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!

The Path to Writing

Young children are often cognitively ready to express themselves through the written word, but have not yet developed their fine motor skills enough to write beautifully themselves. But how do we isolate the cognitive from the physical when it comes to written expression?

Dr Montessori’s insight was that by using printed “movable alphabets”, we can allow children to express themselves with the written word without yet engaging in the physical act of writing! Children as young as 3 can start constructing words phonetically, without worrying about the shape or form of the letters just yet.

This provides the cognitive & expressive practice the child needs, without overwhelming their hands with the physical effort they are not yet ready for. As with other materials, the movable alphabets illuminate a key Montessori principle: to isolate a single, specific concept for the child to thoroughly master — in the case, the skill of word-building.

Muscle Memory In Writing

Maria Montessori famously said, “What the hand does, the mind remembers”. The hand reports to the brain; the brain guides the hand; the cycle continues, resulting in the development of the intellect.

Thus, while learning to write, it is important to not jump too quickly into pen-paper work before building and refining the child’s muscle memory using their hands. The “sandpaper” letters give the child a concrete, tactile experience that helps imprint alphabet patterns in the brain.

In this case, this child is working towards mastering his understanding the letter “v” by tracing the corresponding sandpaper letter. This is critically important preparation before the child physically engages in writing the letter on paper or slates (and the coarse sandpaper is very enjoyable to run their fingers through!).

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.

Practical Life: Matching Keys with Locks

Some Montessori activities are genuinely complex, and can be very confusing for adults unaccustomed to our approach. However, some other Montessori activities are very simple to understand, but can breed endless complexity with little tweaks.

One of our favourite introductory practical life exercises is the lock-and-key set: this is a simple set of locks and keys, with children trying to match the correct pairs. Based on the child's level, the set can contain a variety of differently sized locks, or a larger number of pairs.

It is not unusual for us to see children younger than 3 working on solving this puzzle for an extended duration of time without asking for any help. It is indeed a wonderful activity for developing fine motor skills and problem-solving abilities, and very easy to replicate at home!