Introduction to Mathematics
The basic concepts of math are learned by a child in two ways - either using concrete materials at an age when they enjoy manipulating equipment, or abstractly when they are older and in elementary grades.
Dr. Montessori showed that if a child has access to mathematical materials in their early years, they can easily and happily assimilate many facts and skills of arithmetic. These same concepts on the other hand, may require long hours and drill learning if they are introduced later, in abstract form.
In a Montessori classroom, a child first experiences the concepts of 1, 10, 100, 1000 by holding these quantities in their hands, before they’re introduced to the the symbols for these quantities.
As they get more familiar and comfortable with numbers 1 - 10, the decimal system is introduced moving from quantity to symbol. Fundamentally, they are learning by discovery - not by being told - and slowly they develop an enthusiasm for the world of numbers.
Mathematical operations like addition, subtraction, multiplication and division are done in a similar way - using concrete materials that are manipulated to understand and arrive at the solution. Slowly they’re weaned off materials and moved to the abstract as they grow older and start to gain an understanding of concepts.