
system is the dollar system; the first notational symbol is "¢" and the second notational ~ ~ :
symbol is "$"; and the coin denominations are pennies, nickels, dimes, and quarters.
A further object is to provide for an apparatus for learning to use and refer to ~ :
coins in two notational systems, the a~pa~ s colnyli~illg~
1) a printed surface such as a games board surface or one or more pages in a .
book; the printed surface i,~ h~ted with: :
text giving names of coins; graphics c~ g notational symbols for each no~ational system; a graphic of an amount of money rendered:~
using the first notational system; a graphic of the same amount of money rendered using the second notational system; separate graphics each conl~ ing one symbol for one denollli.ldlion of coin; several separate gMphics each c~ g several identical symbols for a different single dellolllillalion of coin, the number of such symbols in each case being that whose value summed equals the unit value of the second l'ot'~ionql system; a graphic to indicate where a deck of cards is to be placed; and se,,_ ~ -'ly l~.llllbe~d a.~p~ 'r text giving instructions;
2) a storage area such as wells in a box, or pockets in a book page, contahling movable pieces, the pieces co..-l.. ;s:~g~
a plurality of coins or coin-replicas of each denomination of coin; a graphic of each of the notational symbols; a graphic of the same amount of money rendered using the first notational system as listed for the printed surface; a gMphic of this same amount of money :~
7 ;~
~ ~,, --' 2tO8~33 ~ ~
~, rendered using the second notational system; a deck of question cards ; '~ -bearing single amounts in either notational system, the cards optionally bearing text inrlir~a~in~ how the amount can be arrived at using cc.lllbh.ations of coins; and a group of evaluation cards, each of which contain colour-coded coin graphics indjr~tinE~ how a combination of denominations of coins may be summed to the amount on the corresponding question card.
In this apparatus there may be several identical graphics for each type of coin displayed on each evaluation card, and an ai)~J~pliatt, number of graphics for each type of coin that sum to the amount on the corresponding question card may optionally be a uniform different colour from those graphics not required to sum to the amount. There may be different amounts of coin graphics on different evaluation cards, and optionally the total value of the graphics for any one denomination on any evaluation card does not sum to the unit value of the second notational system or a decimal fraction or multiple :.
thereof; in order to help a person using the evaluation cards learn: a) that variable numbers of coins of various deno - ions are used in arriving at the sum on the question card; b) that there is more than one way to arrive at the sum; c) and that not all denominations of coins will always be available to make up the sum. Optionally, the movable pieces are stored or affixed by pockets or VelcroTM, or other known ,.~1 ~!....e means.
.;", ., DETAILEDDESCRIPTIONOFTHE INVENTION
For this description, refer to the following rli~g.L .,.c, wherein like numerals .
refer to like parts:
Figure 1, portion of a first embodiment of the invented system; game board; plan view; ~ .
8 ~ ~
'''..,' ~'' -' 2 1 ~ 8 3 3 3 Figure 2, storage box for game board of the embodiment of Figure l, .
with question and evaluation cards exploded; plan view; and :~
Figu}e 3, second embodiment of the invented system, open book;
perspective view. .
A first embodiment of the invented system is shown as Figures l and 2 talcen together. In Figure I can be seen a printed games board, indicated generally as 10, which has printed graphics such as clouds 12 and 14 and corresponding printed ~1rh~nllmPric text instructions such as "3. Match the two clouds that are the same," generally indicated as 53. Board 10 is here illustrated as the folding type, along dotted center-line 18, and when in storage will collapse and fit into the top of box in Figure 2, illustrated generally as 20, and will cover, (in the manner ~;u ~ lla~ily used for folding board games) the otherwise open resource wells 22, 24, 26, 28, 30, 32, and 34, all visible on Figure 2. Well 22 contains penny-pieces 23; these penny-pieces will customarily be of cardboard or plastic with a penny-like graphic, although the use of real pennies is also possible.
Likewise well 24 contains nickel-pieces 25; well 26 contains dime-pieces 27; well 28 contains quarter-pieces 29; well 30 contains cloud graphic pieces 31a, "2~¢," and 31b, "$.025," and notation graphic pieces 31c, "¢," and 31d, "$"; well 32 contains question cards such as in(lic~Pd generally as 33 and 37; card 37 of which is shown enlarged and e~, ' c d e ~ out of well 32; and well 34 contains evaluation cards indic~t~Pd generally as 35 and 39; similarly evaluation card 39 is enlarged and exploded from well 34.
In practice a child will remove board 10 from inside box 20 and open it to the position in Figure 1. (A top is not illustrated for box 20 but can be S~sumpcl) and assumed to have been removed). The board l0 will be large, perhaps 2 feet by 2 feet, and: ~,ly arranged, including designs such as border 19 and letters of some words ~; :
different colours, such as is shown for the word "PENI~IES," I 1. Other graphic areas could also be dirr~ liated by colour, or texture, or a combination. Texture dirr~ nces .
210~33 are not illustrated in this example, but as a colour example, background of area 44 is here shown red, for quarters; for consistency of the child's understanding, area 44a under text 54d, "Put a quarter in the rectangle," is shown the same colour red; similarly the other d~ v~ ations would each have a colour, although they are not shown in the illustration.
The ~lph~nllmeric text instructions are sequentially numbered, and s~quenti~lly generally indicated on Figure 1, from "1.", indicated as 51, through "6.", ,n d as 56. Either the child can read enough to understand the text associated with each number, such as text Sla, "Place the dollar sign in the cloud," or there is an adult or older child guiding. The first case is often ~IGr~llGd since it will mean the child can learn alone or in groups of peers; on the other hand learning can be more enjoyable in groups with mi~m ~~h~d age, since other forms of learning are frequently also stimu~ d by dir~ ,..t;als in knowledge among the group; the.tl~le both possibilities are important, the first generally for older children and the second for younger. :The child having opened the board and read or heard the instruction Sla, . .: - . . .
"Place the dollar sign in the cloud," she/he then has recourse to resburce well 30 on Figure 2, extracts the piece 31d, and places it on the identical symbol Slb under instruction 51 on Figure 1. Piece 31d may be p~vidcd with a fa~l ning means, such as VelcroTM, and fastened to symbol S lb; or may merely sit freely on the surface of board 10.
Likewise the other ~ --bc,~,d instructions shown on Figure 1 as 51, 52, 53, 54, 55, and 56, are read or heard and followed by the child. These actions are largely self- :
çY~ ' y. However note that the se~ e ~re that they are p-~,seated in has been chosen carefully.
First the child is shown the notation "$" in symbol S lb and "¢" in 52b. This isthe logical beginning since the child, through use of the invented system, will achieve an :~
n~ ~ ~ing of the abstract relation between change and dollars, and hence how smaller '"~ '~
~:' '''.'' -",'..', r- 2108333 amounts of money make up larger amounts. Like the main topic being summari~ed in the introduction to an essay, this goal of the notational relation of lesser to greater amount is being shown at the outset as the object and focus of the exercise.
Next the child is shown an example of this equivalence io full money notation in 53, "3. Match the two clouds that are the same," where 12, "25¢" is shown equivalent to 14, "$.025". The child retrieves pieces 31a and 31b from resource well 30 (Figure 2) and places them on the correct graphics 12 and 14 respectively on Figure 1.
The next step is to have the child physically manipulate examples of the concrete tools required to use this equivalence, in step 4, indi~P,d generally as 54, with 54a, "Put a penny in the l~ anglG;~' 54b, "Put a nickel in the rectangle;" 54c, "Put a dime in the rectangle;" and 54d, "Put a quarter in the rectangle." In each of these the abstract notational equivalence is stressed by having both notations available, such as the " I ¢" in box 40a and the "$0.01," ;r ~ as 40b, ullde -a~h After this the child is ready to ;~ -lC of ~e the learned abstract equivalence by means of the learned physical 'r ~ S-l~ in step 5 ir "~ ' ~,d generally as 55, by following SSa, "Place the coins on the a~pliale chart;" S5b, "Use Pennies to make $1.00;" S5c, "Use Nickels to make$1.00;" 55d, "Use Dimes to make $1.00;" and 55e, "Use Quarters to make $1.00." ;
Finally, in step 6 generally - " - ., as 56: "6. Pick up one card. Use any co.lll~ ath, n of coins to make up that amount," the chi1d is shown that this e~lui~al~,nce is a continuous r~ ti,rl; that is, can be used to co. : u.;l any portion of a dollar using partia1 amounts of change. This is the final step and m~ ring it will allow the child (or other appl~,p-iate user) to interact in the world of buying and selling. For this most important final step, a knowledge of slmple addition math~ "-s is probably ~-: yfor the child working alone (al~hough, as will be rii~cu~ced in a moment, the evaluation cards generally indicated as 35 and 39 on Figure 2 will allow self-çh~l i ~g, and tll~ ,ror~
learning of -~hP.m~ir~1 con.~ ); or an adult or older child could assist.
2~Q~33 The evaluation cards 35 and 39 (and others not shown) are important to the final learning of partial equivalence and require some explanation: each is matched with a question card; for instance on Figure 1, question card 37 (also shown exploded from well 32 on Figure 2) sits waiting to be picked up; for each such question card an evaluation card exists; in this case evaluation card 39 corresponds, shown exploded from storage well 34 on Figure 2. The evaluation cards are not visible on Figure 1 because they are to be used for rllPcl~ing (and learning) only after an attempt is made to "puzzle out" the answer by placing coins. The question cards such as 37 shown on Figure I can be of varying levels of dirr~cully; question card 37 with text~ 0.82. ~/] Use Two of ~ach Coin" is a relatively easy card since explicit directions are given which will lead to the answer. The child merely finds two of each coin-piece, and places them onto the board 10 (this p-~CcJU~b iS not shown). If the child has difficulty with this, or at the discretion of a teacher, parent, or other child, the evaluation card 39 can be consulted for the answer.
The answer can be shown on an evaluation card by colouring the graphics of ~ :
the required number of coins; on evaluation card 39 this is shown as green, with 39b, 39c, ~:
39d, and 39e indir~ing two green one cent, five cent, ten cent, and twenty-five cent g., i(, ~ ,ti~,ly.
An h~t~ ,i,ling point to note about the evaluation cards such as 39 shown e. ~ d on Figure 2 is that the sum of the illu;~ graphics for each coin type (coloured and non-coloured together) is not a dollar or decimal fraction or multiple of a dollar. For instance, there are eight "10¢" graphics on e~. ' on card 39, not ten (the sum of two coloured graphics 39d and six non-coloured graphics 39n); similarly there are three total "2~¢" ~ s, not four; seven "5¢" graphics, not twenty; and there are eight ~: ~
~1¢~ g pl~' ~r, not 10 or 100. This demonstrates the actual situation that the child is faced ;
with in the real world: making a single amount, such as the "$0.82" ~ dir~ed, from a varying number of each type of coin; which is what one generally finds in one's pocket or 21~33 purse. Thus a more difficult question card, but which logically follows, is that shown as 33, with associated evaluation card 35, on Figure 2: the amount, "$().41," is asked for on question card 33, but no text is provided to indicate what coins are to be used. However, coll~,;,pol.(li.~g evaluation card 35 shows one of each coin graphic shaded (here pink), which is similar to the pattern taught explicitly by question card 37, "Use Two of Each Coin." Note that on evaluation card 35 the sum of the illustrated graphics for dimes is again not a dollar, but 60¢; and furfher that this is different from the other evaluation card shown, 39, where the sum of the "10¢" graphics coins is 80¢. Similarly the "25¢"graphics coins sum .lirf~ y for each of evaluation cards 35 and 39; the first to 50¢ and the second to 75¢.
Thus the final concept, that of choice within a structure that has several possibilities, is asked for in the question cards such as 33 and 37, optionally guided by the text such as "Use Two of Each Coin" (which could of course be, "Use One Of Each Coin" or other more complex mixtures); ir~iic~ufed further by the differing sizes of the fileld that each d~ ation of coin is ~ by on the evaluation cards such as 35 and 39; and checked by the colour-coded graphics on the evaluation card, such asde~.ibed above for card 39.
The physical medium that the graphics such as 12 and 14 on board 10 in Figure I are printed on is not ~,~;a~ 1 'y ~ po-~ to the functioning of the invention, so that other emho~ such as the lalge leaved book 90 shown in Figure 3, are equaUy possible. Book 90 is shown with pockets 92 on a facing page 93, to store coin-pieces, cards, and so forth (these are not dic f~ on Figure 3). Or VelcroTM could be used for storage of some or all the movable pieces (again, not shown), or any other applvplia~
attachment means. The printing on page 91, such as "l¢" boxes 95, could be of a small enough size (and the page 91 size large enough) so that the entire contents of board 10 from Figure I would fit onto it; or book 90 could have two or more pages (not shown) 210~333 with some of the resources on different facing pages (not shown).
The reader will be aware by this point that a large number of pe.",ul~lions are possible, including fold-out pages and standing display panels, any of which can carry the graphics described or others associated ones a~p.upliate for the invented system. For ihis rea~son the foregoing is by example only, and the scope of the invention should be limited only by the appended claims.
The present invention relates to children leaming to use money and read money notation. This is an important ski]l in our society, and the recent trends towards more abstract handling of money business--such as banking by personal computer and pu~ asillg by charge-cards or electronic direct payments--indicate that even more of this skill will be required in future. Although it might appear, to some, that not using physical ;
money for transactions makes less need for touch-based learning, this is not the case. An abstract tertn can only be manipulated m~ningfully if it accurately l~,pl~iS~ t~ something which is understood very well. For example, a person who has an imperfect grasp of the meaning of dollars, quarters, dimes, nickels, and pennies, and who needs to make a I,lnchase, is more likely to make a reasonably accurate transaction while exrhqnf~in physical money with a real person (whom they can consult for advice, or whose satisfaction with the transaction they can judge by non-verbal body language) than while balancing their check-book or ordering an item from a catalogue.
Thus both physical money m~nipnlations and ~ cnra~ely knowing the names and notation systems of coinse are necessary to co~n~ ,hend and use the money system of the real world. No previous teaching system appears to exist that satisfies thisre4ui.~,.l,ent to the extent that the present invention will disclose, ~lthough several existing patents address some aspects and will be briefly reviewed below; several are for speciqli7çd sihl ~ioll~, such as for slow-learning children or retarded adults.
Of largelyh;~toli-~' interestarethetollowing: Fisher, 1877, U.S,~188,505, (in what may be the shortest patent on record,) specifies and claims cardboard coins; but ;
how to use them or name them is not addressed. Anderson in 1932 (C:~n ~ n #393,364) shows a cut-out form with numbers written on it; the answers are written into holes in the form and co~ a,bd with the reverse side of the form. No action similar to real-world 2108~33 money-exchanging is provided. Westzstein, Canadian #476, 827, in an ingenious disclosure that may still have relevance for certain situations, claims numbers that are made up of multi-coloured pieces, such that the number of pieces equals the digit being learned; for instance, the numeral "9" is constructed of 9 coloured pieces that iFit together, jig-saw like, to form the digit. While this may make the connection, as he says, of "concrete objects outside the number with the number itself," (by "number itself"
meaning the abstract concept of the number), it still fails to teach either naming or manipulating; in other words, counting and keeping track of counting.
Thomas, U.S. #3,768,177, speci~les "a co~ ,o~it~ a..l..s~ and educational instruction kit for both children and adults," which is largely directed towards the physical layout of the carrying case and drawing tools, coins are addressed only as pictorial rl,~.bsenl~lion of simple addition and subtraction, without hands-on irul~ ~ion or practice in naming or symbol--~cogllilion. Comeaux & Ritchie, U.S.#4,775,321, specify a "System For Teaching Money Values" which is shown as alinear method of ordering items and their money value from smallest to largest; the example is a series of envelopes housed in a box and separated by file-cards. This is s l ~ -lly more complex than is needed for initial recognition usage skills, entailing a record-keeping ''Idbo ~' y" on the file dividers, and would be more a~prt~p. for older children, perhaps, once the basic skills were .lla~t~,~.,d.
Of patents al F h.g to address these basic skills in a s~st~ atic way, two are co~c~ y similar enough that they may be di~cucsed together: H~' qllict~ U.S.
#3,690,017; "Coin Value Teaching Device," (1972) and Shank, C~~ ~ii ~~ #1,212,229, "System for Teaching Coin 12el ~~ion~, s," (1986), both show a 1~ lvulal board with numbers on it that can be covered by a form fitting overtop that bears one or more coins or coin symbols e~ ecWcd or g. r~ ly c..ll~laL ~ ~ In each case several forms are provided, of several sizes, and the child or other user (Holmquist suggests retarded 2 1 0 ~ ~ 3 3 ~ ~
children) learns how many digits are l~nderneath a form of a given size which has a given coin or coins on top. A major and insurmountable d~ l)ack of this al),UIUaCII iS its ~ :~
unreality: the child is being asked to conceptually accept that a (say) six-inch by four-inch pieee of plastic with a quarter glued into it (or drawn on it), or 25 pictures drawn on it, -each of 1¢, is a coin-replica now but is not one later in "real interactions." ;
Finally, Yamin, U.S. #4,752,227, discloses a board game that has recesses that eoins are slipped into. While actual eoins ean be manipulated in this invention, several d-~wl,acks appear: the most important of these is that eonceptually it's still a step ~ ;~
removed from the real-world situation. One face of the board shows gr~phir~lly defined areas that have coin-spaces both for a series of small deno~ -alion eoins and for a larger eoin or bill equivalent to their total. The user plaees eoins into the small series, and then ;
àn equivalent eoin or bill into the adjaeent single spaee. The ehild or other user is ~;
"efol~i being asked to plaee twiee the amount that a transaetion would take into the defined area, in order to "learn" that one part of the area is e~ui~ alc.~, in money terms, to the other part. Fu~ o~, there is no provision for naming in Yamin: the board is :
un~ ,nlil,gly, and col.rus...~ly, made up of a large number of similar sized l~lc~.gles -1~ - g round I~CS5l.J~S (or holes, in one ~ bod ). Scal~,llh~g among these to find, ~ ;
say, where to put 10 pennies (and a dime) eould be a rl~.Sl- t g eYp~ri~n(e7 and not one ~-that would be useful in real-world l, u..s. A separate section on the baek faee of the board, in one err~' o~' --- t, speeifies eards that show how to "build" an amount and place it into similar l~,c~ js - -s; the example given is making 92¢ from, as shown on an accompanying card, a half dollar, a quarter, a dime, a niekel, and a eent. No ehoiee is provided; whieh, again, means this is a '~ g" situation: for instance, how often have any of us been asked to pay 92¢ for an objeet in a store and reaehed into our poeket and pulled out--oh what good luek!--exactly a half-dollar, a quarter, a dime, a niekel, and a ~ ~
eent? ~ -,~ 210~3 :
In contrast, the present system will provide the child with a learning situationthat can be used with a teacher, alone, or with a group of children. The child can learn to recognize money notation ("$" and "¢"); read fhe words S'penny", "nickel", "dime" and "quarter"; and visually recognize the coins co~ .por.dillg to the names. With this invention the child can learn to define and explain the equivalence of only pennies to one dollar (i.e., 100), then nickels to one dollar (20,) dimes (10,) and finally quarters (4). And the child can learn to use any coll-b;nd~ion of coins to add up to one dollar or less. The situation is not competitive, and will be un~ s~..lll;d and enjoyable, and any child using it, either alone or with others, can work at their own pace. Sufficient latitude is provided for creative solutions--choice, in other words--while still providing a framework that defines what needs to be done and how to do it. The visual aspect of the child's need is cc. ~. ~d, and i~ltC.~,;.lif~g symbols, in various colours, such as clouds, boxes, triangles, circles, coloured text, and so on, are used liberally.
In sum, the present invention provides for a display such as a board-game (or single- or multi-leaved large book) showing words, numbers, graphic symbols, andinsl.u.,i - -- on the printed surface and having a resource pouch or box with I
coins and graphic symbols. Notation is taught by ~ ' g a desigr~d graphic resource, such as a plastic piece showing "$" inside a cloud, with the same graphic on the board; a VelcroTM or other ~ft- ~ may opfinqqlly be used. Coin-pieces are matched with labelled spaces on the printed surface to a ~S~ ~ the correct notation, words, and numbers with he coin-piece. Then ~.PIJIUPI'-'- numbers of coin-pieces are placed in graphics ûn the printed surface tû show the addition and equivalence of each coin to a dollar. The se~_ e of events is L~lpc)llallt~ and p~uceGds logically to give the child an integrated und~rstq~ of symbolic notation and the medium of physical ~ ipulq-fion.
Practice and self-testing of the kno~. Icdg., is also ~ as a series of matched cards, with an amount shown on a first card, such as 82¢ (optionally with an ~ ;~
' ~"'; "
2~0~33 instruction, such as "use two of each type of coin.") The child forms 82¢ by placing a~ l iate coin-pieces on the printed surface, and then evaluates by checking a second (matching) card showing how this amount can be achieved in coin-pieces. The graphic -make-up of these second (evaluation) cards indicate to the child that this isn't the only way of making up the answer, given a reasonable number of different coins. While the card gives guidance as to how to that answer could be achieved in one way, it simultaneously sets out the field that the child can use to choose other ways of achieving the same answer in future. -In this way a cooperative learning technique made available, and the children can read and follow instructions at an activity center with no teacher present, even inc!ll-lin~ the evaluation answer key just described. The child then is self-teaching, self-~sP~Sing and self-correcting, so that the method can be used at home or at school, with or without adults, and alone or with other children, in a supportive and interactive group.
An object of the present inven~ion is to provide for a method of learning to useand refer to coins in two n~"dtio.lal systems, the unit of the first notational system referring to a smaller amount of money than the unit of the second notational system; the learning to occur in the following order: to recogni~e and name a notational symbol colresponding to each of the two notational systems; that the two different systems can be ~;
used to express the same amount of money; to a~cocic~ç the physical manipulation of a coin or coin-replica sinlult~-neously with both notational systems; to calculate and physically as~ 'e the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and to calculate and physically ass.,.llblc the amount of coins or coin-replicas of a mixture of denominations that sum to a l~ue~ted amount. Optionally, the learning occurs by following se~luenti~lly l..ullb~ ,d text instructions given on the printed surface or on accompanying cards giving ~ -instructions to match movable pieces bearing graphics onto a printed surface bearing - ;
~; ~10~333 ~ ~
approximately identical graphics. There may be additional final step of checking that the ~ ~ -calculation and assembly of the requested amount has been performed correctly. The method may be used for cases in which the first system is the cent system and the second :
system is the dollar system; the first notational symbol is "¢" and the second notational ~ ~ :
symbol is "$"; and the coin denominations are pennies, nickels, dimes, and quarters.
A further object is to provide for an apparatus for learning to use and refer to ~ :
coins in two notational systems, the a~pa~ s colnyli~illg~
1) a printed surface such as a games board surface or one or more pages in a .
book; the printed surface i,~ h~ted with: :
text giving names of coins; graphics c~ g notational symbols for each no~ational system; a graphic of an amount of money rendered:~
using the first notational system; a graphic of the same amount of money rendered using the second notational system; separate graphics each conl~ ing one symbol for one denollli.ldlion of coin; several separate gMphics each c~ g several identical symbols for a different single dellolllillalion of coin, the number of such symbols in each case being that whose value summed equals the unit value of the second l'ot'~ionql system; a graphic to indicate where a deck of cards is to be placed; and se,,_ ~ -'ly l~.llllbe~d a.~p~ 'r text giving instructions;
2) a storage area such as wells in a box, or pockets in a book page, contahling movable pieces, the pieces co..-l.. ;s:~g~
a plurality of coins or coin-replicas of each denomination of coin; a graphic of each of the notational symbols; a graphic of the same amount of money rendered using the first notational system as listed for the printed surface; a gMphic of this same amount of money :~
7 ;~
~ ~,, --' 2tO8~33 ~ ~
~, rendered using the second notational system; a deck of question cards ; '~ -bearing single amounts in either notational system, the cards optionally bearing text inrlir~a~in~ how the amount can be arrived at using cc.lllbh.ations of coins; and a group of evaluation cards, each of which contain colour-coded coin graphics indjr~tinE~ how a combination of denominations of coins may be summed to the amount on the corresponding question card.
In this apparatus there may be several identical graphics for each type of coin displayed on each evaluation card, and an ai)~J~pliatt, number of graphics for each type of coin that sum to the amount on the corresponding question card may optionally be a uniform different colour from those graphics not required to sum to the amount. There may be different amounts of coin graphics on different evaluation cards, and optionally the total value of the graphics for any one denomination on any evaluation card does not sum to the unit value of the second notational system or a decimal fraction or multiple :.
thereof; in order to help a person using the evaluation cards learn: a) that variable numbers of coins of various deno - ions are used in arriving at the sum on the question card; b) that there is more than one way to arrive at the sum; c) and that not all denominations of coins will always be available to make up the sum. Optionally, the movable pieces are stored or affixed by pockets or VelcroTM, or other known ,.~1 ~!....e means.
.;", ., DETAILEDDESCRIPTIONOFTHE INVENTION
For this description, refer to the following rli~g.L .,.c, wherein like numerals .
refer to like parts:
Figure 1, portion of a first embodiment of the invented system; game board; plan view; ~ .
8 ~ ~
'''..,' ~'' -' 2 1 ~ 8 3 3 3 Figure 2, storage box for game board of the embodiment of Figure l, .
with question and evaluation cards exploded; plan view; and :~
Figu}e 3, second embodiment of the invented system, open book;
perspective view. .
A first embodiment of the invented system is shown as Figures l and 2 talcen together. In Figure I can be seen a printed games board, indicated generally as 10, which has printed graphics such as clouds 12 and 14 and corresponding printed ~1rh~nllmPric text instructions such as "3. Match the two clouds that are the same," generally indicated as 53. Board 10 is here illustrated as the folding type, along dotted center-line 18, and when in storage will collapse and fit into the top of box in Figure 2, illustrated generally as 20, and will cover, (in the manner ~;u ~ lla~ily used for folding board games) the otherwise open resource wells 22, 24, 26, 28, 30, 32, and 34, all visible on Figure 2. Well 22 contains penny-pieces 23; these penny-pieces will customarily be of cardboard or plastic with a penny-like graphic, although the use of real pennies is also possible.
Likewise well 24 contains nickel-pieces 25; well 26 contains dime-pieces 27; well 28 contains quarter-pieces 29; well 30 contains cloud graphic pieces 31a, "2~¢," and 31b, "$.025," and notation graphic pieces 31c, "¢," and 31d, "$"; well 32 contains question cards such as in(lic~Pd generally as 33 and 37; card 37 of which is shown enlarged and e~, ' c d e ~ out of well 32; and well 34 contains evaluation cards indic~t~Pd generally as 35 and 39; similarly evaluation card 39 is enlarged and exploded from well 34.
In practice a child will remove board 10 from inside box 20 and open it to the position in Figure 1. (A top is not illustrated for box 20 but can be S~sumpcl) and assumed to have been removed). The board l0 will be large, perhaps 2 feet by 2 feet, and: ~,ly arranged, including designs such as border 19 and letters of some words ~; :
different colours, such as is shown for the word "PENI~IES," I 1. Other graphic areas could also be dirr~ liated by colour, or texture, or a combination. Texture dirr~ nces .
210~33 are not illustrated in this example, but as a colour example, background of area 44 is here shown red, for quarters; for consistency of the child's understanding, area 44a under text 54d, "Put a quarter in the rectangle," is shown the same colour red; similarly the other d~ v~ ations would each have a colour, although they are not shown in the illustration.
The ~lph~nllmeric text instructions are sequentially numbered, and s~quenti~lly generally indicated on Figure 1, from "1.", indicated as 51, through "6.", ,n d as 56. Either the child can read enough to understand the text associated with each number, such as text Sla, "Place the dollar sign in the cloud," or there is an adult or older child guiding. The first case is often ~IGr~llGd since it will mean the child can learn alone or in groups of peers; on the other hand learning can be more enjoyable in groups with mi~m ~~h~d age, since other forms of learning are frequently also stimu~ d by dir~ ,..t;als in knowledge among the group; the.tl~le both possibilities are important, the first generally for older children and the second for younger. :The child having opened the board and read or heard the instruction Sla, . .: - . . .
"Place the dollar sign in the cloud," she/he then has recourse to resburce well 30 on Figure 2, extracts the piece 31d, and places it on the identical symbol Slb under instruction 51 on Figure 1. Piece 31d may be p~vidcd with a fa~l ning means, such as VelcroTM, and fastened to symbol S lb; or may merely sit freely on the surface of board 10.
Likewise the other ~ --bc,~,d instructions shown on Figure 1 as 51, 52, 53, 54, 55, and 56, are read or heard and followed by the child. These actions are largely self- :
çY~ ' y. However note that the se~ e ~re that they are p-~,seated in has been chosen carefully.
First the child is shown the notation "$" in symbol S lb and "¢" in 52b. This isthe logical beginning since the child, through use of the invented system, will achieve an :~
n~ ~ ~ing of the abstract relation between change and dollars, and hence how smaller '"~ '~
~:' '''.'' -",'..', r- 2108333 amounts of money make up larger amounts. Like the main topic being summari~ed in the introduction to an essay, this goal of the notational relation of lesser to greater amount is being shown at the outset as the object and focus of the exercise.
Next the child is shown an example of this equivalence io full money notation in 53, "3. Match the two clouds that are the same," where 12, "25¢" is shown equivalent to 14, "$.025". The child retrieves pieces 31a and 31b from resource well 30 (Figure 2) and places them on the correct graphics 12 and 14 respectively on Figure 1.
The next step is to have the child physically manipulate examples of the concrete tools required to use this equivalence, in step 4, indi~P,d generally as 54, with 54a, "Put a penny in the l~ anglG;~' 54b, "Put a nickel in the rectangle;" 54c, "Put a dime in the rectangle;" and 54d, "Put a quarter in the rectangle." In each of these the abstract notational equivalence is stressed by having both notations available, such as the " I ¢" in box 40a and the "$0.01," ;r ~ as 40b, ullde -a~h After this the child is ready to ;~ -lC of ~e the learned abstract equivalence by means of the learned physical 'r ~ S-l~ in step 5 ir "~ ' ~,d generally as 55, by following SSa, "Place the coins on the a~pliale chart;" S5b, "Use Pennies to make $1.00;" S5c, "Use Nickels to make$1.00;" 55d, "Use Dimes to make $1.00;" and 55e, "Use Quarters to make $1.00." ;
Finally, in step 6 generally - " - ., as 56: "6. Pick up one card. Use any co.lll~ ath, n of coins to make up that amount," the chi1d is shown that this e~lui~al~,nce is a continuous r~ ti,rl; that is, can be used to co. : u.;l any portion of a dollar using partia1 amounts of change. This is the final step and m~ ring it will allow the child (or other appl~,p-iate user) to interact in the world of buying and selling. For this most important final step, a knowledge of slmple addition math~ "-s is probably ~-: yfor the child working alone (al~hough, as will be rii~cu~ced in a moment, the evaluation cards generally indicated as 35 and 39 on Figure 2 will allow self-çh~l i ~g, and tll~ ,ror~
learning of -~hP.m~ir~1 con.~ ); or an adult or older child could assist.
2~Q~33 The evaluation cards 35 and 39 (and others not shown) are important to the final learning of partial equivalence and require some explanation: each is matched with a question card; for instance on Figure 1, question card 37 (also shown exploded from well 32 on Figure 2) sits waiting to be picked up; for each such question card an evaluation card exists; in this case evaluation card 39 corresponds, shown exploded from storage well 34 on Figure 2. The evaluation cards are not visible on Figure 1 because they are to be used for rllPcl~ing (and learning) only after an attempt is made to "puzzle out" the answer by placing coins. The question cards such as 37 shown on Figure I can be of varying levels of dirr~cully; question card 37 with text~ 0.82. ~/] Use Two of ~ach Coin" is a relatively easy card since explicit directions are given which will lead to the answer. The child merely finds two of each coin-piece, and places them onto the board 10 (this p-~CcJU~b iS not shown). If the child has difficulty with this, or at the discretion of a teacher, parent, or other child, the evaluation card 39 can be consulted for the answer.
The answer can be shown on an evaluation card by colouring the graphics of ~ :
the required number of coins; on evaluation card 39 this is shown as green, with 39b, 39c, ~:
39d, and 39e indir~ing two green one cent, five cent, ten cent, and twenty-five cent g., i(, ~ ,ti~,ly.
An h~t~ ,i,ling point to note about the evaluation cards such as 39 shown e. ~ d on Figure 2 is that the sum of the illu;~ graphics for each coin type (coloured and non-coloured together) is not a dollar or decimal fraction or multiple of a dollar. For instance, there are eight "10¢" graphics on e~. ' on card 39, not ten (the sum of two coloured graphics 39d and six non-coloured graphics 39n); similarly there are three total "2~¢" ~ s, not four; seven "5¢" graphics, not twenty; and there are eight ~: ~
~1¢~ g pl~' ~r, not 10 or 100. This demonstrates the actual situation that the child is faced ;
with in the real world: making a single amount, such as the "$0.82" ~ dir~ed, from a varying number of each type of coin; which is what one generally finds in one's pocket or 21~33 purse. Thus a more difficult question card, but which logically follows, is that shown as 33, with associated evaluation card 35, on Figure 2: the amount, "$().41," is asked for on question card 33, but no text is provided to indicate what coins are to be used. However, coll~,;,pol.(li.~g evaluation card 35 shows one of each coin graphic shaded (here pink), which is similar to the pattern taught explicitly by question card 37, "Use Two of Each Coin." Note that on evaluation card 35 the sum of the illustrated graphics for dimes is again not a dollar, but 60¢; and furfher that this is different from the other evaluation card shown, 39, where the sum of the "10¢" graphics coins is 80¢. Similarly the "25¢"graphics coins sum .lirf~ y for each of evaluation cards 35 and 39; the first to 50¢ and the second to 75¢.
Thus the final concept, that of choice within a structure that has several possibilities, is asked for in the question cards such as 33 and 37, optionally guided by the text such as "Use Two of Each Coin" (which could of course be, "Use One Of Each Coin" or other more complex mixtures); ir~iic~ufed further by the differing sizes of the fileld that each d~ ation of coin is ~ by on the evaluation cards such as 35 and 39; and checked by the colour-coded graphics on the evaluation card, such asde~.ibed above for card 39.
The physical medium that the graphics such as 12 and 14 on board 10 in Figure I are printed on is not ~,~;a~ 1 'y ~ po-~ to the functioning of the invention, so that other emho~ such as the lalge leaved book 90 shown in Figure 3, are equaUy possible. Book 90 is shown with pockets 92 on a facing page 93, to store coin-pieces, cards, and so forth (these are not dic f~ on Figure 3). Or VelcroTM could be used for storage of some or all the movable pieces (again, not shown), or any other applvplia~
attachment means. The printing on page 91, such as "l¢" boxes 95, could be of a small enough size (and the page 91 size large enough) so that the entire contents of board 10 from Figure I would fit onto it; or book 90 could have two or more pages (not shown) 210~333 with some of the resources on different facing pages (not shown).
The reader will be aware by this point that a large number of pe.",ul~lions are possible, including fold-out pages and standing display panels, any of which can carry the graphics described or others associated ones a~p.upliate for the invented system. For ihis rea~son the foregoing is by example only, and the scope of the invention should be limited only by the appended claims.
Claims (15)
1. A method of learning to use and refer to coins in two notational systems, the unit of the first notational system referring to a smaller amount of money than the unit of the second notational system; said method consisting of learning in the following order:
to recognize and name a notational symbol corresponding to each of the two notational systems;
that the two different systems can be used to express the same amount of money;
to associate the physical manipulation of a coin or coin-replica simultaneously with both notational systems;
to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount.
to recognize and name a notational symbol corresponding to each of the two notational systems;
that the two different systems can be used to express the same amount of money;
to associate the physical manipulation of a coin or coin-replica simultaneously with both notational systems;
to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount.
2. A method as in Claim 1, in which the learning occurs by following sequentially numbered text instructions given on the printed surface or on accompanying cards; said text giving instruction to match movable pieces bearing graphics onto a printed surface bearing approximately identical graphics
3. A method as in Claim 1, with an additional final step of checking that the calculation and assembly of the requested amount has been performed correctly.
4. A method as in Claim 1 in which the first system is the cent system and the second system is the dollar system; the first notational symbol is "¢" and the second notational symbol is "$"; and the coin denominations are pennies, nickels, dimes, and quarters.
5. A method of learning to use and refer to coins in two notational systems, the unit of the first notational system referring to a smaller amount than the unit of the second notational system; said method comprising:
a printed surface with graphics and alphanumeric text;
movable pieces matched to said graphic areas as indicated by the alphanumeric text; said matching done in the following order 1) matching a first movable piece, bearing a notational graphic symbol representing the first notational system, onto an approximately identical graphic on the printed surface;
2) matching a second movable piece, bearing a second notational graphic symbol representing the second notational system, onto a graphic on the printed surface approximately identical with said second notational symbol;
3) matching third and fourth movable pieces, said third piece bearing a graphic of a numerical monetary amount rendered in the first notational system and said fourth piece bearing a graphic of the same numerical monetary amount rendered in the second notational system, onto graphics on the printed surface approximately identical with the graphics on said third and fourth movable pieces;
4) matching movable coins or replicas of coins of various denominations with graphics on the printed surface representing the same denominations; each of said graphics comprising at least: the numerical value of a given denomination rendered using the first notational system; and the numerical value of the same denomination rendered using the second notational system;
5) matching movable coins or replicas of coins of each denomination to a graphic on the printed surface; said graphic representing the number of coins of the same denomination required to equal one unit of the second notational system; said graphic comprising at least: the numerical value of the denomination rendered using the first notational system; a graphic representing where each coin or coin piece is to be placed, the sum of the values of said coins equaling the unit value of the second notational system; and said unit value rendered using the second notational system; and
a printed surface with graphics and alphanumeric text;
movable pieces matched to said graphic areas as indicated by the alphanumeric text; said matching done in the following order 1) matching a first movable piece, bearing a notational graphic symbol representing the first notational system, onto an approximately identical graphic on the printed surface;
2) matching a second movable piece, bearing a second notational graphic symbol representing the second notational system, onto a graphic on the printed surface approximately identical with said second notational symbol;
3) matching third and fourth movable pieces, said third piece bearing a graphic of a numerical monetary amount rendered in the first notational system and said fourth piece bearing a graphic of the same numerical monetary amount rendered in the second notational system, onto graphics on the printed surface approximately identical with the graphics on said third and fourth movable pieces;
4) matching movable coins or replicas of coins of various denominations with graphics on the printed surface representing the same denominations; each of said graphics comprising at least: the numerical value of a given denomination rendered using the first notational system; and the numerical value of the same denomination rendered using the second notational system;
5) matching movable coins or replicas of coins of each denomination to a graphic on the printed surface; said graphic representing the number of coins of the same denomination required to equal one unit of the second notational system; said graphic comprising at least: the numerical value of the denomination rendered using the first notational system; a graphic representing where each coin or coin piece is to be placed, the sum of the values of said coins equaling the unit value of the second notational system; and said unit value rendered using the second notational system; and
6) matching a combination of different denominations of coins or coin-pieces to corresponding graphics on the printed surface; the total value of said coins being given in advance on a question card; and thereafter optionally checking whether said matching has been performed correctly by consulting an evaluation card comprising a graphic of a specific combination of coins that will sum to the amount given on the question card;
so that a person learning to use coins and coin notation by the invented system will sequentially learn: to recognize a notational symbol corresponding to each of the two notational systems; that the two different systems can be used to express the same amount of money; to associate the physical manipulation of coins or coin-replicas with both notational systems; to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount.
6. A method as in Claim 5, in which the first system is the cent system and the second system is the dollar system; the first notational symbol is "¢" and the second notational symbol is "$"; and the coin denominations are pennies, nickels, dimes, and quarters.
so that a person learning to use coins and coin notation by the invented system will sequentially learn: to recognize a notational symbol corresponding to each of the two notational systems; that the two different systems can be used to express the same amount of money; to associate the physical manipulation of coins or coin-replicas with both notational systems; to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount.
6. A method as in Claim 5, in which the first system is the cent system and the second system is the dollar system; the first notational symbol is "¢" and the second notational symbol is "$"; and the coin denominations are pennies, nickels, dimes, and quarters.
7. A method as in Claim 6, in which the printed surface is a board like a games board, and the movable pieces are stored in wells in a box where the games board is also stored; and in which each of the coin-replicas are a piece of wood, plastic, or some other suitable material of appropriate size and shape, and bearing appropriate graphics, fashioned to represent either a penny, nickel, dime, or quarter.
8. A method as in Claim 7, except that the printed surface is the page of a book, and the movable pieces are stored by pockets or VelcroTM, or other known attachment means such as magnets, on, or in, a page of the book facing the printed page.
9. A method as in Claim 8, in which the printed surface is divided into two or more parts, each of which is printed on a different page of the book.
10. A method as in Claim 9, in which the movable pieces appropriate for each of said printed pages are stored in, or on, the corresponding facing page.
11. An apparatus for learning to use and refer to coins in two notational systems, the unit of the first notational system referring to a smaller amount than the unit of the second notational system; said apparatus comprising:
a printed surface with:
text giving names of coins;
graphics containing notational symbols for each notational system;
a graphic of the same amount of money rendered in each notational system;
graphics containing symbols for different denominations of coins;
a graphic to indicate where a deck of cards is to be placed; and sequentially numbered alphanumeric text giving instructions;
a storage area containing movable pieces, said pieces comprising:
coins or coin-replicas of each denomination of coin;
a graphic of each of said notational symbols;
two graphics of the same amount of money as listed for the printed surface, one in each notational system;
a deck of question cards bearing single amounts and optionally instruction text; and a group of evaluation cards, each of which corresponds to a question card;
whereby a person may, by following said sequentially numbered alphanumeric text instructions, learn:
to recognize and name a notational symbol corresponding to each of the two notational systems;
that the two different systems can be used to express the same amount of money;
to associate the physical manipulation of a coin or coin-replica simultaneously with both notational systems;
to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount.
a printed surface with:
text giving names of coins;
graphics containing notational symbols for each notational system;
a graphic of the same amount of money rendered in each notational system;
graphics containing symbols for different denominations of coins;
a graphic to indicate where a deck of cards is to be placed; and sequentially numbered alphanumeric text giving instructions;
a storage area containing movable pieces, said pieces comprising:
coins or coin-replicas of each denomination of coin;
a graphic of each of said notational symbols;
two graphics of the same amount of money as listed for the printed surface, one in each notational system;
a deck of question cards bearing single amounts and optionally instruction text; and a group of evaluation cards, each of which corresponds to a question card;
whereby a person may, by following said sequentially numbered alphanumeric text instructions, learn:
to recognize and name a notational symbol corresponding to each of the two notational systems;
that the two different systems can be used to express the same amount of money;
to associate the physical manipulation of a coin or coin-replica simultaneously with both notational systems;
to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system; and to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount.
12. An apparatus as in Claim 11 in which the evaluation cards bear colour-coded graphics indicating how a combination of denominations of coins may be summed to the amount on the corresponding question card.
13. An apparatus as in Claim 11 in which the first system is the cent system and the second system is the dollar system; the first notational symbol is "¢" and the second notational symbol is "$"; and the coin denominations are pennies, nickels, dimes, and quarters.
14. An apparatus for learning to use and refer to coins in two notational systems, the unit of the first notational system referring to a smaller amount than the unit of the second notational system; said apparatus comprising:
a printed surface such as a games board surface or one or more pages in a book; said printed surface imprinted with:
text giving names of coins;
graphics containing notational symbols for each notational system;
a graphic of an amount of money rendered using the first notational system;
a graphic of the same amount of money rendered using the second notational system;
separate graphics each containing one symbol for one denomination of coin;
several separate graphics each containing several identical symbols for a different single denomination of coin; the number of such symbols in each case being that whose value summed equals the unit value of the second notational system;
a graphic to indicate where a deck of cards is to be placed; and sequentially numbered alphanumeric text giving instructions;
a storage area such as wells in a box, or pockets in a book page, containing movable pieces, said pieces comprising:
a plurality of coins or coin-replicas of each denomination of coin;
a graphic of each of said notational symbols;
a graphic of the same amount of money rendered using the first notational system as listed for the printed surface;
a graphic of this same amount of money rendered using the second notational system;
a deck of question cards bearing single amounts in either notational system; said cards optionally bearing text indicating how said amount can be arrived at using combinations of coins; and a group of evaluation cards, each of which contain colour-coded coin graphics indicating how a combination of denominations of coins may be summed to the amount on the corresponding question card;
so that a person may, by following said sequentially numbered instructions:
learn the name and symbol of each notational system by matching movable pieces onto the approximately identical corresponding graphic on the printed surface;
learn that the two systems can be used to express the same amount of money by matching movable pieces with the same amount expressed in both notational systems onto approximately identical corresponding graphics on the printed surface;
learn to associate the physical manipulation of coins or coin-replicas with both notational systems by matching movable coins or coin-replicas for each denomination of coin with corresponding graphics on the printed surface that contain the coin value displayed in both notational systems;
learn to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system by matching movable coins or coin-replicas to corresponding graphics on the printed surface that sum to said unit value;
learn to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount by reading a question card and placing an appropriate number of a mixture of denominations of coins onto graphics on the printed surface; and self-check that said question has been answered correctly by reading an evaluation card corresponding to said question card.
a printed surface such as a games board surface or one or more pages in a book; said printed surface imprinted with:
text giving names of coins;
graphics containing notational symbols for each notational system;
a graphic of an amount of money rendered using the first notational system;
a graphic of the same amount of money rendered using the second notational system;
separate graphics each containing one symbol for one denomination of coin;
several separate graphics each containing several identical symbols for a different single denomination of coin; the number of such symbols in each case being that whose value summed equals the unit value of the second notational system;
a graphic to indicate where a deck of cards is to be placed; and sequentially numbered alphanumeric text giving instructions;
a storage area such as wells in a box, or pockets in a book page, containing movable pieces, said pieces comprising:
a plurality of coins or coin-replicas of each denomination of coin;
a graphic of each of said notational symbols;
a graphic of the same amount of money rendered using the first notational system as listed for the printed surface;
a graphic of this same amount of money rendered using the second notational system;
a deck of question cards bearing single amounts in either notational system; said cards optionally bearing text indicating how said amount can be arrived at using combinations of coins; and a group of evaluation cards, each of which contain colour-coded coin graphics indicating how a combination of denominations of coins may be summed to the amount on the corresponding question card;
so that a person may, by following said sequentially numbered instructions:
learn the name and symbol of each notational system by matching movable pieces onto the approximately identical corresponding graphic on the printed surface;
learn that the two systems can be used to express the same amount of money by matching movable pieces with the same amount expressed in both notational systems onto approximately identical corresponding graphics on the printed surface;
learn to associate the physical manipulation of coins or coin-replicas with both notational systems by matching movable coins or coin-replicas for each denomination of coin with corresponding graphics on the printed surface that contain the coin value displayed in both notational systems;
learn to calculate and physically assemble the amount of coins or coin-replicas of a given denomination that sum to the unit value of the second notational system by matching movable coins or coin-replicas to corresponding graphics on the printed surface that sum to said unit value;
learn to calculate and physically assemble the amount of coins or coin-replicas of a mixture of denominations that sum to a requested amount by reading a question card and placing an appropriate number of a mixture of denominations of coins onto graphics on the printed surface; and self-check that said question has been answered correctly by reading an evaluation card corresponding to said question card.
15. An apparatus as in Claim 14 in which several identical graphics for each type of coin are displayed on each evaluation card, and an appropriate number of graphics for each type of coin that sum to the amount on the corresponding question card are a uniform different colour from those graphics not required to sum to said amount.16. An apparatus as in Claim 14, in which there are different amounts of coin graphics on different evaluation cards, and in which the total value of the graphics for any one denomination on any evaluation card does not sum to the unit value of the second notational system or a decimal fraction or multiple thereof; in order to help a person using the evaluation cards learn:
that variable numbers of coins of various denominations are used in arriving at the sum on the question card;
that there is more than one way to arrive at said sum; and that not all denominations of coins will always be available to make up said sum.
17. An apparatus as in Claim 14 in which the first system is the cent system and the second system is the dollar system; the first notational symbol is "~" and the second notational symbol is "$"; and the coin denominations are pennies, nickels, dimes, and quarters.
18. An apparatus as in Claim 14, in which the movable pieces are stored or affixed by pockets or VelcroTM, or other known attachment means.
that variable numbers of coins of various denominations are used in arriving at the sum on the question card;
that there is more than one way to arrive at said sum; and that not all denominations of coins will always be available to make up said sum.
17. An apparatus as in Claim 14 in which the first system is the cent system and the second system is the dollar system; the first notational symbol is "~" and the second notational symbol is "$"; and the coin denominations are pennies, nickels, dimes, and quarters.
18. An apparatus as in Claim 14, in which the movable pieces are stored or affixed by pockets or VelcroTM, or other known attachment means.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA002108333A CA2108333C (en) | 1993-10-13 | 1993-10-13 | Coin learning method and apparatus |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA002108333A CA2108333C (en) | 1993-10-13 | 1993-10-13 | Coin learning method and apparatus |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2108333A1 CA2108333A1 (en) | 1995-04-14 |
| CA2108333C true CA2108333C (en) | 1998-02-03 |
Family
ID=4152443
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002108333A Expired - Fee Related CA2108333C (en) | 1993-10-13 | 1993-10-13 | Coin learning method and apparatus |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA2108333C (en) |
-
1993
- 1993-10-13 CA CA002108333A patent/CA2108333C/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| CA2108333A1 (en) | 1995-04-14 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Sheffield | Extending the challenge in mathematics: Developing mathematical promise in K-8 students | |
| Micklo | Math portfolios in the primary grades | |
| CA2017482C (en) | Educational system for teaching counting and equation solving strategies | |
| US6224381B1 (en) | Educating special needs children about money | |
| Lappan et al. | Getting to know Connected mathematics | |
| US4752227A (en) | Educational game and method of playing the game | |
| CA2108333C (en) | Coin learning method and apparatus | |
| CA1212229A (en) | System for teaching coin relationships | |
| Homan | The child with a learning disability in arithmetic | |
| Nagel et al. | Students’ explanations of place value in addition and subtraction | |
| Murphy et al. | The penny pot | |
| Brittan | An Introduction to Numeracy Teaching. | |
| Hesemann | A spatial model for the cognitive representation of verbal algebra problems. | |
| Travers | Teaching the Euro to Pupils with General Learning Disabilities | |
| Gottlieb | Playing at the crossroads of religion and law: Historical milieu, context and curriculum hooks in Lost & Found | |
| Mortimer | Maths Words for Little People: Money eBook | |
| Taylor | Low-income first and second grade students' engagement in currency exchange: The relationship to mathematical development | |
| Carman et al. | Quick Arithmetic: A Self-Teaching Guide | |
| Clow et al. | Financial Fitness for Life | |
| Thornton | Binary Numbers | |
| Rule et al. | Poetry for teaching elementary mathematics topics | |
| Clements et al. | Reviewing and Viewing | |
| Anderson et al. | Monetary Concepts of Male and Female Kindergartners. | |
| Bryon | How to Pass Graduate Psychometric Tests | |
| Beattie | The number namer: An aid to understanding place value |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| EEER | Examination request | ||
| MKLA | Lapsed |