The Montessori mathematics materials allow preschoolers to begin their mathematical journey from the concrete to the abstract through manipulation, experimentation and invention. Children internalize math skills (number, symbol, sequence, arithmetic operations, etc.) by first using concrete materials and then through memorization of basic math facts. Rods, spindles, cards, beads, and cubes are some of the tools used to symbolize mathematical concepts. Children experience the thrill of discovery when choosing these materials themselves to perform mathematical operations on their own.