Six-year-old Emma and her five-year-old classmate, Alexandra, are adding 1,756 and 1,268. They’ve penciled the numbers neatly into their notebooks, but the method that they use to come up with the answer, 3,024, isn’t something you’d see in a majority of schools, let alone kindergarten. Each of the children loads a wooden tray with golden beads and sprawled on a mat on the floor, they combine six of Emma’s beads and eight of Alexandra’s beads. "Nine units, ten units!" Alexandra counts triumphantly. With that, she scoops up ten beads and skips across the room to a cabinet, where she trades them in for a "ten bar" – ten beads wired together. Now the two children count in unison: five 10s, six 10s, seven, eight, nine ten 10s! Then, ponytails flying, they run to trade in the ten 10s for 100.

The 21 other children in the multi-age Montessori class seem equally energetic as they follow their own independent agendas. Five-year-old Daniel lays out wooden letters that spell "May is back. I am happy." Nearby two 4-year-old boys stack pink blocks, watch them topple, then stack them again, only this time with the larger ones on the bottom. Three-year-old Kate uses a cotton swab to polish a tiny silver pitcher – a task that refines  her motor skills – while 5-year-old Amanda gets herself a bowl of cereal, eats it at the snack table, then cleans up after herself. Montessori children are usually energized by "big work" such as making responsible choices and taking care of personal needs and the environment.

Going back to Emma and Alexandra, the teacher sits on the floor with them and they show her their notebooks. "Did you exchange your 10 ones for a 10 bar? Did you carry? Did you write it down? How many 100s do you have?

"None," Alexandra replies.

"That’s great!" says the teacher.

The teacher returns to Daniel and together they read his sentences, "May is back. I am happy. Me is flowers." "It doesn’t make sense," the teacher says as Daniel joins the teacher in giggles.

Back to the mathematicians... The teacher says, "Alexandra, please show me a 3 going in the right direction."  Alexandra erases, and writes the numeral "3" again. "Good job! OK, put the beads away. I’m going to give you another problem."

Back to Daniel, whose letters now read, "May is back. I am happy the flowers smell good."

Now 5-year-old Ryan brings the teacher his work. Using pieces from a wooden puzzle, he has traced the states around Texas on a piece of paper, colored them, copied labels and pasted them onto his new map. "Louisiana, Arkansas, Oklahoma, New Mexico," he reads with the teacher.

Throughout the day Ryan and his classmates make responsible choices regarding which learning activities to do next. Each activity engages the children in a number of movement patterns that form a foundation for neurological development. The hands-on learning materials are also concrete models for thinking processes and abstract concepts.

When the day is over each child will have completed ten to fifteen different activities, most representing curriculum content quite advanced for someone who, after all, is pre-kindergarten or kindergarten age. When Montessori parents describe what their children are learning their friends and family are amazed.

Montessori learning always teaches in the natural way Learning begins with the whole and moves to the part Montessori learning is much deeper than traditional learning in a course of study Performance not test based A wide variety of modules Montessori gives each individual the chance to fulfill their potential to become an independent secure and balanced human being It was never her goal to make geniuses

Learning is natural, joyful, creative, optimal and at an individual pace Beautiful, Inviting, Alive, Child-size Environment Intensity does not fatigue Concentration on specific capacities not vice versa Montessori provides an artistic, warm, intellectual, encouraging environment Her ideal was only that the learning experience should occur naturally and joyfully at the proper moment for each individual child.