The Hand is the Pathway to the Mind 

At Qingdao Amerasia International School, mathematics is not merely the memorization of rules but an exciting journey of discovering universal truths. Our Montessori program, catering to children from Toddler to Grade 2, fosters abstract knowledge through concrete, hands-on, and sensorial experiences. Each bead, puzzle, and golden cube serves as a bridge from the tangible world to the abstract universe of numbers. 

Toddler (Ages 1–3) | Order & Exploration 

In these early years, math begins with the development of order, motor coordination, and sensory exploration. Activities like pouring, stacking, and engaging with knobbed puzzles prepare both the body and the mind. The knobs help train a child’s pincer grip for future writing endeavors, while pouring activities develop hand strength, while introducing young children to the basic principles of quantity and measuring and controlling amounts.  Words like “more,” “all gone,” and “heavy/light” lay the groundwork for mathematical language and concepts. 

Early Childhood (Ages 3–6) | Sensorial Discovery 

At this magical stage, math concepts become explicit as children connect quantities to symbols, discovering that numerals represent tangible objects. Using materials such as the Spindle Box, they explore concepts like zero, one-to-one correspondence, and conservation—the understanding that quantity remains constant despite changes in appearance. What makes this stage so enchanting is that children are not given answers; instead, they uncover mathematical truths through exploration. 

Lower Elementary (Ages 6–9) | Transitioning to Abstraction 

By the time students reach the Lower Elementary level, the focus shifts from understanding “What is 100?” to exploring “How can I use my understanding of 100 to solve problems?” The Montessori materials play a crucial role in this transition: 

Golden Beads: Through physically exchanging 10 ten-bars for a hundred square, students grasp place value and the base-10 system. 

Math Operations: Addition, multiplication, subtraction, and division are introduced concretely with beads, as students combine, repeat, remove, or share quantities. 

The Stamp Game: Acts as a bridge from concrete materials to symbolic numbers, akin to transitioning from training wheels to independent cycling. 

The Checkerboard: Provides a vibrant, kinesthetic map of multiplication that explains the logic behind algorithms, not just the procedures. 

As they solve problems on paper, children’s understanding infuses numbers with meaning. They recall the weight of the thousand cube, the texture of the beads, and the logic inherent in the checkerboard.