In contrast to many preschool programs, which focus on math readiness, AIM’s Montessori preschool program actually enables students to learn arithmetic into the thousands while in preschool.
The math program builds upon indirect preparation especially in the sensorial area. It’s build around a systematic progression from very concrete materials to more abstract operations. Montessori math is too rich to explain completely in a short web description, so here are just some highlights to give you a flavor of the different activities and levels of math that Montessori preschool students at AIM discover.
- Counting to 10. 3 ½ year olds may start with math by using the number rods and spindle boxes to learn the numbers of 1 to 10. They learn one-to-one correspondence, and learn that the number "three" doesn’t mean the 3rd in a series, but the fact that three individual things are combined together. (This may seem simple, but it’s a critical skill many children struggle with!)
- Counting beyond 10. Children then get introduced to the colored bead bars. Here, the numbers of 1 to 10 are represented by differently colored beads strung together in bars. Students soon associate the number with the color; they then add the colored 1 to 9 beads to the golden 10 bead to build numbers to 20.
- The decimal system/place value. With the addition of the tens board, students begin to build numbers up to 100, and soon progress to working with the golden beads, which introduce our Montessori preschoolers to the decimal system, and enable them to understand numbers into the thousands (a skill not introduced in California public schools until late 2nd or early 3rd grade!)
- Addition & subtraction (and later, multiplication & division.) Once students know the golden beads and can build four-figure numbers and read them correctly, they learn that addition is nothing more than putting together quantities. In the collective addition game, a teacher has three students make numbers with the golden beads, then combine their quantities. There will be big piles of unit beads, ten-bars, hundred squares and thousand cubes, making it real to each child what huge numbers they are dealing with! Earlier, they had learned that a ten-bar (a bar with ten golden beads strung together) is the equivalent of ten unit beads. Now, they exchange ten units for a ten bar, and thus playfully learn what carrying means.
- Movement to abstraction. Once students really understand what the operations of arithmetic mean with the golden beads, they use the stamp game, the dot game, and the small bead frame to steadily transition to more abstract ways of doing the math. This process continues seamlessly, with the same materials (and additional, well-integrated ones) all the way into our Montessori elementary program.
- Math facts practice. In parallel, children start on math facts practice. With a wide range of materials, it’s fun to add single digit figures, or to subtract them. Students enjoy this practice, and learn to control their own work with control charts: there’s no temptation to cheat, as the work is always at the student’s choice, and now rewards or grades are passed out for doing well.