Concentration is a skill that needs practice to improve and develop. Montessori classrooms provide an environment that offers the time and opportunity to practice deep concentration. The uninterrupted work period enables the children to focus on a task for as long as they wish without an adult-imposed schedule. The adult in the environment is cautious not to interrupt and break the children’s concentration. As the ability to concentrate improves, the children also develop better self-control and self-regulation.
“When the children had completed an absorbing bit of work, they appeared rested and deeply pleased.”
The binomial cube, when first introduced to the child, is presented as a challenging, three-dimensional puzzle. The cube is made up of a number of colored blocks, which fit together in a specific way. Assembling it uses a child’s fine-motor skills and requires the ability to discriminate between the blocks based on multiple characteristics. Unlike Montessori’s iconic pink tower, for example, the binomial cube does not isolate only one quality. Some blocks have one color, others have two. Some blocks are cubes, while others are rectangular prisms. While the pink tower blocks vary only in size, the binomial cube’s blocks vary in color, size, and shape! This makes the binomial cube a more complex sensorial material, and it requires organized thinking to master. The binomial cube’s big brother, the trinomial cube, is a child’s more complex next step.
Like other sensorial materials, the binomial and trinomial cubes are self correcting: when properly assembled, the blocks form a cube that fits perfectly inside of its wooden box! Even if the cube is built outside of its box, visual cues alert the child to any errors they might have made.
Children return to the cubes time after time, manipulating them with a focused sense of purpose. After a child has mastered building the binomial or trinomial cube inside of the box, he may then try building it outside of the box, or building each layer separately in order to observe similarities in patterns. Over time, the child’s familiarity with the cube’s physical aspects will lead to an internalized understanding of the abstract concepts the cube represents. #concretetoabstract#handsonlearning#binomialcube#trinomialcube#sensorial#preparationformath#tma#montessori#privateschool#arlingtontx#arlington#texas#infant#nido#toddler#earlychildhood#kindergarten#elementary#education#privateeducation#themontessoriacademy#themontessoriacademyofarlington
The Montessori materials share certain qualities: they are hands-on, beautiful, and self-correcting. They isolate concepts to be explored and they allow children to understand independently whether they have done the work “correctly.” Many of the materials also include implicit lessons, concepts that are consistently applied in the design of the lessons such that certain relationships are internalized for children before they are ever explicitly taught.
For example, the materials throughout the Sensorial area are presented in series of tens, in which each cylinder or cube or prism differs from its neighbor by a value of ten and in which there are ten of any of those pieces. The Pink Tower, for example, is a series of cubes from 1cm in width to 10cms in width, with each cube 1/10th smaller than its larger neighbor. This orderly internalization of the relationships of tens is an implicit foundation for the Base Ten system, the relationships of numbers in our most commonly used number system. Children learn that units can be counted up to 9, but that once you have counted the tenth of a series, you are working with a new kind of set. Whether you are counting units or tens or hundreds or thousands, you can only count 9 of those things before you have to bump up to the next kind. Nine units plus one equals one ten. Nine tens plus one ten equals one hundred, and so on.
Working with larger numbers, then, is far more manageable for young children in our classrooms. We know they are motivated to operate large numbers (just ask your child how many jelly beans he or she thinks are appropriate for dessert- you are likely to hear something like, “One majillion and eighteen.”) The Golden Beads, then, allow children to combine their internalized understanding of the Base Ten system with materials that let them count very very high. The result is work with naturally motivating materials that supports their developing understanding of numeracy and mathematical operations.