algorithmic learning and its consequences
there is an inherently powerful way of codifying thought which is mathematics. it is perhaps man’s greatest achievement. the insights won by users of mathematical thought have given us this interconnected world of today.
but what is mathematical thought and how does one assemble its strengths?
math is based on patterns and understanding how these complex unified patterns of consequence can be used as languages to describe and delimit. one of the first patternings that man used abstractly i believe is that of number. arithmetic is fundamental to a language of numeracy, and it was historically taught algorithmically. and by making simple concatenations of relationships indelibly memorized one could leap into quick thought about problems of number, statistics, odds, and other simple ways of seeing deeper into number patterns. their systematic study, of course, is something else.
addition flash-cards, multiplication tables, subtraction and division; ah yes, even long division were concatenated. this last bridge of fools often becomes the final blockage for those who are still not becoming fluent in numeracy. this system of learning works, but it can be off putting enough for many who fail miserably a good percentage of the time. how can one teach the value of rote learning of beginnings, and that such practice leads to becoming fluent in abstract thought in the richness of another learned language.
i taught string figures to recalcitrant math learners for a good number of years in a new york city high school and watched as my students became able to think abstractly in simple sets of patternings that i had developed within my own learning of string figures. what i found to be of the most importance was that they were empowered to do some of their neglected hard-early-work in other subjects to catch up as they had done in math. there is a reason why the british insist the subject is maths, plural.
different mathematics are different languages and should be approached in their learning like second languages. when i began my german course in college as a freshman we were asked to stand and point at the window and speak in unison, “das ist das fenster.” my memory says i. a richardson. it works as you build up physical activities with language patterns. think of the old canard about italians and their hands when they talk. the gesture of pointing at the window is a complex reference point for the brain as an instantly retrievable completeness. the small grammatical parts involved in repetitive rote learning pertains in this almost instantaneous retrieval of concepts.
german has a different logic than chinese or spanish. the german phrase is “das ist mir wie ein spanisches dorf” (that’s spanish to me). when other patternings such as swahili, fukienese, or cherokee are heard at normal speed that a fluent person uses, it is gibberish for the rest of us.
early man (before writing and such, or electronics and computers) learned to process complex patterns in ways we do not experience in today’s fractionalized first world upbringing.
and as a last thought. i had a conversation with a navajo man who taught biochemistry in northern arizona university. he described the feeling of wondering why his navajo students were easily the best at visualizing three dimensional complex elements and their reactions. but that now after talking with me it was clear to him that they had trained their minds to think in three dimensional consequential patterning when they played string figures at home.
we need to preserve and enrich such complex language fluencies that are lost in our typing and swiping world of visual and aural control. physical analogs of consequential operations are needed early on in the language gathering processes, and it should always be in the plural.
A recent article in Science magazine discussed the windows of learning which every person experiences early in their life. Note development of the senses begins before birth and that the language window closes during childhood. That is why a second language is so hard to learn if one begins much past 9 or 10 years of age. My especial interest as a teacher is the window of higher cognition.
It is surprising that so much of the plasticity and ease of learning occurs during childhood, and I think that a major mistake is made by the educational establishment in NOT taking advantage of this opportunity to develop and enrich one’s learning skills early on. It is much harder to develop these skills as one nears puberty and beyond. It is a mistake to underestimate the capacity of a young child to handle complex higher cognition learning.
So how should a school system go about incorporating a strategy to take full advantage of this opportunity. I have a simple plan to jump start this process at minimal cost and disruption of the current schools.
i have been involved with teaching string figures to children and teenagers for more than thirty years and have come to some hard and fast conclusions.
• The hands (especially intricate finger patternings) are a remarkably useful tool for the flowering of the brain’s potential.
• Children and teenagers who participate in learning activities using the hands (playing instruments, learning string figures, etc.) do much better in learning all other subject matters than those who have no such experience . I taught in Music and Art high school in New York City and the instrumentalists tended to be the best all round students.
• It is crucial that this training start early and then continue throughout the time period when the human animal is predilected to learn (say 4 to 24).
• I believe the brain’s explosive growth in the evolution of humans was first led by the hands and only later by the throat, tongue, larynx speech acquisition.
• It is a sadness that modern society tends to devalue the hands insofar as what an educated person takes pride in as accomplishment. My father put it best, “The man who washes his hands before he works makes more than one who washes his hands after.”
The first five years of formal schooling should be for preparing the basic systemic neuronal capacities. Then comes an extended time for learning.
This period of time is necessary for all the complex modalities of the adult human to become fully developed. It is crucial that a there be a concentrated effort in learning how to learn and learning the richness of man’s cultural heritage. We all like to be smart, but learning new things can look to be too hard unless one has a history of successful learning to give one the courage to persevere into new challenging spheres. So it is crucial that we try to impart a truly understood accomplishment in learning early on. Children should learn instruments and make music. Children should learn string figures.
james r murphy email inoli@torusflex.com
diamonds
ten men
loom (identity element)
operations
inverses
universes
logic systems
loop transfers
c’aba
c’ Aaba’BcaAa’ab’extend
inuit net
loom (identity element)
operations
inverses
cherokee seven star
murphy’s mouth
loop transfer equivalents
3 loop openings
opA
opB
ldna
rdna
16 diagonals
4 loops
tennis net
www.torusflex.com
plus other pages on why string figures
plus other pages
other systems
http://blogs.wsj.com/speakeasy/2012/09/17/string-theory-can-cats-cradle-help-save-our-schools/
http://www.huffingtonpost.com/james-r-murphy/