Patent Application
20120028229
This invention pertains to teaching and learning tools. And more specifically it relates to the use of an augmented or modified simple abacus to be used with and by very young children, and others, to help then learn to count numbers from one to one hundred; and to help them understand the concepts of: addition, subtraction, multiplication, division, the multiplication tables, fractions, and the value of unknown numbers.
And one of these augmentations or modifications to a simple abacus is to place a grid of printed-numbers or a blank sheet beneath ten rows of rods or ropes that have ten beads on each rod or rope, and are located within a strong square or rectangular frame, (with no bottom). And this grid of numbers that are printed on a sheet of paper or plastic like material. can be fastened to the bottom of this frame in a number of ways. Or this sheet can be placed on a desk top or table top, unfastened to the bottom of the frame of a simple abacus. Or the user, or parent, or teacher may later choose to fasten this blank sheet to the bottom of this abacus frame, and to write, or paste, numbers or symbols on this blank sheet at specific locations. And on the rods or rope segments in this simple abacus are normally ten movable beads per rod or per rope segment.
A simple abacus is different from a traditional type of abacus. A traditional type of abacus has beads of two different values on the same: wire, rod, or rope segment. In a traditional abacus a “counting bar” separates the beads on the same rod into a group of ten beads on one side of the counting bar, and one bead on the other side of this “counting bar” But the beads are only given a value when they or their group are pressed against the counting bar. And on the first rod or rope segment, each of the ten beads is given a value of one each, when that bead, or that group of beads touches the counting bar. And the single bead on the first rod is given a value of ten when it touches the counting bar. And in a traditional abacus, the beads on each successive rod or segment of rope is worth ten fold the amount of a similar bead on the preceding rod—when these beads touch the counting bar. If a bead does not touch the counting bar or is in a group that does not touch the counting bar, that bead and that group are of no value. See
A simple abacus has only one type of bead, but has ten beads per rod or per segment of rope. And with a simple abacus, all beads are of the same value, usually one. And with a simple abacus a bead, or a group of beads are only given value, if that single bead, or that group of beads touch the counter bar. And the counter bar is usually the left side edge piece of the frame of that simple abacus, when the rods that hold the beads are in a horizontal direction. And simple abacuses are usually used to help beginning learners learn the numbers from one to ten, by moving one bead at a time from the “non-counter area” (near the right side of the abacus) to the left so that each bead touches the “counter bar” (usually the left edge piece). And on a simple abacus the first rod (which contains the first row of beads), has ten beads on it that help the beginner learn to count from one to ten. And the second rod also contains ten beads. But as these beads are pushed against the “counter bar”, these beads are called beads number: 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20, And the third rod also has ten beads on it. But these beads are not given a value of one each until they are pushed against the left edge piece, or are pushed against other beads that are pushed against the left edge piece. And on a simple abacus there may be a total of ten rods (or segments of rope). And these additional rods are to help the beginning learner, learn the progressive sets of ten numbers in the twenties, thirties, fourties, fifties, sixties, seventies, eighties, and nineties (of which the last number is 100.)
The abacus was used by the Romans at the time of Julius Caesar. The Romans did their calculations on an abacus, and then wrote down the numbers in Roman numerals on paper like papyrus or parchment with ink. Archaeologists have found Roman abacuses made with bronze and wooden frames, with beads made of wrist bones, ceramic and glass beads, and wooden balls, with holes bored through them so they could be moved back and forth on bronze wires, strings, or on wooden or metal rods.
Until the early 1700's Roman numerals and abacuses were widely used in Europe to help keep records of numerical data. Although the Arabs introduced the Arabic system of numerals and the zero, into Southern Spain in the 1200's; the Arabic system of numbers was not widely used until in the early 1700's in many parts of Europe. And with Roman numerals, the abacus was in common use in Europe.
The most common type of abacus used by the Romans and others had a number of parallel rods of the same diameter and length. And these rods were held within a frame. And on each rod were beads of two values. And this type of abacus is what I refer to as a traditional abacus. Please see paragraph [0005] for details.
And one variation of this current invention is what I call an: Augmented Simple Abacus With an Underlying Printed Grid of Numbers or a Blank Sheet; And I use a simple abacus that has only ten beads per rod, (or short segment of rope), and all beads on all rows, have a value of one when they, or their group, touch the counting bar. And when an individual bead, or that group of beads, touches the right hand edge piece (the non-counting bar) these same beads now have no value.
Simple abacuses are used primarily to help young children learn how to count and to learn how to add and subtract small numbers. And in this use of a simple abacus, all beads have a potential value of one. And in using a simple abacus in this way, all ten locations for a counter bead on a rod are to be filled before you (the user) start working with the ten next ten beads on the next lower rod.
I first encountered the wide use of an abacus in September 1946, in Seoul, Korea, by merchants in their shops, while I was in the U.S. Army. And I purchased several abacuses of conventional or traditional type, while I was in Korea. And these Abacuses were a novelty to many of my friends and relatives when I returned to the USA.
And after medical school, I went into the specialty of psychiatry, and then into child and adolescent psychiatry as my chosen area of work. And between 1957 until I retired in 2003, I spent about 80% of my work time in the area of child and adolescent psychiatry. And in addition to the presenting problem of many of the children and adolescents that I saw and evaluated, some of these children and adolescents had significant problems mastering number concepts. And at times I kept an abacus in my desk, and used it to explain our numbering system with a “base of 10”. And I built a number of abacuses from wood strips; plus wooden or metal rods; plus glue; plus brads or screws; plus beads of various types and sizes. But I found that small diameter beads were a real menace for small children when the abacuses were broken, and the beads were released. And small children liked to put these beads in their mouth. And this presented the real risk of a small child choking on an aspirated small bead that was sucked into their lungs. So I then started using larger diameter beads, to greatly lessen the risk of a small child choking on a bead.
And in the more recent models of simple abacuses that I have built, I have used wooden beads of 0.9 inches in diameter, with an 0.25 inch hole bored through each bead. And I have used a sheet of ¼ inch thick plywood cut to a dimension of 18 inches wide and 12 or 16 inches from top to bottom. And along each side edge I have glued and stapled these strips of wood that are 12 or 16 inches long, 0.75 inches wide, and 0.8 Inches high. And each of these two strips of wood have 10 parallel holes drilled through them that are about one inch or 1.4 inches apart along their 12 or 16 inch length. And the two side edge pieces have ten sets of two holes per set that are 0.25 inches in diameter, And the centers of these holes in each of the two edge pieces are about 0.5 inches above the flat surface of the plywood. This 0.5 inches above the flat bottom surface allows these beads to be moved freely back and forth above the printed grid of numbers which is placed on the flat bottom surface. Thus these beads can be easily moved from the counting area to the non-counting area and back. And each set of two holes is in the same axis, so that a single ¼ inch diameter rod easily goes through a 0.25 inch hole in the left and right side edge pieces, on the same axis. And with this arrangement of holes, a ¼ inch diameter rod, rope or cord, can be pushed through each of these ten sets of 2 holes per set. And ten beads can be placed on each rod, or on each segment of rope or cord.
And with the above arrangement, a ¼ inch diameter rope can be threaded through the top hole on the left side wooden edge piece; and then through the ¼ inch holes in ten wooden beads; and then through the top hole in the right hand edge piece. And the rope can then be looped around and then threaded through the second hole from the top in the strip of wood on the right hand edge piece. And then ten beads can be threaded on this rope. And this rope can then be threaded through the second hole from the top in the left side wooden edge piece. And we can then put a second group of ten beads on this second segment of rope, before we thread this rope through the second hole from the top in the right hand edge piece.
And in a similar way the rope or cord can be threaded through the eight other sets of two holes in the left and right side wooden or molded plastic edge pieces. And also ten beads can be placed on each segment of rope or cord, each time it is passed through one set of two holes in the two wooden or plastic side edge pieces. (Or ten wooden or metal rods can be used for this purpose in place of one long rope or cord.)
And to work with the above arrangement, I have printed sheets of paper with a grid of numbers, where numbers from # 1 to # 10 (font size 36) are printed in a left to right manner in the top row of numbers. And numbers # 11 to # 20, are printed in the second row of numbers. And numbers # 21 to # 30, are printed in the third row of numbers. And so on until the last row of beads and numbers contains numbers 91 through number 100. (See
And this simple abacus is augmented by the placement of this printed grid of numbers, so that when a bead, or a group of beads is pressed against the “counter bar” the number appearing beneath, but slightly above or slightly below that bead, gives that bead its number in this arrangement. See
And in the above described arrangement, each printed number appears beneath, but slightly above a counter bead that is in that position in its proper number sequence; if that bead has been moved from the “non-counter group” into the “counter group” (This assumes that the rods that are nearer the top of this simple abacus have been filled.) And the centers of the beads are about 0.9 inches apart when they are on the rope, cord, or on a wooden or metal rod, and have been pushed against the left edge piece (the counter bar). And the centers of the grid of printed numbers are also about 0.9 inches apart on this printed grid of numbers when it is placed beneath the rows of wooden or plastic beads—when the beads touch the “counter bar” (the left edge piece.) See
And for beginners who are just learning about numbers, their value, and how to count them, and how to add and subtract them; they can first work with only the top one row of ten beads, while under the supervision of an older and more knowledgeable person. And in the top row of numbers are #1 to # 10. And after the beginner has mastered the counting of one to ten, and has also mastered, or at least understood the concepts of addition and subtraction of numbers with a sum of ten or less; then a second row of ten beads can be added. The second row of beads are for the ten numbers, # 11 to # 20. And the beginning learner can then use this total of 20 beads to learn to count to twenty; and also to learn to add and subtract numbers with a sum of twenty or under.
And to not overwhelm the beginning learner with the printed grid of one hundred numbers, plus 100 wooden beads; I have made it possible for the parent, tutor, or teacher to initially limit the number of beads to only the first row of ten beads, and ten printed numbers. And slightly later a parent or teacher can add a second group of ten beads to the first group of ten beads. Thus the new learner then becomes exposed to two rods with ten beads per rod. And if the new learner appears to be confused by the large grid of numbers; a plain sheet of white unmarked paper can be placed over the lower part of the grid of numbers to lessen the amount of data that has to be dealt with. Thus if the upper two rows of printed numbers are being worked with, the lower eight rows of ten printed numbers per row can be covered to lessen distraction and possible confusion in the new learner.
There is a potential problem of having a beginning learner being overwhelmed initially by ten rows of beads, with ten beads per row; plus also having printed numbers from # 1 to # 100 potentially beneath each of these many beads. This problem is partly solved by the type of construction this simple abacus, so that the beginning learner may be initially confronted with only one new row of ten beads at a time. This type of construction is to have each wood or metal rod held in position by a wood screw. This allows the parent, tutor, or teacher to add only one row of ten beads at a time, as the student progresses in their mastery of counting numbers, and in their mastering the concepts of addition and subtraction. The same goal of introducing only one set of ten beads at a time can also be achieved by the use of a long cord or long rope. And with this cord or rope, the teacher, parent, or tutor can add one unit of ten beads at a time by threading this cord through one of the holes in the edge pieces, then placing ten beads on this rope or cord; and then threading this cord through the hole on the same axis on the opposite edge piece. The purpose of this is to prevent “overload” and confusion in the beginning learner, by helping them avoid too much information at the starting point. Thus this simple abacus is set up to add ten beads with one wood or metal rod plus 10 beads at a time, (or adding one segment of rope or cord plus ten beads at a time), if the parent or tutor so chooses.
And another part of preventing “overload and confusion”, in the beginner is to also cover the part of the grid of numbers that is not being used, with a blank sheet of paper. This is illustrated in
And as I looked at this grid of ten beads by ten beads, I thought that this type of grid could also be used to teach the multiplication tables, and also be used to teach beginning multiplication and division. But this would require a second and different type of printed augmentation to help teach the multiplication tables, and division and multiplication. And I then used the numbers that are the “products” that are produced when two numbers that are both ten or under, are multiplied together, to construct this second type of grid. (See
In paragraph # 24 above, I have introduced a second type of augmentation that can extend the use of a simple abacus. And this second grid of numbers can help a learner, learn about multiplication and division and the multiplication tables. And the numbers printed in this second grid of numbers can be printed on the opposite side of the sheet of paper that contains the first grid of numbers.
And in thinking about other uses for this simple abacus, it occurred to me that another type of augmentation could be a “Blank Sheet” that is placed under the ten rods with ten beads per rod. And a blank sheet could be filled in by a parent, tutor, or teacher to teach another type of possible subject matter where this simple abacus could be used. And as an example of a possible additional use, is to help the learner understand the concepts of “unknown numbers”, and of simple equations. And in
And the more advanced student could be given the challenge to pick out one of the letters in the top row of: number “1” plus nine letters of the alphabet. And the student is then directed to pick out a number in the left hand column of numbers. And next the student is asked to build a square or a rectangle of beads in the counter area. And this square or rectangle of beads includes the area in the counter area that is defined by the number that has been picked out from the left hand column; and also by the letter of the alphabet that has been picked out. And next the student is asked to count the number of beds in the square or rectangular counter area. And next the student is then asked to set up an equation such as: “5 times T equals 25”. And the student is to solve this simple equation for the value of letter T. And the student is then told the “math rule” that equals divided by equals are equal. Thus the student can divide both sides of this equation by the number 5 And the student then ends up with the answer, which is: T=5. And thus young students can be given the concept of how to solve an equation that contains one unknown number. And they can see and experience this process of solving an equation in a simple and concrete way by the use of a blank sheet that had been written upon by a parent, tutor, or teacher. And this is illustrated in
With my current model of the: AUGMENTED SIMPLE ABACUS WITH AN UNDERLYING GRID OF NUMBERS OR A BLANK SHEET, there are ten wooden beads that measure 0.9 inches in diameter in each row. And there are ten rows of beads from the top row through the bottom row. And the space occupied by the printed grid of numbers occupies the left half of the 18 inch×16 inch plywood flat surface. And the right half of the flat plywood surface has no printed matter on it's surface. But the wood or metal rods, or the segments of rope extend over both the left half and the right half of this flat surface. This allows the user to move the breads on a rod or on a rope from the right half (the non-counting area), to the left half (the counting area) and back, as the beads are manipulated by the user. And this arrangement of having a large blank (unprinted) space on the right hand side of this augmented simple abacus, makes it much easier to present the multiplication tables And this large blank space on the right hand side in the “non-counting” side allows the squares and rectangles of beads on the left hand side (inside of the counter area), can be viewed without obstructions by the non-counting beads.
Thus if the beads are two beads wide and two beads high in the counting area (contacting the left edge piece), the number 4 will appear above the second bead in the bottom row, if this second type of printed grid lies under the beads in the counting area. And if the beads in the counting area are four rows high with four beads per row, the number 16 will appear above the forth bead in the fourth row—with this second type of printed grid of numbers. And the slightly advanced learner can see in a “concrete” way how multiplication, division, and the multiplication tables work. See
In a typical abacus, and also in this simple augmented abacus, the beads that have no value are pushed away from the “counting bar”. And the beads have a value of one or more per bead are pushed against the counting bar. In this current design of an augmented simple abacus, the left wooden edge piece is used as the counting bar. And for beads that are neutral, or are of no value, these beads are pushed against the right side wooden edge piece (the non-counter bar).
The reasons for such a large working surface (18″×16″) are explained below.
1.) For beginning learners, of three, four, and five years of age, they appear to learn better and quicker from large items, large images, or large objects; than from small Items, small images, or small objects;
2.) A large space is needed to accommodate 100 large wooden beads of 0.9 inches in diameter for each bead; Plus space is also needed for one hundred numbers. Plus space is also needed in the “non-counting” area on the right hand side of the abacus, to temporarily store the beads that are not being actively used.
3.) And for beginning learners I want sufficient space above the flat plywood work surface or a flat desk top, for the “non-counters” to be pushed and stored on the far right side, to make it clear to the user that for the moment these beads are of no value, and are being put in an “out of the way place” for the moment.
A significant part of the background for this invention is my interest and my participation as a consultant with 64 Child Day Care Centers in the City of San Fernando, in La Union Province, in the Philippines for the past five years. These 64 Child Day Care Centers together enroll about 4000 children per year who are three thru six years of age. In the Philippine Public Schools, they have no kindergarten. And children start first grade at six or seven years of age. And many communities have a large number of Child Day Care Centers. Some of these Child Day Care Centers are privately owned and operated; and others are partly locally tax supported and partly supported by tuition.
Prior to five years ago, I was involved with two public schools in San Fernando, La Union Province, in the Philippines, to evaluate the benefit of some of my ideas and related materials that I had developed to help young children learn to read English words by a phonics based method. And several children in the community of San Fernando, La Union, were tutored at home from age four years by this method by their parents. And these children made amazing progress in learning to read English words and in learning English phonics when they were started at four years of age with these two types of reading materials for four or five days per week for two years at home. And when this became known by the local Rotary Club, these Rotary Club members established a literacy committee to look into what should be done with this knowledge. And some of these literacy committee members contacted 25 of the 64 Child Day Care Centers in San Fernando, La Union, to see if they were interested in using this method to have the children in their Child Day Care Center learn English phonics and also learn some English words by these methods. And I was asked by e-mail by some of the members of this literacy committee, if I would participate in setting up a program to help teach these pre-school age children English phonics and to read some English words by these methods. And I was agreeable to do this, with some help from local educators. And I supplied two types of teaching materials, and explained to about 100 child day care workers, and educators, how to use these materials. And this was done with the understanding that at some point in the future, we would test their graduates from Day Care to see how well they had learned English phonics and some English words. And this was a very successful effort on the part of many involved persons. (Some of the details of this are present in my pending patent application: “Progressive Synthetic Phonics”, which has been given application Ser. No. 12/589,878.)
But in recent months I have been thinking, about the pre school age children in these 64 Child Day Care Centers. And I thought: “Wouldn't it be nice if these wonderful child day care workers could also teach some of their three thru six year old children, the numbers from one to one hundred, and also teach them some of the simpler concepts of addition and subtraction?” And as I thought about this, I thought the best way to do this with three, four, and five year old children was with a large simple abacus, that was modified or augmented to meet the developmental needs of very young children.
And as I thought about this, I thought that one of the problems was that many of these 4000 children from three years to six years of age, don't even know their numbers from # 1 to # 20. Therefore, a simple abacus must be augmented or modified so that each very young child of 3 or 4 years of age, could clearly see the relationship between the number of beads in a row, and also see the written number symbol for that number above each bead, in a row of ten beads. Thus the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 should be written slightly above (or slightly below) each bead in the top row of ten beads that are in contact with the left edge of the abacus frame (the counting area). And printed numbers: 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 should be printed in the second row of numbers, on the same sheet of paper. And this printed grid of numbers should be placed beneath the first and second rows of beads that contact the left edge piece of the frame in “the counter area”. And the other eight lower rows of ten beads per row should have their numbers printed slightly above or slightly below each bead. in a similar manner; (when these beads are pressed against the left edge piece.)
And as I thought about this, I thought that perhaps I should just have sheets of paper printed so that the grid of written numbers, from one to one hundred, appeared in ten rows of numbers underneath (but above or below) each of the 100 large beads in ten rows of beads that had ten beads per row. And in this way, each bead was represented by its own particular number. And that the child care workers could be shown how to use this system to help children understand or comprehend the written numbers, from number one to number 100. And that the child day care workers, parents, or teachers, could also be shown how to use this modified or augmented simple abacus to help young children learn some of the concepts of simple addition and subtraction.
And I then thought it was appropriate to see if anyone else had previously developed this type of augmented simple abacus. And I went to a giant children's toy store. And they had a number of types of abacuses, but none were like my “augmented simple type” of abacus; where a printed grid of numbers was placed beneath the rows of beads, and where the individual numbers appear on a printed sheet, slightly above or slightly below each bead that was located on the left side of the abacus in the “counter area”; and directly or indirectly touching the counter bar.
And I recently gave one of these simple augmented or modified abacuses to my grand daughter and her husband at a family “Mother's Day” get-together to use with their four year old son. And I was very impressed at how rapidly on Mother's Day, he picked up the ideas. And he was able to do simple addition and simple subtraction with numbers below 20 with this simple augmented abacus under the supervision of his mother and/or father on Mother's Day, 2010, with less than two hours of help.
And I then thought I should see how much information I could get from the U.S. Patent Office via e-mail, to start my search as to what had been done previously in this area of modified or augmented simple types of abacuses, to be used by very young children under the supervision of an older person. And later I got help from three libraries in the Kansas City area to pursue my search:
And as I looked at the large size of this simple augmented abacus, I thought that there must be a better way to construct it. And one of the problems was the large size of the sphere like round wooden beads. And to print a bead's given number above or below a bead took up additional space. And as I thought about this, I thought that a bead does not need to have a sphere like shape. And what I was looking for was a better way to utilize the space above the flat bottom surface of the simple abacus. But I wanted this modified bead to be of a large enough size to make it very difficult for a small child to suck it into their throat or lungs. And I concluded that this could be done by having each bead made of molded plastic, and constructed to have a small diameter tube like part permanently attached to a larger diameter disk like part. And one hole would extend through both the tube like part, and through the disk like part. (Please refer to
And as I thought about other possibilities for the printed content of this augmentation to place beneath the beads in the counter area of a simple abacus several additional uses came to mind.
Being a child psychiatrist has some benefit in this area, as you understand better than the average person how the brain and mind of children function at different levels of development. And preschool age children seem to learn and remember best, when they use both their major senses (vision, hearing, touch, position sense, and movement sense); and also when their movement systems, or motor systems such as speech (tongue and mouth movements), hand movements, and larger gross body movements are used.
Thus it looked to me like having young children involved with the movements of the beads on a simple abacus, was a very good way to help young children learn about numbers and the different processes in arithmetic, by manipulating the beads on a simple abacus. And this seeing, touching, feeling, moving, speaking about, and discussing, in a concrete way, both the change in the number of beads, and the changes in the printed numbers in the augmentation beneath the beads in the “counter area” (touching the counter bar.) helped them learn about these numbers, And this caused me to increase the number of types of augmentations that may be helpful in learning math concepts, in a concrete and easy to see and easy to understand way. For this see
As noted previously in paragraphs [0035] to [0038] I have been a consultant to 64 Child Day Care Centers in the City of San Fernando in La Union Province in the Philippines for the past five years. Together these 64 Child Day Care Centers enroll about 4000 children ages 3 years through 6 years. My becoming a consultant to these 64 Child Day Care Centers came about because of my developing two methods to help children learn to read English words by phonics based methods. And because of the success of these two methods of learning to read at home by these two phonics based methods by several pre-school age children in that community; the Rotary Club of San Fernando, La Union proposed that these two methods be used by 25 of the Child Day Care Centers in San Fernando La Union, if I were agreeable to this. (And the number of day care centers using these two related methods to learn to read English words were expanded to 64 about six months later.)
And I said that I was agreeable to this. And I said that I would provide the two types of materials for these two phonics based methods of learning to read English words; with the provision or understanding that each child day care center would test their graduates from day care as to each child's degree of mastery of this phonics based Information prior to the day of each child's graduation from day care.
And both of my methods for helping children learn to read by a phonics based method uses 160 different three letter English words that could be easily illustrated by a simple black and white drawing. And the goal of both of these methods was for the child to be able to learn the most common spoken sound (phoneme), assigned to each of the letters in each of these 160 three letter words. And each child was to also to learn to blend the spoken sounds of two side by side letters together.
And to help implement this testing, I devised 16 different “Six Part Tests”. And each of these 16 “Six Part Tests”, tested a total of sixty areas of knowledge about ten of these 160 three letter words. (Thus 10 words per test, times 16 tests=160 words tested.) Thus each of the 160 three letter words was included in one of these 16 tests.
And on each test sheet, six questions were asked about ten of these 160 three letter words. (Thus the name “Six Part Tests”.) And the questions asked were as follows: 1.) Name the picture of this object or action. 2.) Read out loud the name of ten printed three letter words. 3.) Draw a line between 10 pictures, and 10 printed three letter words that names or describes a picture. 4.) Give the name of one of the letters in a three letter word, and also give the most common spoken sound (phoneme) assigned to that letter. 5.) Give the spoken sound of a consonant blended with a short vowel, (10 of these). And 6.) give the spoken sound of a short vowel and a consonant when these two sounds (phonemes) are bended together; (10 of these).
And after 12 to 18 months of the children and day care center staff working together with these two methods of learning about English words by learning the phonics of these 160 three letter English words, the day of testing by the “Six Part Tests” arrived.
But about 3½ months prior to testing, I gave each child day care center staff person one copy each, of the 16 page “Six Part Tests”. And I told these child day care center staff that they were free to use these 16 test sheets with their children to prepare their children for a test by one of these 16 sheets—to be chosen at random, at the time of graduation from day care. And I also told the child day care center staff that they were free to share copies of all 16 of these test sheets with any parent who desired copies of these 16 test sheets for use at their home with their child.
And what was the outcome of this testing? Five of the 64 Child Day Care Centers chose not to participate in the testing. The 59 Child Day Care Centers that did participate in the testing had a total of 609 of their graduates randomly take one of the 16 “Six Part Tests”. And I thought their graduates did quite well on this testing. Each test had six parts, with ten questions per part. And all correct responses or correct answers earned one point. Thus there was a possible maximum score of 60 points per test; or a maximum of ten points on each of six parts. (See paragraph [0051] for details.)
And each “Six Part Test” has six “sub-tests”, with a maximum score of ten points per sub-test. And when the scores on the six sub-tests of all 609 students were averaged together, the average score on each of the six sub-tests ranged from 7.0 to 8.2. (out of a possible ten points per sub-test). And a few graduates made perfect scores of ten each, on all six sub tests.
And a second testing a year later, near the end of the school year, gave similar results on the testing of this group of San Fernando Child Day Care Center graduates. And I was verbally told by the administrative director of day care for San Fernando that the use of these two methods of teaching children 160 English words, and their phonics, had become an established part of their Child Day Care Center program.
And I was told several years ago by the director of the Child Day Care Centers of San Fernando, La Union, that the testing of each graduate from day care on one of the randomly selected “Six Part Tests” was also now a part of each day care centers work.
And this past spring in 2010, as I was pondering the information on the previous three pages, I had the thoughts: “What could or should be next?” And: “Wouldn't it be nice if there were an effective way to have the child day care workers of the 64 Child Day Care Centers in San Fernando, La Union help three and four year old children learn to count numbers from one to one hundred; and to learn to add and subtract small numbers?” And as I thought about this, I thought that the best and simplest way to do this would probably be to use a “simple abacus”, that had modifications or augmentations added to this simple abacus to help very young children learn to count. And then the questions to myself were: “What types of augmentations should and could be made for a simple abacus for this purpose?” And these questions set off a train of thoughts that led to the ideas and concepts outlined, and described in some detail in this patent application. And these ideas, concepts, or innovations are described in the paragraphs that follow:
Since my primary interest was to help young children learn to count, and to learn to add and subtract small numbers; it was obvious to me that I was not interested in modifying a commercial or traditional abacus.
Thus my interest was in modifying or in developing augmentations for a simple abacus with ten beads per row of beads; and where all beads had a value of one when that bead or its neighboring beads were pushed against the counting bar.
And as I thought about the mental development of the average three and four year old child, many can not count from one to ten; And many 3 year old to 4 year old children do not recognize the visual image of the Arabic numerals from 1 to 10. And many three year old children to four year old children do not understand the verbal or spoken meaning of the numbers seven, eight, and nine. Thus a reasonable goal was to see if some type of augmentation to a simple abacus could enhance the development of this knowledge and enhance the development of these simple skills.
Thus as I saw this question, the challenge was to find a type of augmentation that could or should help “tie together” or “link together” in a child's mind and memory three things: 1.) the concrete meaning of the spoken words: one through ten; 2.) recognize one to ten similar objects in a row (like beads); and 3.) link the spoken numbers 1 through 10 with the same number of concrete objects; and also link these spoken numbers of 1 through 10 with printed Arabic numerals from one to ten.
And all of the simple abacuses that I have previously seen—and that I have built myself (15 to 20) in the past 40 years; these simple abacuses did not have a way to illustrate the printed Arabic numerals from one to ten, and then from one to twenty, and then from 30 to 100 in a progressive sequential way with this simple abacus. Thus to my way of thinking, what was needed most was an augmentation that was a sheet of paper or plastic that would meet this need of visually illustrating each Arabic numeral of each bead, in the row of beads in a visual way, where this number was printed or written above or below that bead; (when that bead or its neighboring beads were pushed against the counting bar.) Such an augmentation containing printed numbers may exist, but I have not seen one. And in my search, I was not able to locate this type of augmentation.
Thus my number one priority was to devise a printed augmentation that could be placed beneath all of the horizontal rods and the beads on these horizontal rods, when these beads were in the “counter area”, and were pressed against the counter bar. And with this printed augmentation, the numbers I thru 10 would appear above or below each bead in this top row of beads, when all 10 of these beads were pressed against the counter bar.
And a logical extension of the printed numbers in the top row of this augmentation sheet, was to add additional rows of 10 numbers per row that would correspond to the “number location” of the beads, when each bead, and all previous beads were pushed against the counter bar, (the left edge piece).
And the spacing and location of the numbers on this first augmentation sheet, and on all later augmentation sheets should correspond to the locations of the beads above (or below) these numbers, when these beads and all previous beads were in the “counter area”, and are pressing against the counter bar.
And to make this simple abacus with an augmentation that was a grid of numbers, easier to use, I thought it would be best to have a solid permanent flat bottom piece that extended under all parts of the abacus. And this flat bottom surface would provide a location for the proper placement of each augmentation. And removable tape or other fastening means could hold an augmentation in its proper location, on this flat bottom surface. (And I have not previously seen simple abacuses built with a flat bottom surface that would provide a good location for the placement of a printed augmentation sheet.)
And in the past three months, with the simple abacuses that I have built, I have used small plywood sheets for this flat bottom piece. But other material such as “masonite” or hard board may work as well as plywood.
If a person has a simple abacus without a flat bottom surface there are several options for the placement of the augmentation sheet. An augmentation could be printed on a sheet that is large enough to cover the entire bottom of the frame of a simple abacus, and then tape this augmentation to the bottom of the frame of the simple abacus. And another option would be to have this augmentation sheet printed on a sheet of paper that will cover the entire under surface of the abacus that does not have a solid flat bottom. And also printed on this sheet would be four printed lines that outline the four outer edges of the frame of this simple abacus. This would make the positioning of this simple abacus on this printed sheet an easier task. And such an augmentation that contains 4 lines as a printed rim of the outer edges of the frame would make positioning this combination on a desk or table an easy task.
And this first printed augmentation is illustrated in
And variations of the augmentation shown in
And
And
And
And
In
In
In
And I believe that having the larger sized augmentations illustrated in
But beads # 4 loose this value of one per bead, when they or their neighbor are pushed against non-counter bar # 2.
In
On the second rod, each of ten beads # 7, has a value of ten per bead, when it or its neighbor is pushed against counting bar # 1. And these ten beads # 7, have no value when they are pressed against non-counter bar # 2.
The single bead on the second rod has a value of 100 when it is pushed against counter bar # 1; and it has no value when it is pushed against non-counter bar # 3.
On the third rod are ten beads # 8, that are given a value of 100 each when they are pushed against counter bar # 1. And these same beads are given no value when they or their touching neighbors are pushed against non-counter bar # 2. And on the third rod, on the left side is a single bead. And this single bead on the left side of the abacus has a value of 1000 when it touches counter bar # 1; and it has no value when it touches non-counter bar # 3.
And on the fourth rod are ten beads # 9, that have a value of 1000 each when they, or their touching neighboring beads touch counting bar # 1. But beads # 9 have no value when they or their touching neighbors are touching non-counter bar # 2.
On the fourth rod, on the left hand side is a single bead. And this single bead has a value of 10,000 when it is touching counter bar # 1; and this single bead has no value when it is touching non-counter bar # 3.
And in this typical commercial abacus, the usual pattern of use is to substitute ten counting beads (# 4) on the right that are touching the counter bar for one bead (# 6) on the left that is touching the counter bar. And ten beads (# 4) on on the first rod with a value of one each, may also be exchanged for one bead (# 7), on the second rod that has a value of ten. And this pattern of ten to one exchange persists for the beads on the second, third, and fourth rods
And
And in
And on the second rod (# 5 is used to indicate all rods), there are three beads pressed against the counter bar (# 1) with a value of one each. And on the second rod, there are seven beads pushed against the non-counter bar (# 2), which at this moment have no value. Thus the total value of the beads on rods one and two in
And in
And in
And # 12. in
And in
And # 13 is a printed grid of numbers, where when the beads on the rods are all pressed against the counter bar (#1); all of the beads in the counter area will then show or exhibit the printed number of that bead, above that bead.
And # 18 is to indicate the “non-counter beads” (of which there are eighty seven) in
And the simple abacus shown in
Number 13 shown in
In
In
And in
And with this second type of grid of printed numbers, the young learner should learn to set aside the “rule”, that all of the top rows of beads should be fully in contact with the counter bar, on the left side of the simple abacus to be actually counted. “This second grid of numbers is a “different ball game”, with a “different set of rules”. And in this “different ball game” what is looked for are the building of “squares of beads”, and the building of “rectangles of beads”.
And the rule for building a square of beads, and also a building rectangle of beads is that the left column of beads always starts with the top bead (#1), and may extend to any number below this #1 bead. And the top row of beads always starts at the left hand (#1) bead, and may extend to any number of bead to the right of this #1 bead. And in this “game of multiplicand times multiplier”; their “product” always appears as the printed number at the intersection of this multiplicand and multiplier, in the lower right hand corner of the square or rectangle of beads formed by the beads in this particular set of multiplier and multiplicand.
And the desired result of playing games with these squares and rectangles made up of columns of beads times rows of beads is to gain a concrete understanding of the multiplication tables. And the squares and rectangles of various sizes and shapes are the result of the different combinations of two numbers (of ten and under) that are used in the multiplication tables. And by the use of this simple augmented abacus with the grid of numbers in
And
Much of the detail of this invention is presented in the previous sections, such as: Background; Brief Summary of the Invention; and Brief Description of the Drawings. Thus the following is more of an overview, and information about my search of the prior art.
The basic concept or innovation of this invention is a tool to help very young children learn the numbers from one to ten, and then from one to one hundred. And this tool can also help young children learn to add and subtract small numbers. This tool is an augmentation to a simple abacus. And this augmentation is to add one or more additional parts to a simple abacus. And the first additional part is composed of a printed or written sheet of paper or plastic that contains a grid of printed or written numbers. And this grid of numbers is accurately positioned beneath the rows of ten beads on a simple abacus—when these ten (or fewer) “counter beads” are pressed against the “counter bar”. This “counter bar” is the left side edge piece of this simple abacus. And in this simple abacus, all beads in all rows have a value of one, when that bead, or one of its touching neighbor beads, are touching the counter bar of that simple abacus. And in this simple augmented abacus, all beads have a potential value of one each. And this potential value of one is “made real”, when that bead, or one of its touching neighbors, is pressed against the counter bar.
And all beads on all rows that are not touching the counter bar, or are not touching neighboring beads that are touching the counter bar are considered as “non-counters” and should be pushed against the “non-counter bar” which in this invention is the right edge piece.
And this printed sheet is an augmentation that is a grid of numbers, that go from one to one hundred, with ten successive numbers being beneath beads on the ten rods or ten segments of rope that substitute for rods or wires. And this type of augmentation to a simple abacus is to help young learners, to learn to count numbers in a sequence first from one to ten; then from one to twenty, and then from # 1 to # 100. And this sequence of printed numbers is broken down into ten rows of printed numbers, one row above another; where each row has ten consecutive numbers in it; in a left to right direction. And this printed grid of numbers is designed or “laid out” so that each bead in this abacus that contains ten rows of beads from top to bottom has ten beads per row. And where when all 100 beads are pushed against the left hand edge piece (the counting bar), and the number of each bead in a # 1 to # 100 sequence; will appear on this printed grid above (or below) each bead. And this printed or hand written grid of numbers is positioned beneath the ten rows of ten beads per row. This simple abacus is designed with a viewing space between each row of beads to see the numbers on the printed or hand written grid that is beneath these ten rows of beads.
And in this first variation of this printed grid of numbers are printed numbers that show the number of each bead in a sequence from #1 to # 100. And this sequence of numbers that are beneath the rows of beads appear in the spaces between the rows of beads; when: 1.) this grid is properly positioned beneath the “counter beads”; and 2.) when these counter beads or their touching neighboring beads are all pressed against the left edge “counter bar”.
And this simple abacus is laid out with ten rows of beads, with ten beads per row; where the top row is first. And rows two through ten are located in a sequence below this top row of ten beads. And to make this grid of numbers from one to ten on the first row; and then from number eleven through number twenty on the second row (with rows three through ten following in this pattern); work properly; this grid has to be positioned properly beneath the beads that are touching the counter bar on the left edge of the abacus. And beads that are given no value are pushed against the “non-counter bar” on the right edge of this simple abacus. (The paragraphs: # 127, # 128, #129 and # 139 describe the first variation of an augmentation for this simple abacus in more detail.)
And the other variations of this augmentation have many similar features to those features described for this first variation.
Shown in
A second type of printed augmentation is shown in
And with the augmentation that is shown in
And a blank sheet as is illustrated in
And in a parent or teacher prepared augmentation sheet as is illustrated in
And
My searches to find if anyone else had previously used or patented augmentations to go with an abacus involved five main areas, (listed below)
And I then went to the main library of the University of Missouri at Kansas City and requested the help of one of their librarians in looking up information about abacuses, and their use in education. And she found a number of journal articles of a scientific nature (in journals they did not have). But she also located four books in their library. And one of these four books was checked out. And two of these books were the same books I had obtained at Linda Hall Library, and had partly read. But she found a fourth book that has a chapter on abacuses that was of recent printing. This book has the title of: Tools of American Mathematics in Teaching: 1800 to 2000. And it has three authors: P. G. Kidwell, A. A. Hastings, and D. L. Roberts. And it was published in 2008 by John Hopkins Press. And chapter 6, has the heading: “The Abacus-Palpable Arithmetic.” And it noted a decline in the use of the abacus as a teaching tool in the USA. And this chapter also noted that the abacus was introduced into US elementary schools from France and Great Britain between 1820 and 1830. And this chapter on abacuses noted that most often the abacus was used in “infant schools” (for children from one year through six years of age.) And this book and the two books previously noted, covered a wide variety of types of abacuses used in past and some types that are still in current use. But in my searches I was unable to find anything similar to my current augmentations that are or have been used with an abacus.
From the three books about abacuses mentioned above, it appears that the Russian Abacus was used as a model of the simple type of abacus that has been used in the USA since the 1820's to help children learn to count and to learn to add and subtract small numbers. In the book noted in paragraph [0143] above, it notes that two soldiers from Napoleon's army returned to France from Russia with knowledge of the Russian Abacus, and introduced this type of abacus into French infant schools and French elementary schools in the early 1800's. And the Russian Abacus is very similar to the simple abacus described in this patent application. It uses horizontal wires or rods, with ten beads per rod.
