Montessori, Math for 1-3 ages (Michael Olaf Web)

Toys and books for Age 1-3 that teach math and geometry (see below): 1-2 math

At this age the child is introduced to the world of math and geometry through manipulative toys and puzzles, real work such as the practical lifeactivities, and the natural world of physics (sand and water) and other sciences. Laying the foundation for later math and geometry work.

It is not enough for the teacher to restrict herself to loving and understanding the child; she must first love and understand the universe.
—Maria Montessori, M.D.

An interest in and love for astronomy and geology, sand and water, and all of science begins early. The first lessons come from nature—experiences of the sun and wind, playing in sand and water and mud, seeing the sun rise and set, watching the stars at night, visiting the seashore, and the child’s own collections of rocks and minerals.

First we give the child the rocks, sand, water, mud, oceans, clouds, stars, lakes, and so forth; and then we give the names. All of this experience and knowledge leads to a natural concern and responsibility at a later age because children love what they know.

What is God? He is length, width, height and depth.
—St. Bernard of Clairvaux

There are also many manipulative toys and puzzles that give the child practice in making comparisons, graduated sizes and shapes, all important preparation for math and geometry.

The foundation of a love of math comes not from rote lessons, but from joyful experience in seeing shapes and objects, in exploration with hands, and in moving through space. 
The formation of the mathematical mind, which will last a lifetime, comes from early, simple, everyday activities —collecting, counting, sorting, putting things in order, classifying, comparing sizes and colors, carrying heavy objects by hand or in a wheelbarrow, setting the table, and discovering relationships and patterns through these activities.

In the past, mathematical relationships were wondrous miracles, and so they are still for the young child who is discovering them for the first time. It is a joy for the adult to stand back and observe these discoveries as the child makes them.

Reciting one, two, three, four, five, and so on, is fun for a child, but not nearly so exciting as discovering that these words stand for quantities of anything—buttons, peas, spoons, family members, stars in the sky—and the realization that these concepts are used and understood all over the world!

And we should never underestimate the value of practical life work, real work with the brain and hand working together in building a strong foundation in math and geometry.

If men had used only speech to communicate their thought, if their wisdom had been expressed in words alone, no traces would remain of past generations. It is thanks to the hand, the companion of the mind, that civilization has arisen. The hand has been the organ of this great gift that we inherit. 
—Dr. Maria Montessori