In the early Montessori materials, children explore and practice concepts through concrete, hands-on manipulatives. These materials, from the Pink Tower to the Golden Beads, deconstruct complicated concepts into their simplest parts, allowing children to build their understanding of language, math, cultural, sensorial and practical life skills through increasingly complex activities. A child needs to experience the cubes of the Pink Tower, for example, before she will appreciate the language of "cubing" we use in the advanced math materials. A child needs to develop the sensitivity in his fingers through the sensorial Touch Boards in order to distinguish the small differences between letters as he reads and writes.
When a child has moved through these materials and is beginning to more regularly think abstractly, he is also ready to absorb lots of new facts. The Cultural materials will respond to this by introducing details about cities and landforms around the world. The Language materials will respond by offering to the child more involved reading experiences and introducing the child to research skills. The Math materials begin to introduce math facts, giving the child the opportunity to memorize frequently used operations to add to his or her math fluency. The Strip Boards are a great example of this.
The Addition Strip Board, shown here, gives the child practice with addition facts, increasing her speed and understanding. The child chooses an equation and records it first on paper. Then, by combining the wooden strips to indicate the augend and addend, the child can see the su before checking her work against the the control board. Recording her equations and answers helps to increase the recall and speed for these math facts. Like all Montessori materials, even these more abstract experiences are didactic and self-correcting... and a great opportunity for the child to master the skills he or she will need to explore our world independently.