The Mysterious Trinomial Cube

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Today, we’re going to highlight on one of our students’ favorite works; the trinomial cube. There’s real beauty behind the intricate details of this mathematical work, details that are hard to notice at first glance.

The direct aim of this work is rather obvious; to build a puzzle in a box. The indirect aim, an introduction to algebra and preparation for the formula a+b+c³. DSC_0349 (1)

The child approaches the box with curiosity. It’s elegant details can spark the interest of anyone. Children are inherently captivated by mathematical materials. The colors, the difference is sizes and heights…”Why these specific colors?”, “Why do they fit together like that?”…DSC_0343

While there are many hidden lessons in this puzzle, the child is actively working towards building a concrete foundation for the abstract nature of the formulation, which they will later expand upon. The puzzle helps the child grasp the concept of a+b+c³ at such a young age, rather than simply memorizing the formula.

Through the child’s discovery, they come to unlock the intricate layers of the trinomial cube.DSC_0356 (1)

To begin, the guide carefully opens the box, and lays out all of the pieces, organizing them in different manners. With little, to no words, she places the cubes upon the lid, pairing the colors to one another. Each layer is placed in the box upon completion. The child is then invited to do the work on their own. There are many variations of the trinomial cube that call upon the child’s creativity, imagination and critical thinking.

“These small objects fascinate a child. He must first of all group them according to their color, then arrange them in various ways, making up a kind of little story, in which the three cubes are three kings, each one having a retinue identical to that of the other two, the guards being dressed in black. Many effects can be obtained through the use of this material…when playing with this material, a child forms a visual image of the arrangement of the objects and can thus remember their quantity and order. The sense impressions received from these objects furnish material for the mind. No object is so attractive for four-year-old children. Later on, by calling the kinds a, b, c, and writing the names of the separate pieces according to their dependence upon their own king, five-year-old children, and certainly six-year-olds, can store up in their minds the algebraic formula for the cube of a trinomial without looking at the material, since they have fixed in their visual memory the disposition of the various objects. This gives some idea of the possibilities that can be attained in practice.” (Montessori, The Discovery of the Child)

To see the lesson in full, click on the link below:

https://www.youtube.com/watch?v=ZEZnNFxsnS8#t=13

Less is More – The Beauty in the Simplicity of a Prepared Montessori Environment

“A place for everything and everything in its place.” – Dr. Maria Montessori

Prepared Environment_Flower Arranging

Whether it’s at school or at home, the way you prepare your learning environment is the most important influence on how your child will learn. If it’s an environment well equipped with all the tools they need, including supplies to replenish the ones that are used, then surely they will succeed. If it’s an environment that has clutter, over-stimulating toys, “busy” colors on the wall, items that haven’t been restocked, etc, then you can more than likely expect the same learning experience for your child. The prepared environment is key to their academic success. Especially during their first 6 years of life (and after), a thoroughly prepared environment promotes organization, concentration, order, and an opportunity for the child to capitalize on their spontaneous sensitive periods of development.

Beauty. Simplicity. Order.

Prepared Environment_Plant Polishing

Simple and aesthetically pleasing, the leaf polishing work includes basic, clean and organized materials to help the child focus on the task at hand. Clutter, or too many items on the tray, confuse and frustrate the child, blocking their creative energy.

The most precious gift we can give our children is the opportunity to reach their fullest potential, by fostering an environment prepared to meet each of their learning needs. Children appreciate beauty and organization. The desire for beauty in the environment is not a luxury, it is a need for the child; a way for them to connect to the environment. Dr. Maria Montessori’s works were created with the intention of doing just that; to create materials so that they are beautiful and enticing to the child. She believed that objects should be fragile and beautiful. Children then learn to respect their surroundings by the way that they carry themselves, careful to not knock over or damage the objects around them. These things are precious and beautiful to the child; they are to be respected. Preparing your learning environment is an art, by implementing a layout that requires thought and careful movement from your little ones. Each item should serve a developmental purpose of some sort.

Beauty refreshes the tired spirit.

A classroom well-lit from natural light promotes beauty. Studies have shown that children who work in classrooms that have large, open windows are more successful than those who are kept in classrooms with no windows for the greater part of their academic career. Incorporating sunlight and nature as part of your child’s learning experience greatly enhances their spirit!

The child’s sense of order is extremely essential in their overall success. Unless you’ve had the proper child development training, one often does not consider this factor as an important step in their learning process. Order is key. In order for a child to comfortably and confidently grow, they need to know that the learning material will always be in order and ready for them to use. Order gives the child a means of orienting themselves to their environment. Just as we expect everything to be where we last put it, children work much better if they know exactly where everything is, and that it will be in the same place every day. When a child finds himself in a beautiful, ordered environment, he will work to keep it that way.

Prepared Environment_Cloth Washing

The cloth washing work is always available to the children, complete with all of the necessary tools needed to complete the task. An apron symbolizes that the child is doing important work, while keeping their clothes dry. The mitt is used for wiping up access water spills. The child is able to complete this work successfully because the guide has gently prepared all of the items in advance.

The beauty in Montessori is that it focuses on simplicity and order. Everything in the classroom environment, down to the finest detail, is prepared well in advance with the intention that it will be used to enhance a specific aspect of the child’s development. When preparing your classroom or home learning environment, take the time to quietly sit in silence for a few moments. How do you feel? Is the room inviting, comfortable, soothing? Are there interesting works that will capture the child’s attention? Is each work and activity prepared so that the child does not need to rely on you for help if they run out of something? Is there sufficient table and floor space for working? Try to look at the room from the child’s perspective, and prepare it in such a way that they can work with little to no assistance from the adult.