Children are helped to understand that Maths is not just numbers and algorithms but it is shapes, patterns, problem solving and much more. Thus they are encouraged to see what important role it plays in everyday life. Integrating maths into art and craft, cooking, gardening and nature comes about sometimes through conscious efforts but many times simply arises spontaneously. Geometry lends itself to be integrated with art and craft; fractions with cooking and sharing; measurement with time, shop keeping; and measuring any number of objects in terms of length, width, height, weight, area, perimeter and volume.
When teaching any aspect of maths, great emphasis is laid on the child understanding the underlying concept in a concrete way. This is brought about by introducing a new concept when the child is ready, first through concrete materials, then moving on to pictorial representation and finally abstraction. While Montessori materials play an important role in bringing about this conceptual understanding, inspiration is also drawn from other materials including natural objects, origami, body movements and clay. Montessori materials are designed so that these not only help children understand every intermediate step in understanding a concept, but also in moving gradually towards abstraction. The sensorial aspect of the Montessori materials very much appeals to the young child.
Once any concept is understood, practice helps children gain mastery. For practice work, there are numerous workbooks, worksheets, mental maths problems and games that one can choose from. Teaching a concept to another child is a reinforcing way of showing that a concept has been mastered and as such this is encouraged. Internalisation of addition, subtraction, multiplication and division facts are brought about through practice and playing oral games, and varies very much with each individual child. The importance of reviewing concepts learnt is gently emphasised.
Investigations are also an important part of learning maths and are approached through story problems, two-dimensional and three- dimensional puzzles as well as work with natural materials and clay. These are undertaken individually, with teacher guidance, in groups, or as part of another activity or topic.