In addition to understanding the science behind volcanoes, Upper Elementary students took a broader, social view of the effects of communities living near volcanic sites. Stratovolcano or cinder cone volcanoes are potentially much more dangerous to live near when they blow their tops, than living near a shield volcano where lava is oozing out the crown instead of exploding violently. Students learned about early warning signs that a volcano may soon be erupting by the increased amounts of earthquakes in the area and by measuring increased gasses emitted from the crown of the volcano.
Finally, students researched active volcanoes and studied some of the myths that have evolved to explain some of the natural behaviors of volcanoes, such as the goddess Pele who monitors Kilauea on the Island of Hawaii. Legend has it that Pele is aware of any piece of lava missing from the volcano and responds with fury (flowing lava) until the piece is returned.
The culmination of the volcano studies happened when sulfur (a naturally occurring element in a volcano) and other compounds were added to the volcanoes and then ignited; there were sparks and smoke and the face of the volcano was forever changed, replicating the natural process.
]]>Three different kinds of volcanoes dominate the landscape. Stratovolcanoes are tall and explosive, think Mt. Fuji. Cinder cone volcanoes are not as tall as stratovolcanoes, but are still explosive, such as Mt. St. Helens. Finally, the third variation is call the shield volcano, which is flat and not explosive, but is always putting out steam and oozing magma, like Kilauea on the Big Island of Hawaii.
Once the students had the big picture of why certain volcanoes form in different parts of the Earth, depending upon the plate tectonics, they began to investigate the parts of the volcano (introduced to Montessori primary age students) and started to see why the magma chamber in a stratovolcano looked so different from the magma chamber of a shield volcano. The pressure in a stratovolcano keeps building up, until there is too much force and it explodes violently.
Viscosity is another important feature of volcanic studies. It is the measurement of “the extent to which a fluid resists a tendency to flow.” Some volcanoes have high viscosity such as a shield volcano, where the magma can be observed (relatively safely) as it is oozing slowly out of the main crater of the volcano, cooling and building land as it hardens. In class, the students learned about the concept of viscosity by running a side experiment where they timed the movement of molasses, versus oil, to see which one took more time to reach the end of the board (molasses has higher viscosity).
*Join us on Wednesday as we conclude our two part series on volcanoes.
]]>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.
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