CN105869476A - Decimal system Xiang Shu counting system - Google Patents
Decimal system Xiang Shu counting system Download PDFInfo
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- CN105869476A CN105869476A CN201610408885.8A CN201610408885A CN105869476A CN 105869476 A CN105869476 A CN 105869476A CN 201610408885 A CN201610408885 A CN 201610408885A CN 105869476 A CN105869476 A CN 105869476A
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- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
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Abstract
The invention relates to a mathematics learning tool, in particular to a decimal system Xiang Shu counting system. The imagic vivid and clear effects are achieved; the clear rule and precise decimal system logic performance are realized; the system belongs to a vivid pattern counting system which is independent from a number counting system and is in one-to-one correspondence to a decimal system number counting system. The decimal system Xiang Shu counting system can be generally used for children being 2 to 12 years old to vividly and intuitively recognize and know the abstract number expressed by the abstract number and the significance of the number; through intuitive observation, operation, experience, cooperation and exchange, various relationships between the abstract numbers are known; the abstract number operation principle is known; the calculation problem is solved; the practical problems relevant to life and study are solved. In addition, the decimal system rule of the XiangShu is intuitive; the number bit arranging position significance is intuitive; the counting unit value significance is also intuitive; in addition, both the significance and the decimal system rule logic are intuitive; the understanding and the study are very easy.
Description
Technical field
The present invention relates to mathematics teaching instrument, specifically, relate to a kind of decimal scale as counting number system.
Background technology
Between number and number, the law of development of relational learning is to be progressively reached abstract thinking by imaginal thinking, logic directly perceived progressively develop into abstract logic.In global rudimentary maths initiation education, institute is commonly used is digital counting method.
Digital counting method is by abstract numeric symbols list registration, it it is all concealment due to system standard, numerical digit meaning and digit's meaning, so, wondering the numerical value meaning of each number, premise is position meaning and the numerical value meaning of digit of system numerical digit regular, the clear and definite arrangement that must be known by the meaning of each numeral, association's digital counting.The abstractness of these numerals is invisible with rule, and the study to the abecedarian such as child, child causes no small difficulty, needs to put into the study of substantial amounts of time and efforts, and a part of child still has half knowledge.Briefly, digital counting method is the meaning representing number abstractively, except abstract of numeral itself, this method or a kind of hiding system meaning, numerical digit meaning and the method for digit's meaning, superposing of abstract and hiding meaning, causes being the devil of children for learning.
At present, in order to overcome the abstract problem existing for digital counting method, the mathematical education of primary school of China use spillikin, beads etc. as the intuitional instruction apparatus of auxiliary.Although spillikin, beads can intuitively characterize quantity, but the ambiguity of its structure, the uncertainty of profile, easily cause quantity, the meaning of ten and the ambiguity of system rule, affect clearly understanding of child's logarithm and relation thereof.Such as, primary school math teaching is bundled into a bundle with several 10 spillikins and represents ten.But, a bundle can not become the proprietary concept of ten, and 9 spillikins, 11 spillikins can be a bundles, and they are similar to the spillikin abnormality in outer shape of 10 a bundles, it is difficult to distinguishes.Therefore, utilizing spillikin to learn, the concept of ten is still that fuzzy in child's brain.The most still ten, owing to the visual quantity of people is 5 to the maximum, the quantity of the discrete object more than 5, it is necessary to every time through counting just can know that how many.Therefore, learn quantity with spillikin, more than 5, be all fuzzy for child.Concept and the concept of ten more than 5 are all fuzzy, cause child to be difficult to get a real idea of to number concept.Concept does not understands, and the relation between number and number that solves only has by memorize mechanicalling.Beads also has same problem.The size of beads, the length of beads string all affect child's judgement to quantity, thus affect the foundation of number concept.Therefore, these learning aids all can not allow child store the accurate presentation of meaning of number in the brain, and presentation is the material of imaginal thinking, the mathematical thinking not having thinking material becomes empty verbiage, has a strong impact on and the delayed knowledge understanding of child, skill master, ability of thinking development and the lifting of math quality.Design invention is a set of can really liberate children mathmatics introduction study abstractness, the real instrument promoting the development of children mathmatics ability of thinking, is whole world children education and thing that primary school education worker, researcher are dreamed of.
On the basis of analysing in depth Arabic numerals decade counter method, it is appreciated that Arabic numerals decade counter system is made up of bi-material and two kinds of rules.Wherein, ten numerals of 0---9 are a kind of materials, and are the most basic materials of composition number；Another kind of material is the digit of each progression, the unit " 1 " of the most each progression, such as: the unit " 1 " of ten represents 10, and the unit " 1 " of hundred represents 100, and by that analogy, each progression has the unit " 1 " of oneself, is the material forming this progression.One of rule is that the relation between adjacent several levels unit " 1 " is described, decimal scale is to say that the rate of entering between adjacent several levels unit " 1 " is ten；It two is the i.e. numerical digit that puts in order of digital material, and digital counting uses " right low left high " to be arranged in order.Such as 1 year 365 days, we were shown as 365 days by numeral in decimal scale rule following table.Wherein, 3,6,5 is digital material, is the material constituting the number in each several levels." 5 " expression 51,1 is the unit " 1 " of units, is the material of composition units, and the actual value that " 5 " represent 5 is abstract；" 6 " expression 6 10,10 is the unit " 1 " of tens, is the material of composition tens, and not only " 6 " represent 6 10 is abstract, and actual value 60 is hidden especially；" 3 " represent 3 100,100 it is the unit " 1 " of hundreds, and the abstractness of numeral 3 and the invisible of actual value 300 are the same with the 6 of the 5 of position, ten.The unit " 1 " of the unit " 1 " of individual position, the unit " 1 " of ten and hundred adjacent enter rate be system rule for " ten ", the array of 365 is, ten, hundred " right low left highs ".
From analyzing, as long as the corresponding pictorial symbol representing digital 0-9 intuitively can be found, we just can represent the meaning of each numeral with visual pattern；As long as finding the pictorial symbol of each several levels unit " 1 ", it is possible to visual pattern ground represents each number of this several levels；As long as finding the pictorial symbol of system relation, it is possible to visual pattern ground represents system rule；Then, arrange by the numerical digit of digital counting method, it is possible to each is showed by abstract numeral and hiding digit, several visual patterns of system Rule Expression and strict logic.In this manner it is possible to the several visual patterns represented as several each numerals fresh and alive present.
Summary of the invention
It is an object of the invention to, it is provided that a kind of decimal scale is as counting number system, to solve above-mentioned technical problem.
For solving the problems referred to above, the technical solution adopted in the present invention is:
A kind of decimal scale is as counting number system, it is characterised in that: include 10 as numerical symbol, 1 decimal scale are as the elephant counting number unit amount symbol of several hex notation with several corresponding each several levels unit amounts of difference；Described 10 as numerical symbol be respectively represent numeral 0-9 as several nil symbols, as several symbols, as several two symbols, as several three symbols, as several four symbols, as several five symbols, as several six symbols, as several seven symbols, as several eight symbols with as symbol in the nine periods；Described as several nil symbols corresponding be blank circular card；Described as several symbols corresponding be to comprise the fan-shaped graph card that central angle number of degrees are 36 °；Described as several two symbols corresponding be to comprise the fan-shaped graph card that two central angle number of degrees are 36 °；By that analogy, as several three symbols, as several four symbols, as several five symbols, as several six symbols, as several seven symbols, as several eight symbols, as symbol in the nine periods respectively corresponding comprise three, four, five, six, seven, eight, nine central angle number of degrees be the fan-shaped graph card of 36 °；That is: two as several one symbols form one as several two symbols, three as several one symbols form one as several three symbols, by that analogy, nine as several one symbols form one as symbol in the nine periods；
Described decimal scale as several hex notation corresponding be containing the fan-shaped graph card that 10 central angle number of degrees are 36 °；
Described by the unit amount symbol of each several levels and characterize form as several symbols of unit " 1 " as counting number unit amount symbol, including digit's numerical symbol of Ge Wei digit numerical symbol, ten digit's numerical symbols, hundred digit's numerical symbols, kilobit digit numerical symbol, myriabit digit numerical symbol, ten myriabit digit numerical symbols, megabit digit numerical symbol, ten million count value unit symbol, hundred million digit's numerical symbols and extremely all numerical digits；What described Ge Wei digit numerical symbol was corresponding is comprises the fan-shaped graph card that central angle number of degrees are 36 °；What described ten digit's numerical symbols were corresponding is containing the fan-shaped graph card that 10 central angle number of degrees are 36 °；Described decimal scale is described hundred digit's numerical symbols as being respectively implanted ten digit's numerical symbols in each sector of several hex notation；Described decimal scale is described kilobit digit numerical symbol as being respectively implanted hundred digit's numerical symbols in each sector of several hex notation；By that analogy, available myriabit digit numerical symbol, ten myriabit digit numerical symbols, megabit digit numerical symbol, ten million digit's numerical symbol, hundred million digit's numerical symbols and the digit's numerical symbol to all numerical digits；
Described as counting number unit amount symbol be as counting number unit symbol as several symbols combine, it may be assumed that it be that the elephant counting number unit symbol of " 1 ", ten digit's numerical symbols insert as characterizing numerical value in several symbols be that the elephant counting number unit symbol of " 10 ", hundred digit's numerical symbols are inserted as in several symbols, sign numerical value is that the elephant counting number unit symbol of " 100 ", kilobit digit numerical symbol are inserted as in several symbols, sign numerical value is the elephant counting number unit symbol of " 1000 " that single Ge Wei digit numerical symbol characterizes numerical value；By that analogy, digit's symbol of all numerical digits can be obtained.
Beneficial effect: compared with prior art, the present invention is the most visual in image clearly, and have cheer and bright regularity and rigorous tight decimal scale logicality, be a kind of independent of digital counting system outside, again with ten's digit number system visual picture number system one to one.Specifically, the present invention is not only as several numerical symbol meaning visual patterns, can intuitively present decimal scale meaning, numerical digit meaning and digit's meaning simultaneously, the several meanings represented are very clear, 2-12 year children image can be commonly used to, be appreciated and understood by the meaning of abstract several sums that abstract number word table shows intuitively, by intuitively observing, operate, experience, coming to realize, cooperation and exchange, understand the various relations between abstract number and number, understand the principle of abstract several computings and solve computational problem, solve and live, learn relevant practical problem.Additionally, as the decimal scale rule of number is intuitively, the position meaning of numerical digit arrangement is intuitively, and the numerical value meaning of digit is also intuitively, and, not only meaning is intuitively, and decimal scale logic rules is also intuitively, and study be can very easy be interpreted.
Accompanying drawing explanation
Fig. 1 be of the present invention 10 as the schematic diagram of numerical symbol；
Fig. 2 is that decimal scale of the present invention is as the schematic diagram of several hex notation；
Fig. 3 is of the present invention as the exemplary plot in counting number unit amount symbol；
Fig. 4 is of the present invention as the exemplary plot in counting number unit symbol；
Fig. 5 is that decimal scale of the present invention is as the exemplary plot of counting number system representation numerical value.
Detailed description of the invention
The invention will be further described with detailed description of the invention below in conjunction with the accompanying drawings.
Decimal scale of the present invention is as counting number system, including 10 as numerical symbol, 1 decimal scale are as the elephant counting number unit amount symbol of several hex notation with several corresponding each several levels unit amounts of difference.
As it is shown in figure 1, described 10 as numerical symbol be respectively represent numeral 0-9 as several nil symbols, as several symbols, as several two symbols, as several three symbols, as several four symbols, as several five symbols, as several six symbols, as several seven symbols, as several eight symbols with as symbol in the nine periods；Described as several nil symbols corresponding be blank circular card；Described as several symbols corresponding be to comprise the fan-shaped graph card that central angle number of degrees are 36 °；Described as several two symbols corresponding be to comprise the fan-shaped graph card that two central angle number of degrees are 36 °；By that analogy, as several three symbols, as several four symbols, as several five symbols, as several six symbols, as several seven symbols, as several eight symbols, as symbol in the nine periods respectively corresponding comprise three, four, five, six, seven, eight, nine central angle number of degrees be the fan-shaped graph card of 36 °.That is: two as several one symbols form one as several two symbols, three as several one symbols form one as several three symbols, by that analogy, nine as several one symbols form one as symbol in the nine periods.
As in figure 2 it is shown, described decimal scale as several hex notation corresponding be containing the fan-shaped graph card that 10 central angle number of degrees are 36 °.
Described by the unit amount symbol of each several levels and characterizing form as several symbols of unit " 1 " as counting number unit amount symbol, symbol includes digit's numerical symbol of Ge Wei digit numerical symbol, ten digit's numerical symbols, hundred digit's numerical symbols, kilobit digit numerical symbol, myriabit digit numerical symbol, ten myriabit digit numerical symbols, megabit digit numerical symbol, ten million count value unit symbol, hundred million digit's numerical symbols and extremely all numerical digits；What described Ge Wei digit numerical symbol was corresponding is comprises the fan-shaped graph card that central angle number of degrees are 36 °；What described ten digit's numerical symbols were corresponding is containing the fan-shaped graph card that 10 central angle number of degrees are 36 °；Described decimal scale is described hundred digit's numerical symbols as being respectively implanted ten digit's numerical symbols in each sector of several hex notation；Described decimal scale is described kilobit digit numerical symbol as being respectively implanted hundred digit's numerical symbols in each sector of several hex notation；By that analogy, available myriabit digit numerical symbol, ten myriabit digit numerical symbols, megabit digit numerical symbol, ten million digit's numerical symbol, hundred million digit's numerical symbols and the digit's numerical symbol to all numerical digits.Fig. 3 show as three examples in counting number unit amount symbol, it may be assumed that Ge Wei digit numerical symbol, ten digit's numerical symbols and hundred digit's numerical symbols.
Described as counting number unit amount symbol be as counting number unit symbol as several symbols combine, it may be assumed that it be that the elephant counting number unit symbol of " 1 ", ten digit's numerical symbols insert as characterizing numerical value in several symbols be that the elephant counting number unit symbol of " 10 ", hundred digit's numerical symbols are inserted as in several symbols, sign numerical value is that the elephant counting number unit symbol of " 100 ", kilobit digit numerical symbol are inserted as in several symbols, sign numerical value is the elephant counting number unit symbol of " 1000 " that single Ge Wei digit numerical symbol characterizes numerical value；By that analogy, digit's symbol of all numerical digits can be obtained.It is to say, described decimal scale forms as several symbols by ten as several hex notation, each as several symbols in often insert ten digit's numerical symbols by level, the numerical value of expression i.e. expands ten times greater, thus characterize system rule.
Fig. 3 show as three examples in counting number unit symbol, it may be assumed that sign numerical value is the elephant counting number unit symbol of " 1 ", characterizes the elephant counting number unit symbol that numerical value is " 10 " and the elephant counting number unit symbol that sign numerical value is " 100 ".
Fig. 5 show employing decimal scale of the present invention as the numerical value 324 of counting number system representation, it may be assumed that is respectively implanted hundred digit's numerical symbols in as three sectors of several three symbols, represents numerical value " 300 "；In as two sectors of several two symbols, it is respectively implanted ten digit's numerical symbols, represents numerical value " 20 "；Add four each and every one numerical value " 4 " represented by position digit numerical symbol.
Decimal scale of the present invention is described below as the function and significance of counting number system:
(1) effect
1, according to decimal scale as counting number system principle, unlike material, different colours, the teaching aid varied in size, learning aid can be designed.Our regularity of design is central angle, and material, color, the size of radius are impossible to change fan-shaped and circle shape.It is generally applicable to the meaning of abstract several sums that 2-12 year children image, intuitively the cognition and comprehension abstract number word table show, as number is the best teacher without language；By intuitively observing, operate, experience, coming to realize, cooperation and exchange, understand abstract number and number between various relations, as number is speechless tutor；By intuitively observing, operate, experience, coming to realize, cooperation and exchange, understand abstract several computings principle and solve computational problem, solve and live, learn relevant practical problem, as number is noiseless teacher.The pictorial diagram of correspondence it is pasted into, as number represents that the quantity of things just has real intuitive in each each fan-shaped color lump as counting.Do not paste anything and just can represent the things of any respective amount with high level overview, and there is fresh and alive intuitive and certain abstractness.It is the solid bridge of intercommunication between life-stylize mathematics and mathematicization mathematics.This is also " 3-6 year children for learning and development guide " and " compulsory education Mathematical Curriculum Standard (version in 2011) " is emphasized repeatedly emphasis and difficulties.
2, according to the design principle of the present invention, the elephant counting number system of many kinds of systems of N can be designed, in order to the number under the many kinds of system rules of N such as visual in image sign binary system, octal system, the duodecimal notation, binary-coded decimal and mutual relation thereof.Because Arabic numerals only have 10, they can only characterize the system relation of below decimal scale, exceedes decimal scale, and such as the duodecimal notation, hexadecimal, binary-coded decimal, sexagesimal etc., algorism is helpless.And our elephant counting number system can be accomplished completely.Such as the duodecimal notation, we can specify that the sector that central angle is 30 degree is " one ".As long as there being " one ", all just have.Principle is completely the same with decade counter system, furthermore, it is possible to mutually change between different systems.
3, decimal scale is fabricated to the learning aid with concave-convex sense as counting number system by wooden, non-toxic organic plastic or other material, it is also possible to help and promote that blind child learns number knowledge and understands quantitative relation.
4, between number and number, the study law of development of relation is to be progressively reached abstract thinking by imaginal thinking, logic directly perceived progressively develop into abstract logic.As the design of several learning tooles is also according to this rule: the learning aid for baby stages and child's design has meaning intuitionistic feature directly perceived, regular；Be two, the learning aid of Third school grade child design have that rule is directly perceived, the feature of the meaning imagination；The learning aid designed for the child of higher primary school pupil has the rule imagination, meaning imagination feature；Finally reach the understanding based on abstract digital display circuit and ability of thinking.
5, learning aid---spillikin general in China's primary school math teaching is substituted.Although spillikin can characterize quantity, but the ambiguity of its structure, the uncertainty of shape, cause quantity, the meaning of ten and the ambiguity of system rule, affect the understanding of child's logarithm and relation thereof.Such as, primary school math teaching is bundled into a bundle with several 10 spillikins and represents ten.A bundle can not become the proprietary concept of ten, and 8 spillikins, 13 spillikins can be a bundles, and they outward appearances are much like, it is difficult to distinguishes.Therefore, utilizing spillikin to learn, the concept of ten is still that fuzzy in child's brain.Decimal scale is visual and clear as counting number system structure, so, quantity is visual and clear, and the meaning of ten is visual and clear, decimal scale rule visual and clear and regular clear, logicality is tight.Each number that has its source in corresponding one distinctive as, the meaning of ten as being again uniquely to be easiest to the circle that memory understands.The number of each numerical digit level has oneself distinctive visual in image elephant counting number unit meaning symbol, profile the most all circulates between as numerical symbol 1-9, therefore, decimal scale is the most visual in image clearly as mathematics tool, and have cheer and bright regularity and rigorous tight logicality, the learning aid such as spillikin, beads can be substituted completely.
In sum, decimal scale is equivalent to a JINYAOSHI opening mathematics kingdom gate as counting number system, by the bridge in abstract great river, is also the aircraft carrier marched to mathematics kingdom knowledge ocean simultaneously.From this, extreme this Wangwu Shan Mountain abstract of number represented by numeral is no longer had before the child of kindergarten and the children with ocular of primary school, the most no longer there are the terrifying waves that quantitative relation is abstract, the bright road of wide flat is had plenty of on the road of their mathematical studying, have plenty of right up and down knowledge ocean, have plenty of happy, the joyful and sense of accomplishment easily obtaining knowledge expertise.
(2) meaning
Visual in image figure is universal language, it is mankind's all-purpose languages, China's normal children and the mathematical studying of blind mute child can be greatly facilitated with it, equally promote the mathematical studying of the whole world children such as Asia, America, Europe, Africa, Oceania, Latin America.Therefore, decimal scale has world significance as the invention of counting number system！She rewrites the history of children mathmatics learning from this, has historic significance！From the point of view of faster and better succession human culture, there is human progress meaning！She, come from the ancient wisdom of China---The book of Changes as several thinking modeies, be born this sheet of China ancient to prolong continuous constantly civilization big on the ground, be Chinese nation's contribution for the world！It is Chinese people's contributions for Development of Human Civilization！
Claims (1)
1. a decimal scale is as counting number system, it is characterised in that: include 10 as numerical symbol, 1 ten enter
Make as the elephant counting number unit amount symbol of several hex notation with several corresponding each several levels unit amounts of difference
Number；Described 10 as numerical symbol be respectively represent numeral 0-9 as several nil symbols, as several symbols, as number
Two symbols, as several three symbols, as several four symbols, as several five symbols, as several six symbols, as several seven symbols,
As several eight symbols with as symbol in the nine periods；Described as several nil symbols corresponding be blank circular card；Described as number
What one symbol was corresponding is comprises the fan-shaped graph card that central angle number of degrees are 36 °；Described as several two symbols pair
Answer is to comprise the fan-shaped graph card that two central angle number of degrees are 36 °；By that analogy, as several three symbols, as
Several four symbols, as several five symbols, as several six symbols, as several seven symbols, as several eight symbols, as symbol in the nine periods
Respectively correspondence comprise three, four, five, six, seven, eight, nine central angle number of degrees be 36 °
Fan-shaped graph card；That is: two as several symbols form one as several two symbols, three as several symbols
Become one as several three symbols, by that analogy, nine as several one symbols form one as symbol in the nine periods；
Described decimal scale as several hex notation corresponding be containing the fan-shaped figure that 10 central angle number of degrees are 36 °
Card；
Described as counting number unit amount symbol is by the unit amount symbol of each several levels and sign unit " 1 "
As several symbols compositions, including Ge Wei digit numerical symbol, ten digit's numerical symbols, hundred
Digit's numerical symbol, kilobit digit numerical symbol, myriabit digit numerical symbol, ten myriabits
Digit's numerical symbol, megabit digit numerical symbol, ten million count value unit symbol, hundred million
Position digit's numerical symbol and the digit's numerical symbol to all numerical digits；Described Ge Wei digit number
What value symbol was corresponding is comprises the fan-shaped graph card that central angle number of degrees are 36 °；Described ten digits
What numerical symbol was corresponding is containing the fan-shaped graph card that 10 central angle number of degrees are 36 °；Described decimal scale is as number
Each sector of hex notation is respectively implanted ten digit's numerical symbols and is described hundred countings
Unit amount symbol；Described decimal scale is as being respectively implanted one hundred countings in each sector of several hex notation
Unit amount symbol is described kilobit digit numerical symbol；By that analogy, available myriabit counting is single
Bit value symbol, ten myriabit digit numerical symbols, megabit digit numerical symbol, ten million meter
Number unit amount symbol, hundred million digit's numerical symbols and the digit's numerical symbol to all numerical digits；
Described as counting number unit amount symbol be as counting number unit symbol as several symbols combine,
That is: single Ge Wei digit numerical symbol characterizes numerical value is the elephant counting number unit symbol of " 1 ", ten meters
Number unit amount symbols insert as in several symbols characterize numerical value be the elephant counting number unit symbol of " 10 ", hundred
Position digit numerical symbol insert as characterize in several symbols elephant counting number unit symbol that numerical value is " 100 ",
Kilobit digit numerical symbol is inserted as characterizing the elephant counting number unit that numerical value is " 1000 " in several symbols
Symbol；By that analogy, digit's symbol of all numerical digits can be obtained.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN201340662Y (en) * | 2009-01-06 | 2009-11-04 | 徐越 | Intelligent arithmetic card |
| US7914287B2 (en) * | 2005-05-05 | 2011-03-29 | Huong Nguyen | System and method of teaching and learning mathematics |
| CN203250443U (en) * | 2013-05-29 | 2013-10-23 | 张鹏 | Number model system |
| CN104751701A (en) * | 2013-12-31 | 2015-07-01 | 淄博高新技术产业开发区第五小学 | Teaching aid for sector combination demonstration |
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2016
- 2016-06-07 CN CN201610408885.8A patent/CN105869476A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7914287B2 (en) * | 2005-05-05 | 2011-03-29 | Huong Nguyen | System and method of teaching and learning mathematics |
| CN201340662Y (en) * | 2009-01-06 | 2009-11-04 | 徐越 | Intelligent arithmetic card |
| CN203250443U (en) * | 2013-05-29 | 2013-10-23 | 张鹏 | Number model system |
| CN104751701A (en) * | 2013-12-31 | 2015-07-01 | 淄博高新技术产业开发区第五小学 | Teaching aid for sector combination demonstration |
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