Mathematics

Dr. Montessori observed that the mathematical mind is something that is innate in all humans and all cultures. The child has the need and ability for logic, sequence and grouping of numbers and concepts. In the Math area, each material provides for a physical exploration of math. Because the 3-6 year old child is gifted with an absorbent mind, he has the ability to learn mathematical concepts and figures with ease. By allowing the child the opportunity to experience all four mathematical operations (addition, subtraction, multiplication and division) through concrete materials before moving to abstract concepts, the math area acts as an aid to the child in the memorization of math facts.

In the Bayit we offer to the child the experience of mathematics through the use of concrete, sensorial materials. Dr. Montessori referred to them as "Materialized Abstractions"; specific physical objects which have been designed to present to the child the abstract concepts of mathematics and allow for manipulation in the hands of the child through his own will of movements. The Montessori math materials allow the child access to the abstract ideas that the physical materials represent. Traditional education relies on only the abstract, while the Montessori math materials bring to the child the missing elements and relationships of mathematics in a concrete form.

There are three reasons that the Montessori Bayit is able to have mathematics materials for the 3-6 year old child to explore:

1. The 3-6 year old child learns best through hands on experiences with real objects. The child begins by manipulating elements and relationships of mathematics with the hand so that he can move to a place where he can manipulate elements and relationships in the mind only. Eventually he will no longer need the concrete materials and will complete what Dr. Montessori referred to as the “passage to abstraction.” This generally happens a few years into the 2nd Plane of Development, around 7-8 years of age.
2. Indirect and direct preparations have taken place in other areas of the Bayit (i.e. Practical Life and Sensorial).
3. The child is born with a mathematical mind which has a natural interest in the elements and relationships of mathematics.

The materials are organized into sets of exercises organized around six specific key mathematical experiences, the names of which are a clue to each of their key mathematical experiences.

The main function is to introduce the base 10 number system. Once the child has a solid understanding of the base 10 number system, he may be introduced to one of two parallel directions. Derech Eretz Montessori will include the foundation of 1-10 in Hebrew Numerals.

The main function is to introduce large quantities that are organized in groups of 10 and show how quantities are formed in the decimal system. The child will hear and experience what is done with large quantities (i.e. add/multiply and subtract/divide).

The main function is to allow exploration of quantities through the linear sequence of counting and incorporate the conventional language of counting. Derech Eretz Montessori will include the continuation of counting for Hebrew Numerals.

The main function is for the child to be able to explore and systematically extract the essential combinations of addition, subtraction, multiplication and division (i.e. the tables). Rather than the rote memorization through the utilization of flash cards that is generally experienced in traditional Elementary, the child will explore, extract and naturally memorize the essential combinations of all four mathematical functions.

The bulk of the child’s work in mathematics will be with concrete materials, but at some point the previous work will converge and the child will apply everything he has previously learned. Depending upon the child, he may have an opportunity to engage in a purely abstract activity and completely leave behind the manipulative materials. This can happen suddenly, usually when the child realizes he knows the answer without using the manipulative materials.

The main function is for the child to have the opportunity to work with quantities less than 1. Fractions are very abstract concepts when thought of mathematically, but they become concrete when thought of in the real world experience of the child (i.e. sharing cookies).

The beauty of these simplistic materials is that they are not simplistic at all. The Golden Beads that allow the four-year-old to form numbers such as 9314, later serve as concrete examples of the geometric progression from a dot, to a line, to a square (area), and then finally a cube (volume). Additionally, this same material serves as a concrete example of the algebraic ideas of 10⁰, 10¹, 10², and 10³. The four-year-old child does not yet know the depth of the mathematical foundation of knowledge that he has taken in with his senses.