Think Abstractness

Why some students can learn abstract Math easily while most can’t ?

Education Psychologists help to reduce abstraction level when learning
Abstract Math Concepts.

There are 3 abstract levels:

1) Quality of the relationship between the object of thought and the students:
The opposite of abstract is concrete.
Some students can relate the abstract math objects to concrete
familiar concepts, the closer the relationship the more concrete the
objects are.
eg. Relate abstract ‘Ring’ to familiar concrete object ‘Integer Z’.

2). Process conception and Object conception:
The mental process that leads from process conception to object
conception is called “Reflective Abstraction”. (Piaget).

eg. Quotient Group = G/H = {Hg = gH | g ∈ G}
Process Conception (Canonical procedure ): take all elements from H,
multiply them on the right with some element from G. Similarly for
multiplication on the left.
Object Conception: Partition called Quotient Group.

3). Degree of Complexity of the concept:
eg. Group of prime p, called p-iadic group is more complex than any group.

Music is abstract par excellence, hence a good training for kids to study later abstract subjects in Advanced Physics or Advanced Mathematics. Great scientists like Albert Einstein and great Mathematicians played quite well musical instruments (Violin for Einstein).

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