Funforms is a new mathematical numerical notation learning system. "Fun" stands for fundamental functional and fun. "Forms" stands for formulae. Funforms are fundamental formulae that are fun to work with. They allow math functions to take place mechanically on paper. So they are quite functional. A colleague of mine [Harold Larson] and I developed the system more than 20 years ago.
HISTORY: Before humankind began to use counting numbers, tally marks were used. A tally mark simply consisted of a cut in a stick or a knot in a piece of rope or a mark on a piece of paper [or some other similar representation]. It stood for an object in a collection on a one-to-one basis. It was not a true counting system, but it did allow for a person to keep track of whether or not all members of a group were still present in the group when it was "recounted" [compared]. Later tally marks were grouped for convenience in visualizing the total number of members in a group.
Until Arabic numerals were introduced to Europe in the 12th century, the numerical system in common usage in the western world was the Roman numeral system. Most scholars agree that Roman numerals were suitable only for writing down results of calculations made on an abacus or by using some other system. They were not easily manipulable by the individual who was writing them down. Roman numerals primarily served as a permanent record of the results of a calculation.
To go to a slide show that also contains audio, click here. This is a 55 megabyte download, do not be in too great a hurry.� After downloading it, extract it to have it work properly
BENEFITS OF HINDU-ARABIC NUMERALS: Hindu-Arabic numerals were a major step forward. They emphasized place order to indicate what power of ten the particular coefficient of 10 being written stood for. Many scholars have regarded the introduction of the 0, which kept the place order if there were no powers of 10 for that particular column as a step forward, but it also introduced problems such as dividing by zero.
Arabic numerals are arbitrary symbols, so their intrinsic meaning is not immediately apparent. Their big advantage was/is that by learning a variety of rules, they could be manipulated by the individual using them and they still served the purpose of functioning as a peripheral memory/record keeping system. They had all of the advantages of the Roman numerals system plus the advantage of being manipulable.
FUNFORMS: Funforms are basically binary in design (although a trinary system also exists). The idea of place order is preserved, but coefficients are unnecessary except transiently during manipulation. The meaning of the number is obvious to anyone with passing familiarity. That is to say that the formulae are iconic or ideographic. Most importantly, as the user applies Funforms, mathematical operations become transparent, and understanding of the nature of the mathematical transaction becomes apparent to the user.
Funforms is a geometrically progressive system as opposed to our own number system, which is arithmetically progressive. In Funforms, arithmetic progression is preserved if one looks at the exponents, however. In Funforms there is no symbol for zero because none is needed
We believe that Funforms can be taught to preschoolers as a game. We believe that there may be advantages for learners who have dyscalculia to learn Funforms. We also believe that for the general student and the gifted Funforms will have a benefit just like the benefit of learning a foreign language. There is much to be earned about one's own language by studying another language.
CONCEPTS BEHIND THE DEVELOPMENT OF THIS NEW SYMBOL SYSTEM: I am a psychiatrist with a major interest in the nature of consciousness and cognition. Funforms is an outgrowth of the idea that, in the same way that "A carpenter is only as good as his tools", abstract thought seems highly dependent on the symbols used for those thought constructs, even though use of those symbols does not change the underlying capability of the user. Use of those symbols does change the ability of the thinker to utilize his or her underlying capabilities.
Some indigenous tribes have counting systems that only go to three or four. People from these tribes are numerically impaired until they have the opportunity to learn a more advanced numbering system. Once they learn a new system, they demonstrate math abilities similar to those that people from cultures with sophsticated number systems have.
The effects of learning a system like Funforms still have not been investigated, but there is ever reason to believe that it will at least offer the benefits to the learner that learning a foreign language confers on the learner, a better understanding of that person's native language. It is conceivable that there might even be more important benefits, just like the benefits of learning a more sophisticated number system confers on the member of an indigenous group that does not have the benefits of such a number system.
Our number system is more that 1000 years old! [And, of course still working quite well.]
DEFINITIONS FOR USING FUNFORMS: Go to the Power Point Slide show by using the link at the bottom of this page. Recently I have been able to add the audio component to the Power Point slide show.
Shortly it will be available on this website. A link to obtain it will be here.
It will make these ideas much more easily understood. Please use it.
In Funforms we use a vertical line called a staff.
It has various possible positions ("points") at which particular number values can be indicated as present. These positions occur at regular intervals. By using lined paper, each line can conveniently serve as such a potential position.
A line perpendicular to the staff called a flag can be drawn at any of the potential positions.
A point is chosen to represent unity point.
A flag drawn to the right of the staff at unity point has a numerical value of one.
By convention number values double at each successive position going down the staff.
Positive values are drawn to the right of the staff.
Negative values are drawn to the left of the staff.
All potential positions ("points") below unity point have a whole number value that corresponds to a whole number power of 2.
All points above unity point are fractional in nature and represent whole number negative powers of 2.
Thus, going down successive points on the staff, the number values would be: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, etc. [representing]:
2 to the zero power, 2 to the first power, 2 squared, 2 to the third power, etc.
By convention number value double at each succeeding position as we go down the staff.
In other words, numerical values double each time a flag [or a series of flags] moves down one position
Numerical values halve each time a flag [or a series of flags] moves up one position.
No more than one flag can be at any one potential position (except temporarily during manipulation). [That is, there is either one flag at any given point (potential position), or there is no flag there.]
Any two flags at a position are the equivalent of one flag at the next position down.
(And conversely any single flag at a position is the same as two flags at the preceding position going up.)
TO REITERATE SEVERAL IMPORTANT POINTS FROM THE DEFINITION SECTION:
Positive integers have flags to the right of the staff.
Negative integers have flags to the left of the staff.
By convention, the first position on the staff, which is marked by a flag extending to the right, represents the number one. This position is called unity point.
Whole numbers are written at and below unity point.
Any flags written above unity point represent fractional numbers.
With that introduction, please let us begin counting:
At this point we can provide you with information regardingthe binary form of Funforms.The emphasis of our site is on parents who want to enrich their child's mathematical education.
You can reach us by fax at 1 440 946 4117. We look forward to hearing from you. You
To see the power point slide show, you will need power point reader, if you do not have power point. Power point reader is available at no cost from http://snipurl.com/2fz9
![zipped narrated [audio] power point](./templates/Explore/img/navi/19804_n.gif?cc=1170085473153)
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