By the time a student has transversed fundamental math concepts, and is entering FMS middle school (7th & 8th grade); they are amply prepared for experiencing pre-algebra, algebra and pre-geometry. Not only do the students perceive the “why” behind the concept presented, there is a context in their minds for the fundamental ideas being addressed.
When they are asked to perform a computation from more of an abstract level, they have a visual and tactile memory of using the Montessori materials concretely. They are the owners of their math skills, instead of simply being a retainer of math facts.
Our FMS graduates are so well prepared for high school math, that the majority of our students successfully test into honors geometry as freshman. They know how and why math concepts are employed to solve equations. They are also steeped in the joy of being able to use their knowledge as a language into solving real life problems, such as creating a matrix that analyzes the costs of doing a school dance, or for solving other real life math questions.
Math is demystified and made accessible to all students using the Montessori method, because the steps are presented with concrete materials, and the explanations for using the materials are methodically explained. The consistency of using the same materials from primary lessons through their elementary lessons (such as using the bead stair) forms a strong foundation of understanding math concepts from a concrete perspective. When more abstract math is introduced, FMS graduates have a true conceptual understanding of the math principles used.
]]>In Lower Elementary (6-9 years old), students explore operations using the checkerboard (multiplication), racks and tubes (division), and also using the bead frames to bring home the concepts of place value and manipulating numbers to solve 4 and 5 digit equations.
Multiplication boards are employed for learning math facts, first in a tangible way and then as a tool for memorizing math facts so there is rapid recall; thus preparing them for the next big leap in doing Math in Upper Elementary (9-12 years old). Students at this level become very familiar with practical life skills of using a ruler, telling time and working with money.
It is during the Upper Elementary years that we see a significant jump in standardized test scores, where the underlying concrete understanding of fundamental math concepts and functions help the students to outperform their peers from more traditional backgrounds. It is at this time, that students spend time working with Montessori materials to understand fractions, decimals, percentages, positive and negative place value in the decimal system, and operations with whole numbers (addition and subtraction).
Some of the critical foundations of doing higher math in high school are laid in the Upper Elementary grades.
Students become very familiar with counting, adding and subtracting fractions, percents, and converting percents to decimals. Using negative numbers and delving into pre-algebra by creating and solving algebraic equations is routine for students in these grades. Finally, substantial effort is made to make square roots an easily understood concept.
*Join us next Tuesday as we continue to look at Montessori Math
]]>The Montessori Math program at FMS is a pathway to a deep, concrete and useful relationship with the power and recognition of numbers and their corresponding values. One of the early math works for our primary aged students are found in using the sandpaper numbers. The student feels the rough impression of the number on their finger tips, while the teacher is saying the name of the number.
As the primary-aged student begins to understand the correspondence between the number and the quantity, they have elevated their understanding to a new level of mastery.
Within the primary aged classroom, the Montessori math materials create an array of tools that solidify the child’s grasp of recognizing 1-10, the concept of 0, recognizing and creating teens and tens, and then being able to put the whole picture together by doing the 100 board.
Seeing the child connect the concept of counting 10 on a ten bar and then adding 1 single red bed to now create 11, is a milestone in their development.
Number chains afford the student the opportunity to count the beads and see the patterns emerge, such as the “2 chain” which is made up of two sets of two beads. Number chains are eventually used to demonstrate skip counting (i.e. counting by twos). Each number 1-10 has its own unique chain.
As the primary aged student learns about the golden beads, they are able to do the decimal layout and tangibly work with place value of units, tens, hundreds, and thousands.
This is truly a stepping point for the students because once this is mastered, they are now ready for performing the operation of addition (4 digits), followed by multiplication, subtraction and division.
Eventually, golden beads are replaced with the stamp game. The stamp game is made of color coded wooden tiles representing units, tens, hundreds and thousands. The work is used to do the operations of addition, multiplication, subtraction and division; affording the student the same advantage of using golden bead materials to solve the problems (and reallysee place value), but in a more contained manner.
Join us on Thursday we discuss Montessori Math in the Lower and Upper Elementary Years.
]]>FMS participated in “The Great Kindness Challenge,” a week long event sponsored by Kids for Peace and by Dignity Health. Kids for Peace was started by two women, Danielle Gram and Jill McManigal, in 2006. Much of their philosophy mirrors the Montessori vision of cultivating peace mindfully and developing interpersonal tools for conflict resolution. FMS was delighted to participate in this worthy event creating intentional acts of kindness on our campus.
]]>As an extension of learning about the body, Ms. Melissa spent time recently talking about the spinal cord and its very important function of connecting commands sent to the mind, and executing the command through the body. She played the game of “Simon Says” with the children and they got to experience the sensation of really listening to the instructions, or not, and feeling the disconnect when they realized they had moved with out the “Simon Says” directive.
We explored the five senses this week and the children were quickly able to isolate which of their five senses they had used to match color tablets, identify sounds with their eyes closed, smell the difference between an orange and a piece of chocolate, and watch Ms. Melissa grade (put in order) the wooden cylinders with her eyes closed using only her sense of touch to guide her.
These lessons help the children identify aspects of themselves that they have in common with each other and it gives them labels that help them communicate more clearly with each other.
Sometimes, when a child is having a hard time emotionally, it simply is a matter of helping them identify their emotions, such as “were you mad about that?” You can see the tension drain from them as they know that they have been heard and they are more willing to soften their stance and work through the disagreement.
Every peace lesson is closed with “Making Silence”, a centering exercise that is as simple as it is profound. We encourage you to ask your child about it and if you want, let them lead you through it. Here are the words:
I cross my legs,
I place my hands on my knees,
I make my back very straight,
I tell my body to be still,
I tell my mouth to be quiet,
I take a deep breath,
I close my eyes,
I make silence and feel my love
There are three color boxes. The first has the three primary colors (red, blue, and yellow). The second has 12 different colors. The third box has nine colors, but in different grades from light to dark.
Ten Geometric three-dimensional shapes made from wood and usually painted blue. The shapes are:
Sphere
Cone
Ovoid
Ellipsoid
Triangle-based pyramid
Square-based pyramid
Cube
Cylinder
Rectangular prism
Triangular prism
Touch boards groom the student’s sense of touch and enhances their ability to distinguish between the smooth and rough.
Sound cylinders are sensitizing the child to the gradations of sound from soft to loud and at the same time, teaching the child how to match the sounds from the red box with the exact same sound in the blue box.
Once the basic sensorial lessons are mastered, numerous extensions can be practiced with each of the materials. Often sensorial materials will engage the interest of the child for long periods of time because the materials are concrete and the “control of error” is so immediate. There are also many math and language applications using the sensorial materials, such as labeling the materials, or taking a moment to count the quantity of materials used in a particular job. Sensorial is part of the classroom that uses all five senses and draws directly from the wisdom of Dr. Montessori in a concrete, useful and vivid way.
Montessori material descriptions taken from Wikipedia “Montessori Sensorial Materials”
The binomial and trinomial cubes are more advanced works that not only teach specific pattern matching prisms together, there is an underlying algebraic equation that can be explored Lower Elementary classes.
The constructive triangles are put together to form various shapes. Shapes made with the triangles include the parallelogram, hexagon, rhombus, and trapezoid.
Join us on Wednesday as wrap up our series on Sensorial.
]]>Another set of ten pieces is the red rods. “The red rods are rods of equal diameter, varying only in length. The smallest is 10 cm long and the largest is one meter long. Each rod is 1 square inch thick. By holding the ends of the rods with two hands, the material is designed to give the child a sense of short and long.”
Here is an example of more advance extensions of using the brown stairs, the red rods and the knobless cylinders:
“The cylinder blocks are ten wooden cylinders of various dimensions that can be removed from a fitted container block using a knobbed handle. To remove the cylinders, the child is taught to use the same three-finger grip used to hold pencils. Several activities can be done with the cylinder blocks. The main activity involves removing the cylinders from the block and finding the right hole to replace the cylinder in. Small, tall and short, thick and thin, are the concepts being conveyed to the children as they handle the cylinder blocks.”
Also called the knobless cylinders, the colored cylinders are exactly the same dimensions as the cylinder blocks mentioned above.
There are 4 boxes of cylinders:
Yellow cylinders that vary in height and width. The shortest cylinder is the thinnest and the tallest cylinder is the thickest.
Red cylinders that are the same height, but vary in width.
Blue cylinders that have the same width, but vary in height.
Green cylinders that vary in height and width. The shortest cylinder is the thickest and the tallest cylinder is the thinnest.
The child can do a variety of exercises with these materials, including matching them with the cylinder bloc
ks, stacking them on top of each other to form a tower, and arranging them in size or different patterns.
Here, the knobless cylinders are used with the cylinders from the cylinder block.
Below, a student has combined the knobless cylinders and the pink tower, ordering the materials in sequence from the biggest to the smallest.
Join us on Monday as we continue to study Sensorial.
]]>Many of the exercises in the Practical Life area are preparation exercises of Sensorial works. The exercises help to fine tune the development of the child’s senses. Many uses of the five senses occur in the Practical Life area: sound, sight, and touch are used in equipment-bases activities, such as bean scooping; smelling and tasting are involved in the preparation of food.
Practical Life not only develops the child’s senses and teaches real life skills, but sets the basic foundation for other areas to come. For example, understanding size, weight, and equal distribution are skills which are vital when the child is introduced to the Math area of the classroom.
Perhaps the most significant is the development of the pincer grip, which allows the child to correctly grip a pencil and begin working in the Language area.
]]>As the child begins to explore the sensorial works, one of the first jobs introduced is called the pink tower. “The pink tower has ten pinkcubes of different sizes, from 1 centimeter up to 10 cm in increments of 1 cm. The work is designed to provide the child with a concept of small and big.” The child starts with the largest cube and puts the second-largest cube on top of it. This continues until all ten cubes are stacked on top of each other. The control of error is visual. The child sees the cubes are in the wrong order and the tower becomes unstable if a larger cube is placed on top of a smaller cube.
Many of the sensorial materials are made with 10 components so that the students get used to counting 1-10 quite naturally.
For instance, the brown stairs is made up of 10 sets of wooden prisms and introduces the concept of thin to thick. “Each stair is 20 cm in length and varies in thickness from 1 to 10 cm. When put together from thickest to thinnest, they make an even staircase.” After the initial pink tower and brown stair lessons are mastered, both materials can be used together forming interesting combinations.
Join us next week as we continue looking at the Sensorial part of a Montessori classroom.
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