The aim of these different materials is for your child to familiarise himself/herself with a given learning process, first in the concrete, and then gradually to move towards abstraction.
Indeed, between the ages of 3 and 6, your child will discover abstraction. The Montessori pedagogy and materials will nurture him/her on the intellectual path from the concrete to the abstract.
Thus, for example, to explain the same mathematical concept - addition, subtraction, multiplication or division - the Montessori pedagogy uses concrete materials - beads, sticks, tokens, etc. - to move towards abstraction, the concept.
Your child is an actor of his or her own knowledge and not a passive recipient of transmitted knowledge.