Mathematical structure
An abstract hypothetical structure that begins with concepts that are not defined or taken for granted, concepts defined through concepts that are not defined, so we come up with expressions and terminology of mathematical proven sentences that are called theories.
Mathematical building properties:
Compatibility: the lack of contradiction between any of the axioms.
Independence: It is not possible to reach one axiom to another. In other words, the axiom does not have one consequence of another.
Completeness: the set of axioms is sufficient to demonstrate any issue or theory linking terms.
Classification: that is, the different models of the same hypothetical structure are the same. In this case, it is called the release structure.
** Why focus on the mathematical structure ??
Jerome Bruner says that the task of education is to prepare the individual to face the future life by providing him with thinking and life skills
Necessary for it and is done in two ways:
The first: Exposing him to situations in which he applies what he has learned, which is called the transmission of the learning effect.
The second: learning the basic cognitive structures that provide an opportunity for meaningful learning.
Focusing on the mathematical structure in the curriculum is essential for:
1) It is supposed to be the means for transferring the impact of knowledge and training to new situations.
2) Make the individual more interested and his ability to comprehend and understand better.
3) It increases the individual's ability to remember ideas and thus helps to quickly retain and not to forget.
4) A narrowing of the gap between the advanced knowledge of the subject and the subsequent knowledge acquired by the individual to help him to continue his lifelong learning on his own.
An example of a mathematical system:
The group and the element can be represented by a point or a number
And group items are numbers or points
The elements of one group are linked to another group through relationship and association.
There are basic relationships are: order, valence, and conjugation.
Learning: It is a change in behavior acquired through some experience, so learning mathematics in the elementary stage achieves multiple goals that start from training it to deal with physical things when counting, calculating and measuring until it is able to symbolically deal with mental images, and educators see that there is a gradient that can be placed in a form. Sequential, which are:
(1) Learn Sensory Motor Skills:
For example, using a caliper and a ruler to draw a straight line or an angle segment.
(2) Learning perceptual motor skills:
Like using a protractor to measure an angle, or a graduated ruler to measure a specific length, or to draw a triangle with known dimensions.
(3) learning mental interconnections:
Such as learning math operations (addition and multiplication) and some terms (factor, multiplier, and prime factors).
(4) Learning the concepts:
Learn the concept of counting.
(5) Learning to solve problems:
Such as the interrelation between physical sensibilities and mathematical abstractions.