The Nature of Mathematics Thingking

Let's check your knowledge! Okay, I want you to choose the correct answer from my question.
4 x 6 =  a.6+6+6+6 or b. 4+4+4+4+4+4 ???
If you choose b that's the wrong answer, yup the correct answer is a. Why? Okay, let's read the question slowly. 'four times six' it's mean we have six plus six until four times. You get it?  I hope yes. :)

In our mind we have 2 parts, there are rationality or abstracted, and idealized or experience thingking. The abstracted part to think only selected characteristic of object. It is contain about the mathematics object, and abstract object, for example number, field, cube, plus, etc. The idealized part assuming to be perfect or real characteristic. It is contain about the daily experience, value, color, price, etc. So, what happen in our mind? The information will be process in memory, then we are understand about that, we apply that, make a symbolize then we evaluate that. That process make us have willing, knowledge, attitude, skill and experience.

Volcano of Mathematics

The concrete mathematics is the object in our reality for example, there are two birds in the air. That's just for a kindergarden school. The model concrete of mathematics is about operation sign, for example there are two apples plus three apples equals five apples. This level for Primary School and Junior High School. The formal model of mathematics is a symbol for the operation, for example use point or x or y. This level use in Senior High School. And finally the formal mathematics is about the object of mathematics for example we use the number 3+2=5, a cube, why it's call cube, small, big. What is the definition of small? You cannot definite that, but you know that. So, in our level we must use our intuitive and our knowledge.