saxon math : a new math learning system
Introductory Comments regarding the Value of Systematic Numerical Systems
The source for most of these comments in this paragraph and the two following paragraphs is Professor Brian Butterworthæ¯ book, WHAT COUNTS, How Every Brain Is Hardwired for Math. There is scientific evidence that human infants and many other mammals [and birds] have the innate ability to recognize numbers up to three or four. Human infants also seem to be aware of expected changes after one member is added or subtracted to a small group when that activity takes place behind a screen.
Some primitive tribes do not count past a number value of 3 or 4. Other primitive tribes count up to about 30 by using the names of specific body parts to stand for specific numbers. They have only very limited ability to manipulate numbers, however. When these primitives are taught how to use Hindu Arabic numerals, they rapidly attain the ability to carry out standard operations such as adding and subtracting large numbers; multiplying and dividing numbers. That is, they become much more numerically empowered
Similarly, although there is no evidence that the human of today is any more intelligent than the human of 1000 years ago, most Europeans in the middle Ages and before were virtually without the ability to use numbers. When they did, they relied on scholars who were more numerate and/or they used tables or used counting boards or an abacus. Then the outcome of those calculations was recorded in Roman numerals.
These facts suggest that even though the capability to handle sophisticated math concepts exists in the brain, unless the symbolic language tools useful for handling numbers are available to the person, the ability to utilize that portion of the brain cannot be nearly fully realized.
Thus, not all cultures provide the same kinds of conceptual mathematical tools. If that is true, then in a manner and analogous to the old statement about a carpenter only being as good as his tools, a person in a culture that fails to provide a proper conceptual tools may remain innumerate or nearly so.
It is my unproven belief that by learning a symbolic system substantially different from the one that the person learned from youth, understandings about mathematical operations can be enhanced. It might also be true that certain people who cannot manage Hindu Arabic numbers could learn some simpler system and use it.
Funforms is such a system. It is a tally-mark, place-order, geometrically progressive binary system. It consists simply of lines perpendicular to one another and specific points where those tally marks can appear [or be omitted] (spaces). Funforms was designed to be as simple as possible. It is not arbitrary in design, like Hindu Arabic numbers. Funforms is iconic and ideographic. It is easily learned because the rules are minimal.
Posted by: Joel Steinberg
The source for most of these comments in this paragraph and the two following paragraphs is Professor Brian Butterworthæ¯ book, WHAT COUNTS, How Every Brain Is Hardwired for Math. There is scientific evidence that human infants and many other mammals [and birds] have the innate ability to recognize numbers up to three or four. Human infants also seem to be aware of expected changes after one member is added or subtracted to a small group when that activity takes place behind a screen.
Some primitive tribes do not count past a number value of 3 or 4. Other primitive tribes count up to about 30 by using the names of specific body parts to stand for specific numbers. They have only very limited ability to manipulate numbers, however. When these primitives are taught how to use Hindu Arabic numerals, they rapidly attain the ability to carry out standard operations such as adding and subtracting large numbers; multiplying and dividing numbers. That is, they become much more numerically empowered
Similarly, although there is no evidence that the human of today is any more intelligent than the human of 1000 years ago, most Europeans in the middle Ages and before were virtually without the ability to use numbers. When they did, they relied on scholars who were more numerate and/or they used tables or used counting boards or an abacus. Then the outcome of those calculations was recorded in Roman numerals.
These facts suggest that even though the capability to handle sophisticated math concepts exists in the brain, unless the symbolic language tools useful for handling numbers are available to the person, the ability to utilize that portion of the brain cannot be nearly fully realized.
Thus, not all cultures provide the same kinds of conceptual mathematical tools. If that is true, then in a manner and analogous to the old statement about a carpenter only being as good as his tools, a person in a culture that fails to provide a proper conceptual tools may remain innumerate or nearly so.
It is my unproven belief that by learning a symbolic system substantially different from the one that the person learned from youth, understandings about mathematical operations can be enhanced. It might also be true that certain people who cannot manage Hindu Arabic numbers could learn some simpler system and use it.
Funforms is such a system. It is a tally-mark, place-order, geometrically progressive binary system. It consists simply of lines perpendicular to one another and specific points where those tally marks can appear [or be omitted] (spaces). Funforms was designed to be as simple as possible. It is not arbitrary in design, like Hindu Arabic numbers. Funforms is iconic and ideographic. It is easily learned because the rules are minimal.
Posted by: Joel Steinberg
0 Comments:
Post a Comment
<< Home