Algebra In Early Years ?!

One of the amazing things about Montessori education is the subtle, indirect introduction of complex mathematical ideas (algebra!) right in the preschool years.

For instance, this 3 year old is working intently on the "Trinomial Cube” material. On the face of it, this is a fascinating puzzle that requires the child to place 27 different cubes in a manner that allows the box to close. However, there’s something much deeper going on: this cube is actually the geometrical representation of the algebraic equation (a+b+c)^3. As the child grows older, this serves as a foundation for understanding the concept of “cubing” a number or set of numbers.

By converting a dense equation into a wonderful, self-correcting puzzle, Montessori shows us that even young children can understand and subsequently master concepts far beyond what we may normally expect!

The Road to Memorisation

In conventional education, it usually transpires that rote memorisation comes first, and then conceptual understanding arrives (if at all).

In Montessori, conceptual understanding combined with sufficient practice leads to memorisation in a very natural manner. The addition strip board is a typical example of this process: the child works on single digit addition using concrete material.

After sufficient practice — along with recording the sums on slate or paper — the child is able to naturally increase her recall of individual sums & eventually memorise them.

Further, the concrete materials allow the child to make her own discoveries; for example, it is common to see children discover the commutative law of addition on their own (a + b = b + a), or in the case pictured above, that the number 10 can be split into two smaller numbers in many different ways!

Nesting Dolls in Montessori

The first Russian nested doll ("matryoshka") set was carved in 1890 by a couple of Russian craftsmen; today they can be found across the world, including in Montessori environments. We love our Indian version of the original Russian matryoshka dolls!

What do these dolls have to do with Montessori, you ask?

Initially, young children love the surprise of opening these beautiful dolls to find another inside. Soon they begin working to undo and put together the dolls in the right order. Nesting materials like these dolls help children understand spatial relationships, develop fine-motor co-ordination, build the language of comparison (big, bigger, small, smaller), as well as prepositions (inside, outside, under). These dolls also give children the opportunity to concretely experience the concept of a whole object that contains individual parts that are nestled within.