a child engaged in building with Montessori constructive triangles

Expanding the Mathematical Mindset

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Recent neuroscience research has shown that our brains are capable of growing and developing our entire life time. Furthermore, approaching the teaching of mathematics using a ”growth mindset” and embracing mistakes/struggles actually strengthens the synapses in the brain to learn more deeply. These are some of the cutting edge concepts being applied by researchers at Stanford University. Recently, Ms. Amy and Ms. Danna, FMS lead teachers of 4th – 6th grade, had the privilege of attending the training facilitated by Jo Boaler, Professor of Mathematics at Stanford University and co-founder of “You Cubed.”

What they learned is that many students feel limited in their abilities to grasp and perform mathematical functions when they rely on traditional tactics of memorization of facts and developing the ability to produce right answers in a timed manner.  The science shows that “many of our mathematical concepts are held in our visual and sensory motor memories.”(Journal of Applied Computational Mathematics: J. Boaler, L.Chen, C.Williams, M. Cordero) So by giving  greater emphasis on visual and physical mathematics, students are using more of their brains to actually grasp underlying math principles.  When it comes time to test their knowledge, students who have used this process have performed better than their peers relying on traditional teaching methods. We can actively stimulate the visual representation of math concepts such as graphing equations and using pictures to represent computations which takes nothing away from getting to the right answer, it simply expands the way math concepts are presented and then understood.

To further explore these concepts and see the research on this innovative approach to teaching and learning mathematics, we encourage you to visit the You Cubed website at https://www.youcubed.org/professional-development-at-stanford/

Dr. Maryam Mirzakhani, Professor of Mathematics at Stanford and the first female mathematician to receive the Fields Medal (the Mathematics equivalent of the Nobel Prize), was a strong proponent of “doodling on large sheets of white paper, scribbling formulas on the periphery of her drawings.”

According to her colleagues, “Mirzakhani was able to conjure aspects of such spaces to consider, doodling on a white sheet of paper to try an idea, or remember one, or search for a new one; only later would she transcribe her adventures in the conventional symbols of mathematics.” “You don’t want to write down all the details,” she once told a journalist. “But the process of drawing something helps you somehow to stay connected.” Her Ph.D. thesis began with counting simple loops on surfaces and led to a calculation of the total volume of moduli spaces. This allowed the young scholar to publish three separate papers in top mathematical journals, one of which contained a surprising new proof of the famous “Witten conjecture,” a milestone in theoretical physics connecting mathematics and quantum gravity. Mirzakhani’s mathematics is treasured for its great creative leaps, for the connections it has revealed between distant fields, for its sense of grandeur. (New York Times Magazine)

As we go further into the technological age and the era of information, it will become more relevant for workers of the future to be able to absorb and analyze large amounts of data, and to be able to see relevant patterns of usable information. FMS students will have the benefit of understanding Mathematical concepts more deeply by using visual tools, and to potentially explore some of the hidden complexities that Dr. Maryam Mirzakhani did.

Gardening at Foothills Montessori

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Over the years, FMS has had many green thumbs planting flowers, herbs, and plants on campus including the greenhouse. Ms Val manages in the primary outdoor classroom.  Last year, there was a concerted effort, led by Ms. Kerri(E6), to partner with Green Our Planet and create a sustainable gardening program.  The fruits of her labor are coming to fruition as we see the plants thriving in the new brick planters located in the campus courtyard.  Every classroom is represented on the gardening committee and exciting results are starting to bloom.

There are essentially four areas on campus that are dedicated to growing plants: the center courtyard, the east side behind the lower elementary classrooms, the green house in the primary outdoor classroom, and the pollinator garden found outside E6 (upper elementary) on the west side.  Each area has its purpose and the students, teachers, and parent volunteers are involved with the maintenance and growth of the areas. In addition, primary classes are focused on creating a sensory garden with plants which feel, taste and smell amazing. We are even considering starting a seed library.

As stated by the committee, The FMS garden is a learning garden. Maria Montessori observed, “When children come into contact with nature, they reveal their strength.” Our garden encourages students to experience the natural world, gain insight into how all living things work together, demonstrate respect, adopt peaceful practices and develop an awareness of personal responsibility for contributing in a positive way to the world. Teachers and staff utilize the garden to facilitate outdoor learning across all domains and school subjects, and to nurture self-reflection, mindfulness, and family engagement. Garden lessons increase opportunities for outdoor learning, support healthy eating, and inspire students to protect, conserve and improve the natural environment around the world. “Education is not something which a teacher does, but that it is a natural process which develops spontaneously in the human being. It is not acquired by listening to words, but in virtue of experiences in which the child acts on his environment.” (Maria Montessori)

As the garden grows, elementary students will participate in professional chef demonstrations using produce from our harvest. Also, be on the lookout for notification of upcoming farmers’ markets where students will be selling items from the garden.

Ambassador Leaders

Ambassador Leaders

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Leadership is a complex and useful skill that may lay dormant in a young person until they are actually called upon to use it. This summer, six FMS middle school students were invited to attend a week-long leadership training program sponsored by the Ambassador Leaders program.  Some of our students attended the training at Harvard Law School and others went to UCLA.  Each student was nominated by their teachers and then submitted an application to be chosen to attend the training.

Their week was filled with seminars on team building, communications, and learning how to identify their own leadership styles. Successful business people presented during the week modeling many of the leadership traits the students had learned about.  Our students were challenged with creating a community service project and figuring out its motto, purpose, and a strategy for implementing the idea.  Some of our students came up with an idea focused on water; preserving it and providing clean water supplies to communities which they called “One Drop.”

When asked, “What did you learn about yourself through this experience?” One student commented that the experience “opened her up,” another had to “step out of her comfort zone and engage in conversations with people she had just met.”  A student also commented that his group had to speak about their community project idea in front of an audience of over 100 people, and he was “pleased with his performance.”  The experience certainly provided opportunities for students to become more confident in public speaking and collaborating with peers.

children exploring Montessori sensorial materials to enhance tactile learning

A Blended Montessori Approach

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FMS is a blended Montessori program.  Montessori materials for teaching Math, Language, Reading, Science and Cultural lessons are the foundation for lesson giving at the primary level and are used in varying degrees in the upper grades.  We follow the tenet of presenting the concrete material first, such as using a single red bead to represent “one” and the green bead bar to represent “two.”  Then, as the student becomes more familiar with the process of handling the concrete materials and their knowledge solidifies, they are introduced to more abstract representations, such as writing the number 1 and then eventually learning the functions of addition, subtraction, multiplication, and division.

Sounds are presented first when teaching language to 3 and 4 year olds so that when letter recognition is developed, a young student begins to see the letters put in a pattern to form words, which eventually leads to pre-k students reading simple books.

The Montessori method is one that is “hands on” and process driven.  This methodology is used throughout each of the ascending grades at FMS.  Much of the teaching is done in small groups, where again, specific needs and abilities of the students are addressed.   Once a student is in lower elementary (first through third grade), Montessori materials are still used in the classroom, but traditional learning materials are used to solidify a students knowledge, preparing them to function effectively in any school setting.  For example, “Words Their Way” is a spelling and comprehension tool used to develop writing skills, as well. This starts in first grade and carries through sixth grade. Middle school students focus on etymology, while learning the deeper connections of how words were created and applying their meaning in their writing.

Starting in third grade, each student is given the Stanford 10 Achievement Test rating the student’s reading, comprehension, spelling, vocabulary, math and listening skills.  A record of these scores is posted on our website under the ABOUT category then under TEST SCORES.  For over ten years, FMS Montessori students have consistently demonstrated above grade level  mastery as a mean population. These results are measurable indicators that FMS students are standing on solid academic ground and can compete effectively when measured against traditional school standards. Chrome notebooks are introduced to upper elementary (fourth through sixth) students as a tool for researching and writing papers.  Middle school students continue to use Chrome notebooks for research and Google classroom.

All of the “non-Montessori” tools are used to solidify and refine the education process at FMS.  We are committed to helping each student develop to the best of their abilities, both on an academic and social/emotional basis.  Learning “how to be with other people” is just as vital as learning the sounds of the alphabet, or composing a well written paper.  FMS is an institution that feels warm and inviting. Children, parents, teachers, and administrators take an active role in our learning community, contributing to the collective experience we share during the school year.  FMS is a community of learners, inspired by the Montessori philosophy to do our very best every day.

students working together on a Montessori geography puzzle map

Planet Lesson

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Cooking projects in the FMS kitchen happen on a regular basis, filling the office with delicious scents and actively involving students in the preparation of food.  Sometimes, the food that is being made is to celebrate birthdays for the month.  Often there is an opportunity for our students to experience an academic lesson represented in a food item.  Last week, P2 students entered the kitchen and found that the entire solar system was laid out on the table in front of them.

The task was to paint a plate with yogurt signifying the atmosphere and the boundless space around us.  The sun was represented by an orange slice, with Earth showing up as a slice of kiwi.  The asteroid belt was laid out by using raisins.  Each piece of fruit was proportional in size, representing the scale of the planets in space. This visual and tactile lesson was further enhanced when the students were able to eat the fruit and use their sense of taste.  Space was explored, a lesson imparted, and a memory made when the fruit was eaten…a true Montessori experience.

 

a child focused on counting with Montessori golden beads

Training the Mind

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The FMS teaching staff began the new year with a training in mindfulness.  It was given by Tessa Stephenson, MS MFT, and Regional Director for the Endeavor network.  Mindfulness is an old idea getting new traction in our fast paced world.   As per Ms. Stephenson, mindfulness is a perspective that cultivates “an attitude of openness and curiosity no matter the circumstances, including situations that are unwanted or unpleasant.” Mindfulness offers tools for regulating emotions in order for a person to stay present and focused in the moment they are in, instead of reacting automatically to their own emotional states.

Simply taking a deep breath can calm the mind long enough to integrate the right and left sides of the brain so a person can think clearer about the situation at hand. Many studies have shown that teaching young children mindfulness techniques gives them life skills for coping with frustrations and disappointments.  The studies have also shown that as young children are taught mindfulness techniques, they begin to experience themselves moving from a reactive to a receptive state.  Not only does this help them in the immediate moment where they feel challenged, but this simple training can facilitate long term positive brain development.

Integrating the left and right sides of the brain is the ideal state of mind. The right side of the brain controls senses, emotions, nonverbal communications, and gives the whole picture context. Studies demonstrate connecting with the right side of the brain where emotions are generated is critical to effectively redirecting behavior.   Once the emotions are addressed, then conversation can proceed to utilizing the left side of the brain. The left side of the brain is the logical, linear, literal, and linguistic driver. Solutions can be offered and boundaries reinstated.

One of the mindful techniques brought to the classroom was a simple hand gesture. For example: holding a hand up, then folding the thumb into the palm, followed by letting the four fingers move rapidly, the child takes a breath and then slowly folds the four fingers over the thumb in a closed fist position.  As the breath is being exhaled and the fingers are moving slowly over the thumb, “pull it together” is repeated silently.  “Pull it together” is a verbal cue for integrating both sides of the brain. As a recent example: a primary class (ages 3-6) taught this technique to the students during a whole group circle.

During lunch that same day, a kindergartener looked at a younger peer who was having difficulty controlling their body while eating and simply held up her hand, folded her fingers over her thumb, and the other child redirected their behavior. This action was unprompted by a teacher and demonstrates the power of mindfulness.