Tag: middle school

Beauty and Big Ideas: How We Teach Math

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“We are all mathematics learners, and we can all develop active, inquiring relationships with mathematics,” writes Stanford math education researcher Jo Boaler in the research paper “Prove It to Me!” “When we do, and mathematics becomes a creative, open space of inquiry, mathematics learners will find that they can do anything, and their mathematical ideas and thinking can extend to the sky—and beyond!”

Boaler and her colleagues are on the forefront of math education research, which shows that with good teachers and self-confidence, all children are capable of achieving in math. According to her research, building a strong foundation in number sense—a feel for numbers and the ability to use them creatively—is key to becoming a successful math thinker, as is an ability to grasp big ideas and make connections between them. 

At Marin Waldorf School, our approach to math is designed to do just that: Through a multidisciplinary, multilayered approach to math, starting at the earliest ages, students learn to see the joy and beauty in numbers, approach math work from many perspectives, and eventually build up to the conceptual ideas that fuel advanced-level math in middle school. Here’s how we do it.

Early Childhood: Encouraged to Explore

“In our preschool and kindergarten classrooms, math education is intentional, but not as directly articulated as you’d find in a traditional classroom,” explains Daniella Baker, MS, early childhood director at Marin Waldorf School. “Math is taught through songs with numbers, counting, jump rope, marching, and other activities.” 

“The approach is layered,” Ms. Daniella continues. “Activities in kindergarten lay the groundwork for math instruction in grades 1, 2, and 3, when students practice multiplication tables by skip counting on jump ropes or in songs, and begin to master math facts.”

They are also given ample time to play, the best way for young children to explore the world and their ability to discover and make connections on their own. In an interview with Ed Source, Gennie Gorback, president of the California Kindergarten Association, explains, “Children learn high-level, intangible concepts such as the laws of gravity, conservation of liquids/mass, mathematical concepts such as more vs. less, all through hands-on, interactive play.”

Children learn about volume, weight, measurements, gravity, teamwork, problem solving
and more during immersive play.

Elementary School: Building Skills and Enthusiasm

“My task as a second grade teacher is to ignite the fire of enthusiasm for learning. So right now my students are at play in the field of numbers, opening their eyes to the artistic beauty and wonder in math,” says Roland Baril, second grade class teacher, who uses a blend of artistic exercises and math drills to build a foundation for his students. 

At the beginning of the school year, Mr. Baril guided second graders in drawing geometric forms that are created by placing 10 dots equidistant around a circle, numbering them 1-10, then connecting them with straight lines via counting by the various times tables. Building on their first diagram of a decagon, children drew decagrams, pentagons, and pentagrams, finding number patterns in each. 

Later in the semester, students studied the patterns created by magic squares and worked in pairs to create times table charts to hang up at home, a project that requires students to accurately mark along the length of a ruler, connect the dots with a yardstick without slipping, and work together to fill in the chart. “We also do lots of drills around the four processes—addition, subtraction, multiplication, and division—so the children are very strong in calculations,” Mr. Baril.

“Good mathematics teachers typically use visuals, manipulative and motion to enhance students’ understanding of mathematical concepts, and the US national organizations for mathematics, such as the National Council for the Teaching of Mathematics (NCTM) and the Mathematical Association of America (MAA) have long advocated for the use of multiple representations in students’ learning of mathematics,” write the researchers in the Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning.

Mr. Baril’s visual exercises, alongside mental math games, skip counting, and the use of wood manipulatives, help build an awareness of numbers and an enthusiasm for math. With this sense of wonder and play imbued in their math work, second graders are naturally drawn to the more complex problems they encounter in second grade, like regrouping (carrying and borrowing), word problems, and multi-digit operations. In fact, ask our second graders and many will say math is their favorite subject! 

Middle School: Growth Mindset and Big Ideas

By 6th grade, students are ready for more complex and abstract mathematical thinking, and the curriculum meets their growing abilities with big ideas in math. Middle school math teacher Julia McIlroy aims to show students how mathematics is integral to all parts of life by looking at big ideas, patterns, and relationships between mathematical ideas and by grounding all subjects in experiential learning before moving to abstract principles. 

6th grade geometric drawings are made using a compass and straightedge.

In 7th grade, for example, students measure large circles on campus to discover the relationship between the diameter and circumference (which we know as pi), before looking at it through the lenses of geometry, ratios, and algebra. Group work is also a key component to Ms. McIlroy’s teaching, requiring students to work together to solve unfamiliar problems in both concrete and abstract situations—to find patterns, make conjectures, and test those conjectures, and to understand that mathematical structures are useful as representations of phenomena in the physical world.

“What I’m trying to do is bring more complex tasks, where there are no immediate right or wrong answers. This prepares them for higher education and the workplace and keeps everyone engaged,” explains Ms. McIlroy. “If you have rich tasks, the students who may be behind academically can do something, and the students who are really high-achieving can take it to the highest levels.”

“My number one goal is to keep students interested and engaged in math so they will continue on with it in college and beyond,” Ms. McIlroy says. “I want to have as many of our students go into STEM fields as we possibly can. Our students have a complex and ethical view of the world and their contributions to science and technology would be profound.

A Gift to Our School

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Before our 8th grade students departed, they worked together to create three large abstract sculptures to be displayed in our school’s Peace Garden, a central courtyard filled with native plants and flowers—and a hub for migrating monarch butterflies. Below, the director of the Bay Area Center for Waldorf Teacher Training, Ken Smith, who oversaw the project, describes the creation of this unique gift to our school.

There has been some unusual activity in the corner of the Peace Garden as the 8th Grade students are busy creating 3 concrete sculptures as a leaving gift for the school. I worked with the whole class to create a sequence of shapes that capture something of the experience of the last 8 years (less for some students and more for others if they began in Kindergarten) of learning and growing at MWS.

We began with trying to bring back memories of the 4th grade to recall key moments and strong memories and then to put these into sculptural shapes. The next class we moved back in time to find a shape for the earlier years. Then we worked to discover how to make one shape after the other in a sequence – something unfolding and developing in time. One of the challenges for the students was to work with nonfigurative shapes – pure form and gesture – which leaves the viewer free and will allow the sculptures to have many meanings and interpretations in the years to come.

Lastly the class was asked explore the present – coming to the end of their time at MWS.

Then a smaller group of students worked to bring the many ideas together into a sequence that could represent the experiences of the whole class.

These 3 shapes were then enlarged into wire armatures, set into position on concrete foundations and finished in cement.

It was a pleasure to work with the 8th Grade on this project and to be able to harvest their many years of artistic and sculpture work with Ms Deason. 

Ken Smith
Director
Bay Area Center for Waldorf Teacher Training

Class of 2021: 8th Grade Projects

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At Marin Waldorf School, 8th grade students spend a full year planning, researching, and working to complete an individual project, which, at year’s end, they present to their classmates and the school community. Below, our 8th grade class teacher, Kristine Deason, shares more about the process.

Eighth grade projects allow students to reveal their capacities as inquirers, investigators, researchers, explorers, inventors, artists, and communicators. Throughout the course of their projects as well as in the culminating presentations, students reveal themselves. No other pursuit more clearly demonstrates how important it is to be “original”—that is, to be the originator of the interest, the question, and the direction that leads to creating something new.

The long process of shaping these projects began in June 2020. Students were asked to read The Boy Who Harnessed the Wind as inspiration for finding something they wanted to learn how to do or make. Over the summer, they were also asked to create a “Rube Goldberg” machine, again with the objective to work at making and creating something, not just researching. At the start of the school year, they submitted a well-crafted proposal to our middle school committee for approval. For many, just choosing a project drove home the reality that discovery always begins with the question, not the information!

Over the course of the year, students worked with outside mentors, conducted background research, wrote annotated bibliographies, and shaped a long research paper as they simultaneously worked on their physical project. They were asked to maintain a project journal to track their progress and submitted this journal often. On a regular basis, they also reported to the class and supported each other in shaping their final projects. Everyone made changes on a regular basis as they all encountered unforeseen challenges. In fact, no one carried out their project exactly as first proposed, and this provided an honest picture of the very real and uncertain world of original research and exploration!

In the end, over the course of two evenings, we were graced by a wide variety of in-person presentations, delivered with articulate confidence. The subjects were wide-ranging, revealing the broad interests of the students:

  • Catching Rainwater; Low-Water Landscaping
  • Carving Stone
  • Constructing a Raised Studio
  • Learning to Freedive
  • Pruning and Grafting; Fruit Tree Care
  • Learning Blacksmithing
  • Building a Tule Reed Boat
  • Restoring and Refinishing Furniture
  • Building an Electric Bike
  • Exploring Survival Skills and Techniques
  • Building and Using a Pole Lathe
  • Capturing Images; the Evolution of Photography
  • Learning to Catch a Wave
  • Constructing and Using a Newtonian Telescope
  • Speaking without Sound; American Sign Language
  • Creating a Board Game
  • Creating and Painting a Mural
  • Building a Go-Kart

8th Grade Block: The Struggle for Rights

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By Kristine Deason, 8th grade class teacher

Our last history block of 8th grade was called “The Struggle for Rights.” Using this theme as a lens into the past, students honed their understanding for the multiplicity, diversity and interrelationship of life, and connected with increasing responsibility to the necessary challenges posed by the need to live with each other in genuine freedom.  Questions, more than facts, guided our discussions.  As a culminating artistic experience, students learned the long poem, “Freedom’s Plow” by Langston Hughes.  They quickly noticed that the poem did not mention many groups who have struggled and continue to struggle for their rights: indigenous people and women, among others.  In response, they composed stanzas of their own in the style of the original which they later transformed into the following group stanzas.

            We are happy to share this work with you!

Group Stanzas, Inspired by “Freedom’s Plow” by Langston Hughes

I.
A long time ago, but not too long ago
Someone said:
“He has withheld her from her rights which are given to the most ignorant and degraded men –
Both natives and foreigners. Having deprived her of this first right of a citizen he has oppressed her on all sides.”
And what Elizabeth Cady Stanton and Susan B. Anthony said was true.
It wasn’t only women who suffered.
When the whites came to America
They stole the land from the indigenous tribes,
Forcing them west, taking their lives.
Ancient ways of living were destroyed.
Indigenous people were marched
To unfamiliar lands,
Holding in their hearts the hopes and dreams
Of FREEDOM!

(by Kenzie, Caroline, Cammie, Leo)

II.
Settlers came, wanting to be master of all,
Without respect for the land and the people already there,
And drove them out from their peaceful homes.
Tribes eradicated,
Battles fought,
Blood drawn.
Few remained, none thrived.

(by Luka, Tessa, Lucien, Avi)

III.
A long time ago, but not too long ago,
The nation expanded westward, seeking a greater freedom.
The price for freedom was paid by people,
People who had nourished this land long before it became
America.
With the help of native hands, they began to grow this land.
As towns and cities grew, native people were pushed
From their homes.
From their sacrifice and the help of their hands,
We built America.
All men are created equal,
That is a great American ideal,
But the day will come when the ideal must triumph
And the American goal of centuries will be fulfilled.

(by Gus, Bodhi, Lili, Sydney, Luca)

IV.
A long time ago,
But not too long ago,
America was expanding, growing,
But at a cost.
Spreading through the land,
The colonists came,
Building houses and barns,
Communities and farms.
Spreading sickness and disease
Among the native people,
Pushing them off the land,
Slaughtering many.
The cost for America was the death of millions.
America as a whole was bloody and suffering.
People persevered, America toiled,
Survived.

(by Feodor, Aurelius, Johannes, Grace, Oona)

Below, please watch the 8th grade perform the poem “Freedom’s Plow” in the amphitheater.

Igniting Curiosity in Middle School Science

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A spirit of inquiry, experiential learning, and an integration of academic disciplines are cornerstones of our school’s approach to education.

In our middle school classrooms, where 6th, 7th, and 8th graders explore complex topics in chemistry, physics, physiology, biology, and geology, science isn’t presented in concepts and lectures. It begins with observation. Through observation, our students learn to think like scientists, asking questions and posing theories before being given all the answers.

Even art, which is integrated throughout our curriculum, is used as a tool for understanding STEM topics. For example, in their studies of combustion as part of the 7th grade chemistry block, students were asked to observe and then draw a bonfire and a candle. You can see a few examples of our students’ work below.

As a capstone to the study of combustion, teacher Ms. Terziev performed a demonstration for the class, asking them to watch silently and then offer their theories on what they’d observed.

After watching the experiment, students brought their questions and theories to the group, inspiring both curiosity and critical thinking in the classroom. This approach helps students build a meaningful understanding of complex scientific concepts. In Waldorf education, this is called a phenomenological approach to science. In this way, 7th graders at Marin Waldorf School connect and internalize complex topics in chemistry, like combustion, as well as crystallization, acids/bases, and the lime cycle.

The study of science at Marin Waldorf School begins in early childhood, with the simple observation of the seasons and the natural world, and through nature stories. In elementary school, students learn to ask questions and to learn through doing, laying the groundwork for more complex critical thinking that they will need to tackle their studies of chemistry, biology, physiology, geology, and physics in middle school.

The Advent Spiral & the Class of 2021’s Last Walk As a Class

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Every December, all the children in our school gather to walk the advent spiral. In the past, this beautiful tradition took place in a hushed and darkened room, accompanied by harp music and candle light.

This year, we went out with our hats and gloves on. The breeze and the blue jays joined us. Rather than candles, children carried apples, bulbs, oranges, and pine cones. And though it looked and felt very different, it was still a gorgeous way to acknowledge the season.

The MWS Parent Association set up this gorgeous outdoor spiral in a quiet corner of campus. We are so grateful!

The Class of 2020 walked the Advent Spiral as a class for the last time on Thursday. Some of them had been walking a similar spiral since they were in preschool. Others walked it for the first time. After the ceremony, class teacher Kristine Deason shared her thoughts with 8th grade parents, who, unlike in years past, weren’t able to witness the tradition as usual. We want to share what she wrote, below, as well as some of the beautiful photos our staff took of the day.

Dear Families,

Earlier today, the 8th grade class walked our outdoor Advent Spiral, beautifully built by the Parent Association over the weekend.  Out of respect for fire danger, we carried bright oranges instead of candles — each student carrying the “fruits of their labors” into the center of the spiral. 

We have walked the spiral together every year since First Grade, and this was our last time as a class.  Beforehand, I recapitulated the experience, mindful of those students who would be experiencing it for the first time.  I described how, at this time of year, walking the spiral invites us to bring our own light into the darkness and thereby illuminate it.  It is harder to experience this in the light of day, but I described to the class that this year our walk would be a journey inward.  The students took it up with thoughtfulness and reverence.  It was a gift to take part in this with them.

Please enjoy the photos.  We hope they convey some small measure of the mood we experienced. 

We walked the spiral today mindful of those friends who could not join us.  You were in our hearts and we miss you very much.

Kristine

Gallery: 6th Grade Geometric Drawings

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Beginning in first grade, Waldorf students study form drawing, working on increasingly complex renderings as they grow. This work is done freehand until the 6th grade, when students begin to work with the aid of a straight edge and compass.

We’re proud to share the beautiful work our 6th grade class is doing this year, under the guidance of skier, philosopher, and 6th grade lead teacher Mr. Stopeck.

MWS Boletin Escolar: Primera Edición

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As part of his advanced study of the Spanish language, eighth grader Luca is working with Maestra Pineda to write articles and essays in Spanish about things happening on campus this fall. In the first edition of the Boletín Escolar (School Bulletin), Luca describes how 8th graders constructed their own outdoor classroom in the Magic Forest.

En este año escolar, a causa de Covid 19, construir aulas al aire libre era la única opción que teníamos para regresar a la escuela. Muchos grados armaron sus aulas debajo de los árboles grandes que nos rodean, a excepción de la clase de octavo grado quienes no teníamos un lugar físico bajo la sombra de los árboles. Construir un aula y proveer la sombra con una lona fue el comienzo de nuestro año escolar.

Durante las primeras semanas de escuela construimos nuestra aula en el Bosque Mágico.  Los estudiantes nos encargamos  de construir casi toda el aula.  Sacando  la corteza de los troncos, cortando  ramas y excavando varios pozos de dos y tres pies de profundidad fueron algunas de las muchas cosas que tuvimos que hacer. A pesar de los días de mucho humo, calor y además de todos los protocolos que tenemos con respecto a Covid logramos levantar la lona que nos cubrirá del sol.   Durante los días siguientes, agregamos otra lona y construimos un pizarrón para el aula, además El Señor Neale trajo troncos que usamos como asientos.  

Fue muy lindo ver que nuestra aula empezó con una pila de troncos y después de unas semanas se convirtió en la estructura completa que es ahora.  Fue mucho trabajo, pero con la ayuda del señor Neale y toda mi clase trabajando juntos pudimos construir el aula que vamos a usar este año. Empezamos el año escolar el Martes, 29 de Septiembre al aire libre con la vista de las colinas de fondo. 

In this school year, because of Covid 19, building outdoor classrooms was the only option we had to go back to school. Many grades set up their classrooms under the large trees on campus, with the exception of the eighth grade class, which did not have a physical place under the shade of the trees. Building an outdoor classroom and creating shade with a tarp was how we began our school year.

During the first weeks of school, we built our classroom in the Magic Forest. The students were in charge of building almost the entire classroom. Removing the bark from the logs, cutting branches, and digging several two- and three-foot deep pits were some of the many things we had to do. Despite days with lots of smoke and heat, and in addition to all the protocols that we have regarding Covid, we managed to lift the canvas that will cover us from the sun. Over the next few days, we added another tarp and built a blackboard for the classroom. Mr. Neale brought logs that we used as seats.

It was very nice to see that our classroom started with a pile of logs and after a few weeks it became the complete structure that it is now. It was a lot of work, but with the help of Mr. Neale and my entire class working together we were able to build the classroom that we are going to use this year. We started the school year on Tuesday, September 29th outdoors with the view of the hills in the background.

[p.s. We have more pictures and stories from the 7th and 8th graders’ return to campus here.]

Welcome Back, Classes of 2021 and 2022

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At last we’re (almost) all back on campus together! Just yesterday, we welcomed our 7th and 8th grade back to campus for in-person instruction.

While school resumed for preK to 6th grade a few weeks back, our 7th and 8th graders have been meeting for instruction on Zoom and coming together in small cohorts on campus for recreational time, as permitted by the county. The 8th grade spent the past two weeks to constructing an amazing shaded classroom in the far east corner of school.

On the far right, Ms. Deason, our 8th grade class teacher, calls the front office from her walkie-talkie — our school’s new communication system now that our classrooms are scattered beneath the oaks and across the fields of our 11-acre campus.

Seventh grade has been busy preparing a beautiful display for Michaelmas in the Peace Garden, right in the middle of school. Although we won’t be holding our traditional Michaelmas festival this year, we are still marking the day with performances and decorations.

The 7th grade’s outdoor classroom is in a particularly beautiful spot, out in a part of campus we often refer to as The Magic Forest. Here’s the Class of 2022 practicing strings in their outdoor classroom.

So beautiful!

Now That’s Impressive!

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If you’ve spent any amount of time on the Marin Waldorf School campus, you’ve likely seen middle school students circling around on their unicycles. Unicycling is perhaps the most memorable aspect of our movement curriculum in the upper grades. As movement and games teacher Ms. O’Ryan says, “Unicycling and juggling help empower the students to make a new relationship with their sense of balance and make sense out of chaos—two hands, three bean bags.”

In this short, clip one of our 6th graders shows off her incredible balance and coordination while juggling on a unicycle.