21 Century Math Method in Pedagogy and Psychology

- What we have been researching?
- We were researching vectors.
- But what we should research?
- We should research arrows of vectors.

21 Century Math Method™ (21MM™) is a new mathematical method developed by me. 21MM is to replace 20 century axiomatic method at least in fundamental mathematical research and probably in other aspects of life, including pedagogy, particularly study of mathematics and programming.

This article is to discuss possible pedagogic and psychological issues related with teaching and studying of 21MM in universities as well as in lower schools.

About Possible Influence of 21MM on People's Minds

People's brains function accordingly a variant of neural nets principles (at least, it is so in the present sinner state). People's spirit, soul, and heart (as information system related with the immune system) probably also are neural nets.

Unlike any other universal logical method we ever used before, 21MM is comparably simple compared with the principles of neural nets. It is probably also comparably powerful as a foundation for a mind.

This may probably cause some affecting of our brains by this method, I even do not exclude the possibility of physiological changes.

Firstly, don't afraid. I have already years long been thinking based on principles of 21MM (not yet formulated or understood by me that time but used intuitively) and this has caused no ill effects. Probably it even caused certain positive changes. Accordingly my personal experience (especially during research of Algebraic General Topology), it seems to make the psychic somehow more calm and persistent and reduces unneeded nervous tension. It is so even despite of I was much troubled, beaten, hungry and even seriously brain damaged by beating during the time of my beginning research of Algebraic General Topology (No, the discovery of AGT was not a consequence of these troubles.), the elements of this method seems positive even in such hard conditions. An additional argument is that the ancient philosopher Socrates seems to have been using some similar method and this has not caused him a brain damage.

I deem that a possible effect of studying 21MM is that it may partially replace the base principle of neural nets as a base principle of our minds (the neural net remains but it may fix on using a definite method). Many scientists are used to think that when a free neural net fixes on one principle, it is bad as it loses freedom of changing to different principles. But is it a possible case with 21MM? Probably not because inside 21MM may be probably not less freedom and adaptation than inside neural nets.

So, my personal recommendation is to encourage study of 21MM and training in its frequent and constant usage.

21MM is so simple that it can be formulated (at least partially) in a form understandable by pre graduates. However we yet need to research how studying this method may influence psychic of children of different ages. Presently teachers can safely experiment by teaching it at high courses of mathematical faculties of universities.

Study Order

Probably the main pedagogic issues related to 21MM which we need to research is:

whether 21MM can be teached before quantifier based logic (e.g. using teaching by example with a teacher showing the pupils patterns of usage of 21MM, or teaching 21MM based on simple propositional logic without quantifiers if possible);
whether it is reasonable to teach 21MM before the predicate logic (and teach predicate logic after it, using 21MM to explain what is a quantifier), considered from different positions (social, professional, personal development, psychological etc.)

Note that here by quantifier logic I understand not only the formal system of predicates but also informal notion of words "all", "any", "exists" as it may be teached e.g. in the native language courses in low schools

Also note that in fact low school teachers already teach some elements of 21MM during centuries, as these are intuitively understood. Probably we already have all elements of 21MM in low school, a missing thing is the system. But can we teach the system which was understood only in 21 century at lower levels than universities? My opinion is that scholars (at least of specialized mathematical schools) indeed can understand it.

References

21 Century Math Method. Victor Porton

Ad: More than 1500 books about Mathematical and Symbolic Logic

My homepage | My math page | My math news | Donate for the research