“Montessori believed that ‘what the hand does, the mind remembers’, and then internalizes”. NAMC training blog 2018/07
Abstraction is the point when the Child no longer needs concrete materials to solve mathematical equations. At this point they can use their cognitive skills to understand the concepts and calculate the answer.
Montessori materials isolate a certain concept that the Child discovers sensorially. When they have mastered these materials, they can turn to calculating equations with pencil and paper, remembering the ‘feel’ of the materials. This is the point of abstraction.