One of the most noticeable characteristics when you walk into a Montessori classroom are the many materials. The Montessori method focuses on concrete, "hands on" materials which are carefully placed on shelves throughout the room at the child's height. Children are given lessons with these hands-on materials, each of which isolate a single concept in order to make it clear. In later years, these materials and lessons re-emerge and evolve, becoming more complex and abstract as the child progresses through elementary school. This evolving pattern of concrete to abstract learning is prominent in most Montessori school curriculums, and CVMCS is no exception.

Children's House Classrooms

In early Children's House years, several important concepts and objectives are introduced to children via these specially designed, concrete materials. And likewise, over time, works will gradually be extended to include increasingly abstract concepts. For example: In language, the child uses sandpaper letters to touch, trace, and hear letter sounds before undertaking the more abstract work of writing those letters on paper. In science, the child can experience real animals and plants before progressing to the more advanced work of studying related facts. In math, a set of 10 number rods is available for children to experience and count the quantities, which serves as a foundation for later abstract math concepts and procedures.

E1 Classrooms

In the E1 classroom, all materials are designed to guide student thought from concrete, to abstract, to critical thinking. An example of this is the standardized color coding used to understand place value in math. Students learn the hierarchies of place value according to color, such as: units are always green, tens are always blue, and hundreds are always red. The cycle continues in that the one thousands are green, ten thousands are blue, and one hundred thousands are red. This pattern continues as numbers continue.

All of our CVMCS materials, even written materials, make use of this color coding. This helps students internalize these concepts, which helps them on the journey to abstract thinking.

Once students have internalized the concept of place value using color coded materials, they are introduced to more traditional math concepts.

Students in E1 take this thought progression to the next level, engaging in critical thinking by applying their math skills in our Number Talks discussions, Science work, and various other projects.

E2 Classrooms

Each E2 classroom has the same standard tactile Montessori math materials from E1, which provide opportunities for concrete math application. Our math curriculum then moves student understanding to an abstract level by supplementing concrete materials with pictures, place value charts, algorithms, and mental math strategies. Students are encouraged to use the concrete materials to fully understand or review a concept at any time.  For the child, the longstanding tactile familiarity of these materials helps create a deeper relationship to any newly-introduced abstract concepts in E2.
Critical thinking skills are developed by using application problems — multiple step problems that stem from real-life situations like designing structures or understanding budgets.  Students explore mental math fluency by engaging in Number Talks, a structured conversation around number relationships. In E2, students also share multiple strategies in open dialogue.

If you would like to read more on this topic, please read the wonderful article below on the use of concrete materials and math in the Montessori classroom:

What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education