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How do we respond?

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On November 12, 2016

In communication, community, connection, conversation, emotional intelligence, faculty, K-12 Schools, learning, parents

Between stimulus and response there is a space. In that space is our power to choose our response. In our response lies our growth and our freedom.

-Victor Frankel

Walking through our halls Wednesday morning after Tuesday’s election, discussions about the election results could be overheard everywhere. Most children sought out friends with which to share their collective surprise over the news; others parroted remarks they may have heard on TV or from various adults. Some others said nothing.

I can only speak for myself, but watching the results the night before I couldn’t help but wonder: what do I say to the kids tomorrow? Regardless of one’s own personal political persuasion, the nature of this campaign and its surprising end made for an election night like no other. Contemplating spending Wednesday with young children eager to discuss this at school, I asked myself: how do we respond?

Waking up Wednesday, I thought of Victor Frankel’s famous quote (above). One of our most challenging jobs as educators is to live in the space between stimulus and response, to appropriately model for our students the importance of taking the time to pause and be thoughtful before we react to the words and actions around us. Imagining my conversation with a student about the election, I resolved to offer more questions than answers, especially open-ended ones like “How are you feeling?” or “What’s making you anxious?” so that students feel they have a safe space to process their emotions or concerns.

Shortly after arriving at school, I saw an email in my inbox from Lisa, our Head of School, stating that we would be meeting as a faculty after school to discuss our school-wide response to the election.

During our discussion, we heard from various teachers about their experiences throughout the day, many of them similar to my own. We all agreed on the need to acknowledge feelings, encourage conversation, and allow for differing points of view. Lisa reminded us that the RULER emotional intelligence tools we’ve been implementing in classrooms over the last year and a half are truly powerful for times like these. (Read a short message on the election from Yale’s Emotional Intelligence team here)

Different grade levels shared specific moments and activities from the day. During their morning meeting, first graders plotted themselves on the classroom mood meter; one student acknowledged the news of the election had left him feeling “uncomfortable,” after plotting his mood somewhere between blue and red.

One third grade teacher felt that the activities surrounding a mock election held at school had really helped her students learn to be respectful of others’ choices and to deal with feelings surrounding winning and losing an election. In the middle school, certain math classes had studied polling surrounding the various California ballot propositions, and their discussion Wednesday morning covered not only the predicted versus actual outcomes, but also about the vital need to cultivate a mathematically-informed electorate in our country.

Although it is unclear what the next four years will bring, it is certain that plenty of emotions and other stimuli in need of our collective responses await. Of the many things I saw on social media Wednesday, one short passage shared with the staff by third grade teacher Stephanie Wald helps show a path to the growth and freedom Victor Frankel spoke about:

Let’s start small. Let’s start by looking each other in the eye. By smiling to a stranger. By picking up a piece of trash. By being helpful in your community and commit to listening to each other. Let’s start with more mindfulness, more self-care, more reading and writing. Let’s take it day by day. We have a lot of work to do, but today let’s be really kind to each other. Let’s be honest, generous, and forgiving and connect through our hearts rather than through our minds. Let’s start small, and with love. Let’s start now.

Some helpful links for parents and educators:
http://betsybrownbraun.com/2016/11/09/talking-to-your-kids-about-the-election/
http://www.tolerance.org/blog/day-after
http://www.huffingtonpost.com/entry/what-should-we-tell-the-children_us_5822aa90e4b0334571e0a30b

 

 

The Power of Trust

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On November 2, 2016

In community, connection, K-12 Schools, learning

I was listening recently to a podcast from Tara Brach, a psychologist and meditation teacher, and she began by revisiting a famous quote from Albert Einstein:

 I think the most important question facing humanity is, ‘Is the universe a friendly place?’ This is the first and most basic question all people must answer for themselves.

If we consider the universe to be unfriendly, he posits, we will direct all of our effort and scientific resources towards building defense systems to protect us from all that seeks to harm us. Perhaps we consider the universe to be neutral, devoid of purpose or meaning, neither friendly nor unfriendly – hence Einstein’s well-known description of a randomized cosmic order (“God playing dice with the universe”).

However, if we decide that the universe is inherently friendly – that is, if we trust that there is some underlying order and goodness to the systems around us, then we may actually feel empowered to try to understand our universe. Power and safety is a result of our efforts not to protect ourselves by building up walls but instead to trust and connect with others, working to understand the world around us.

These ideas reminded me of a recent TED talk led by Marc Slors entitled “Cultivating Trust,” which our faculty watched as part of our Learning Lunch series held each month at The Willows.

[youtube https://www.youtube.com/watch?v=53cIQTvJlxE]

Slors acknowledges that while trust involves making ourselves vulnerable to others and all kinds of potential disappointments and calamities, it is also a vital component of successful human communities. In any workplace, people need to be able to trust others in order to focus their cognitive abilities on the work they are responsible for – as a teacher, I trust that our facilities manager keeps our campus safe so that I can devote my time to understanding how best to help students learn. Slors argues that trusting gives us the freedom to be present with the work at hand, as opposed to worrying about all that could possibly go wrong throughout our day.

From this point of view, trusting is ultimately an act of empowerment. Consider various relationships that exist within our school community. Parents trust teachers and the leadership at the school to provide the right conditions for learning to take place. They trust that we will teach the whole child, that teachers will strive to see their child and hear their interests and needs. They trust that they have a partner with open lines of communication. Though they make themselves vulnerable by sharing their children with us each day, by putting trust in us we are able to build stronger partnerships that support students; we feel empowered to join forces together.orig_photo391775_3846309

Also, teachers at the Willows trust their students. In my maker class, I trust that (under my supervision) students will capably utilize a wide variety of tools that could prove harmful if used carelessly – hot glue guns, hand saws, soldering irons, even the internet! Teachers at our school trust that students are competent and capable of taking on problems put before them, or, even better, problems that they come up with on their own. Willows students are not passive learners waiting to be spoon-fed information but in fact feel empowered to construct meaning and think deeply alongside teachers who are guiding the way.

One message we also try to consistently deliver from Developmental Kindergarten to eighth grade is that students need to trust themselves. Children need to feel confident to take risks and potentially make mistakes in order to develop into the kinds of learners described above. Trust in oneself surely instills power, in school and beyond.

Designing with Empathy

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On October 5, 2016

In community, creativity, emotional intelligence, ideas, innovation, inspiration, K-12 Schools, Maker, technology

I teach in a makerspace each day. Design thinking and the steps of the design process are interwoven into so much of what takes place within my maker classes. During each hour-long class, students learn by engaging in work similar to real-world designers: facing challenges, coming up with creative solutions, and tinkering and experimenting their way towards a finished product.

In this space, I see myself as a coach or a guide, providing assistance, resources, and encouragement throughout the design process. When inevitable frustrations occur, I try to be present and listen to the needs of my students so I can provide a useful perspective to enable them to persist with the problem they’re trying to solve.

Do I see myself as someone who’s teaching children to develop their emotional intelligence? I have to admit that in the past I have not, or at least not in the same way as I see my colleagues, who are directly teaching tools for developing emotional intelligence in the classroom. However, recent events at The Willows have caused me to contemplate the connections between design thinking and the work we’re doing with emotional intelligence within our community.

As we begin our second year of work with Yale’s RULER program, I am reminded that the “R” and “U” in the RULER acronym stands for “recognizing” and “understanding.” Taking a second look at the design thinking process outlined by Stanford’s d.School, the first step, “Empathy” matches perfectly with these ideas.

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dschool.stanford.edu

 

When designers are beginning a project, it is important that they ask questions like:

  • Who am I designing for?
  • What are their motivations?
  • What needs am I seeking to meet?

Stepping into the shoes of whom you are designing for and understanding the world from their perspective is crucial to the design process. Similarly, successfully navigating our interactions with the members of our community also requires recognizing and understanding the feelings of others. There is a spirit of inquiry and openness that is essential to both, and empathy is a key component to developing collaborative skills across the curriculum.

I give full credit to Christina Kim, our Director of Student Life, for helping me fully connect these ideas together. She was part of a group of Willows teachers and administrators that visited the d.School last spring while in the Bay Area for the NAIS (National Association of Independent Schools) conference, who came back inspired to redesign a space in our Middle School based on what they had observed on their trip.

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Shortly after their return, I found myself in a meeting that exemplified for me this intersection of design thinking and empathy. Lisa Rosenstein, our Head of School, brought together an eclectic group of 8th graders, Middle School teachers, administrators, and specialists in IT, ed tech and maker to engage in a dialogue about how to best transform one Middle School classroom into what has now become our designLab.

In a sense, all those assembled were being asked to empathize with the future users of the space – incoming 6th, 7th and 8th grade students (as well as their teachers). I was most impressed in this dialogue by the 8th graders; even with only weeks to go before graduation, they were full of constructive suggestions and comfortable sharing ideas at a large table full of adults. I saw a group of students reflecting on their experiences and imagining how the space could best serve the Middle School after they leave, and I also saw the kind of collaborative effort between different members of our community that makes me inspired to work at The Willows.

 

 

 

 

 

 

What’s next?

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On May 31, 2016

In conversation, creativity, growth, ideas, Independent Schools, innovation, inspiration, K-12 Schools, Maker

This time of the school year, parents and educators alike have their eye on the calendar, counting down the last days of school. For teachers, a much-needed break awaits, and school days are often consumed with wrapping up end-of-year projects, preparing final grades and/or narrative reports, and packing things away for next school year. During this busy time, it’s tempting to feel a sense of finality, as if the work of the school year is all but done.

However, this time of year I find myself thinking of one of my all time favorite phrases:

                    What’s next?

The genius of this phrase is its utility across a variety of disciplines, with children and adults alike. As a teacher, I annoy kids daily when they come up to me with something they think is finished and I prompt them with “What’s next?” They might be showing me a piece of writing, an animation programmed in Scratch or a maker project constructed out of cardboard and foam, but my intention for using this particular prompt is identical for each.

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Ideally, “What’s next?” prompts learners to take ownership over the project at hand, and to adopt the mindset that most projects are, in fact, works-in-progress, always able to be revised, extended, and improved. Echoing the best ideas from the design thinking movement, this mindset embraces the idea that projects can always be taken to another iteration. Additional layers of complexity and sophistication can be introduced, and some documentation of the creative process can be cultivated in anticipation of sharing the project with a wider audience. Even during these waning weeks of the school year, we are compelled to ask our students, “What’s next?” even only to hope that they at some point begin to ask this question themselves.

Of course, “What’s next?” is also a useful prompt for teachers and school administrators at this time of year. Reflecting on the ups and downs of the year behind us, what was learned that should be applied to the next year ahead? What points of interest and excitement must be capitalized upon and carried forward? What projects or endeavors almost worked in the way we intended, and with a bit more fine-tuning could really have the impact we desire?

Asking “What’s next?” is, however, not enough. What actually lies next after that depends on the willingness of all parties to put in the work needed to grow and improve based on the conversations that spring forth.

What’s next for you?

 

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March Madness: Non-NCAA edition

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On March 16, 2016

In Independent Schools, K-12 Schools, parents, Private School

It’s fitting that we have noted New York Times bestselling columnist author Frank Bruni coming to speak to our school community this week about his latest book, Where You Go Is Not Who You’ll Be. While many associate the term “March Madness” with the upcoming NCAA college basketball tournament, anyone who works in education knows that a different kind of madness grips parents around this same time of year: admissions madness.pbcover-whereyougo

Acceptance letters go out to new students at The Willows this week, and anxious parents nationwide await word from both K-12 independent schools and universities as well, crossing fingers in anticipation not just for acceptance at a school but also for the implied promise for the future this acceptance carries with it.

In his book, Bruni tries to reassure anxious parents that life will carry on even if one’s first choice is not realized. He quotes Anthony Carnevale, Georgetown’s Director of Center on Education and the Workforce:

Life is something that happens slowly, and whether or not they go to their first choice isn’t that important…It’s not the difference between Yale and jail. It’s the difference between Yale and the University of Wisconsin or some other school where they can get an excellent education.

While I hope this anxiety does not consume our middle school students and parents at The Willows applying out for secondary school, the reality for some is that not getting one’s first choice – or worse yet, not getting your second or third choice either – can be panic-inducing. Bruni also reminds us that this anxiety isn’t just for parents of children over the age of 10, recounting familiar stories of status-obsessed New Yorkers clamoring to get into the perfect preschool, heartbroken when their child does not “perform” adequately during his or her school visit.

Unknown unknowns

What all of this boils down to for me is, whether we are talking about admission into the best preschool, lower school, secondary school or university, the focus is squarely on the future, and the implied promise that accompanies acceptance to a school.

But the future is ultimately unknown, and a parent’s list of unknown unknowns (to paraphrase former Defense Secretary Donald Rumsfeld’s famous line) is endless: what kind of people will our children grow up to be? Will they have steady, secure employment (or a job at all)? All parents want the best for their children, and in the face of a scary, uncertain future modern parents especially seem compelled to obsess over what they can do today to make tomorrow (i.e. 8-12 years later) easier for their sons and daughters.

Bruni’s book is meant to remind us that parents have always had to wrestle with worrying over their children’s future. Throughout, he writes compassionately about the plight of children and parents swept up in all of this madness. I’d really like to believe that his message will help assuage the anxiety of the professional class and its progeny. However, no one can deny the power of an elite degree, and competition still drives so much of our society. Bruni’s argument is well researched and articulated clearly – will it be heard by those who need to hear it most?

“Don’t Dissect the Frog, Build It”

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On February 12, 2016

In 21st century learning, creativity, curriculum, Education, ideas, innovation, K-12 Schools, knowledge, learning, Maker

All of sudden, learning by doing has become the standard rather than the exception. Since computer simulation of just about anything is now possible, one need not learn about a frog by dissecting it. Instead, children can be asked to design frogs, to build an animal with froglike behavior, to modify that behavior, to simulate the muscles, to play with the frog.

In advance of a visit to The Willows next week from Nicholas Negroponte, one of the world’s most innovative, revolutionary thinkers (and grandfather to one of our Kindergarteners), I was inspired to revisit an incredibly prescient short piece he wrote for Wired magazine 22 years ago, from which the above quote was taken. The whole piece, “Learning By Doing: Don’t Dissect the Frog, Build It,” is short and worth taking the time to read in full.

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Negroponte is well known as one of the co-founders of the MIT Media Lab and for giving the very first TED talk, where he predicted much of the modern technology we use today (see links below). Reading this Wired article again, I found it fascinating to reflect on which of his predictions for education and society at large actually came true.

One quote that really caught my eye in the  article:

In the 1960s, most pioneers in computers and education advocated a crummy drill-and-practice approach, using computers on a one-on-one basis, in a self-paced fashion, to teach those same God-awful facts more effectively. Now with multimedia, we are faced with a number of closet drill-and-practice believers, who think they can colonize the pizazz of a Sega game to squirt a bit more information into the thick heads of children.

What was true in the 1960s and the 1990s is still true today. Now more than ever, what sells in Ed-tech are just shinier devices and platforms for delivering facts and practicing rote skills. Arguably, there are times and places for facts and skills, but Negroponte reminds us here that educators need to imagine all the ways to use computers to help people learn something besides Googling facts.

Learning By Doing

Negroponte’s insistence that schools promote more learning by doing resonates most today. Essentially, this is the ethos of the maker movement, and one that informs many of the projects I choose for the maker classes that I teach at The Willows.

For example, our third graders are learning about the Native American tribes of California, specifically the villages of the Chumash tribe. Naturally, the classroom teachers and I thought it would be a good idea for the students to make their own interactive version of a Chumash village, complete with littleBits circuits and other tech-related components.

However, before even beginning to create the Chumash village, I asked students to first just build a village. To kill two birds with one stone, I actually asked them to draw and program a village using the software Microworlds EX, so they could practice coding skills while sharing what they know about villages.

The direction I gave was simple: think about what you would find in a village and try to represent that on your screen. As they worked, spontaneous discussions arose about the difference between villages versus cities; students would identify certain components (shelter, food sources and storage, water), inspiring others to add on to their villages in an organic manner. By observing and taking notes as I circulated, I was certainly learning from their doing, and as they designed I noticed they were learning a few things too.

First, given a finite space on which to build, they had to carefully consider where to place different elements of their village, and how much space each could occupy. For example, most students showed that a village has more than one building some for inhabitants to live in and others for various communal purposes; each had to be scaled and placed properly, and much revision was needed as they tinkered with their designs. Second, many students learned that in their first iterations they had omitted certain vital features; for example, only certain students included some means of transportation to move people in and out of their hypothetical village.

Of course, I could have simply read a book or showed a video about villages to them beforehand if I wanted to ensure that they all had close to identical villages with all of the same elements. But my goal was for these third graders to construct their own understanding about how villages work, rather than mimic what I told them should go into a village. Or, echoing Negroponte’s words, I asked them to build their own village instead of dissecting someone else’s.

By asking them to learn by doing, I was actively engaging them, and also allowing them to teach me what they knew or didn’t know, to inform the rest of our project.

For more on Nicholas Negroponte, here are a few links, old and new:

 

 

 

 

Learning Commons=Maximize Space & Optimize Learning

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On February 4, 2016

In 21st century learning, academics, community, innovation, K-12 Schools, learning commons

Our Library/Media Center is the heart and hub of our campus, the soul of our school, and a center for collaborative and cross-disciplinary learning. At The Willows, “learning commons” are not limited to our library space but encompass many areas on campus and together create a vibrant 21st century environment that encourages creativity and meaningful social exchange. The importance of common space in primary, secondary, and higher education is gaining attention and changing the landscape of schools.14_Campus__Construction_Photographer040

Last week, I presented with Dwight Long, Principal, and Kami Kincaid, Senior Project Manager, Pfau-Long Architecture and Elizabeth DuPuis, Associate University Librarian for Educational Initiatives & User Services Director of Doe, Moffitt, and the Subject Specialty Libraries, UC Berkeley at the 2016 California Association of Independent School (CAIS) Trustee/Head of School Conference in San Francisco on “The Evolution of the Traditional Library into Learning Commons.”

Elizabeth INT_16_intersession_GM046and I were aligned philosophically on the need for learning commons for elementary, middle, and college students with comfortable, flexible spaces to learn and collaborate as a group and study individually. Like Berkeley, our own Director of Library Services, Cathy Leverkus, has been very forward thinking, envisioning our library as a communal space, adaptable and ready to offer differentiated learning and new configurations that best meet our students’ needs in our constantly changing world.

Collaboration Builds a School Culture and Community

Our Learning Commons facilitates many different types of collaboration:STF_16_Liz-Brian001

  • Student to Student
  • Student to teacher
  • Teacher to teacher

It also allows a constant dialogue between lower and middle school teachers and teachers from different disciplines and specialties. Our campus environment is dynamic and generates an exceptionally joyful community of learners.

MS_16_CAIS_SS011We share, question, and grow together. Our learning commons enhances this collaboration, which is a hallmark of The Willows educational approach, and is instrumental in shaping the soul and culture of our school.

Intellectually and Architecturally Open

“The ideal school is designed to reflect an educational process that is nonlinear and encourages personal expression,” writes Eric Lloyd Wright, the Architect.

Our open and spacious environment inspires listening and learning on all sides. The campus is alive with endless possibilities in a climate of accessibility, creativity and companionship. 14_Campus__Construction_Photographer062The space is almost museum-like with high walls and skylights. The light and air are conducive to learning.

Hallways and common areas also serve as extensions of learning as art galleries and areas to display student work. Learning and sharing continues in this way as students are immersed in The Willows creative environment that values student work and provides students with daily proof of their own ability to impact the world with their own ideas and perspective. Teachers and students both see the projects and the work going on around them–there is great sharing and symbiosis.

Maximize Space – Optimize Learning

The learning commons configuration extends the classroom allowing for small group work and large project creation. The learning commons offers additional area to create a project too large for a classroom; teachers don’t limit their ideas knowing they may expand a concept into a commons area. KM_15_Mayflower-Experience010An example is the Kindergarten Maker replica of the Mayflower complete with wind machine, which would be impossible in a classroom, but is an exciting learning experience in the Willows 1 common space. All our spaces are intentionally flexible offering a myriad of learning experiences and cross-disciplinary and multi-age opportunities. In our learning commons, our middle school students often buddy with our youngest students assisting in hands-on projects that are the very heart of our DK-8 model, building empathy and offering leadership opportunities.

Educational leader John Dewey wrote, “If we teach today’s students as we taught yesterday’s, we rob them of tomorrow.” The Willows mission statement says that “each child brings our community an extraordinary gift: a curious mind, ready to explore and eager to learn.” Our mission is to grow that gift and to give them every opportunity to engage with each other and the ever-changing modern world around them.ALL_15_ViewBook129

What better way to do this than on an open, expansive learning commons and campus?

 

 

 

Time + Engagement = Intersession

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On January 29, 2016

In 21st century learning, community, creativity, innovation, inspiration, K-12 Schools

Each year after Winter break, The Willows school community participates in an annual tradition known as Intersession.

Essentially, Intersession is best described by what it is not­ – a time where “normal” school time, usually chopped up into discrete blocks devoted to different disciplines, is disrupted in favor of long, less-structured sessions where both teachers and students work on complex and engaging projects. Depending on the age range, these sessions last 3-4 hours per day; with our middle school, Intersession lasted all day for an entire week.

(Click here to learn more about the nuts and bolts plus specific projects undertaken during Intersession)

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Why take this departure from normalcy? Essentially, I see Intersession is an answer to the following questions:

What if teachers were allowed to create projects they were extremely passionate about?

 What if these projects were heavily student-driven with students choosing which project best suited their interests?  

 What if teachers and students had long periods of time to engage deeply with the ideas and skills associated with these projects?

There are myriad aspects of Intersession worth celebrating and discussing at length, but I’d like to focus on two that I feel are the most powerful: time and engagement.

The gift of time

Releasing everyone from the constraints of their normal schedules is one of the greatest gifts a school can give itself.

DSC_0126With unprecedented amounts of time, our students were able to build real expertise, often with new skills or concepts. Immersed in their projects, they were more willing to take risks, to persevere through difficulties, to collaborate and problem-solve with peers, and to see the true value in what we call “hard fun.”

Personally, I was involved in a project called Robot Theater, inspired by Disneyland’s Enchanted Tiki Room. For six days, groups of students created interactive “rooms” featuring a variety of small robots with lights, motors, and sensors powered by Hummingbird controllers. Students wrestled with unfamiliar tech tools (and the occasional frustrations that go along with connecting and programming them!), built backdrops for their robot “characters,” and presented to groups of amazed parents afterwards. This work takes time – especially if you want to do things right. IMG_0951

Time + Engagement

While any school can simply abandon its regular schedule for some period of time, doing so may not always result in the kind of engagement Intersession delivers. There’s a palpable sense of excitement pervading every space of each building. There’s also plenty of intensity and creative struggle, as children work to realize the shared vision for each project. One easy indicator of engagement that I saw with my robot designers: instead of going outside for snack and recess, they would regularly stay inside to test a new light or motor or finish just one more block of code!

IMG_8594Ultimately, in my mind, time and engagement go hand in hand. Without the time to really dive deeply into something, engagement will always remain superficial while everyone moves on to the next regularly scheduled block of learning. When children are shown that educators truly value their strengths and interests and are willing to give them time to immerse themselves in meaningful projects, they really rise to the occasion.

** Check back for a video we’re preparing highlighting many of the amazing Intersession projects – coming soon!

 

Reinventing Math Pt. II: Post-Symposium

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On January 15, 2016

In K-12 Schools

“50% of all mathematics was invented after WWII” – NCTM, 1989

This piece of information was displayed during an introductory presentation at the Reinventing Mathematics Education Symposium held at the Willows on our first day back from winter break. And so began a fascinating day of learning that served to not only challenge many of the beliefs and assumptions teachers have about math education but to also push us to envision what’s needed to truly make math engaging for all students going forward.

Organized by our esteemed Special Assistant to the Head of School for Innovation Dr. Gary Stager and our Director of Technology Amy Dugré, The Willows hosted roughly 80 educators from all over the U.S. plus international attendees from India, South Korea, and Australia. Keynotes, 90-minute workshops, and a concluding panel were offered by presenters Dr. Ilana Horn, Dr. Constance Kamii, and Conrad Wolfram.

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Key ideas

 Throughout our day, each speaker lamented the current diet of mathematics offered in schools, which leads to widespread student disengagement and a lack of appreciation for math as a connected, meaningful and beautiful subject. As mentioned in my last post , many teachers feel uncomfortable teaching math, and students see math as a separate, almost alien segment of their school day, where pointless problems and procedures are put before them, often resulting in confusion or, even worse, regular blows to their self-esteem.

So, what else is possible? Each speaker shared different thoughts on the subject, and each brought unique perspectives from their research and experiences to share with our attendees.

Overall, listening to each presentation, I felt like there were three main underlying questions that were addressed:

  • What should math class look like?
  • How do young children build math understanding?
  • What should we teach in math class?

Let’s take a look at each in a little more depth.

What should math class look like?

We heard first from Dr. Ilana Horn, Associate Professor at Vanderbilt University, whose research has focused on creating conditions in classrooms where all students feel comfortable exploring mathematical ideas within supportive environments. She spoke about math class being a “risky” environment for many kids, where the benefits of not participating greatly outweigh the rewards. To lessen risks towards lowering social and academic standing amongst peers, she suggests we should show kids that math class can be a bit of a playground, where instead of our current overemphasis on right or wrong answers, we present interesting, playful problems worth engaging with. One example of this she offered was a problem asking students to create a bungee jump for a Barbie doll; the challenge is to give Barbie a thrilling ride while still keeping her safe (i.e. don’t let her touch the floor).

Later, in her workshop, she presented some interesting insights into two important elements teachers need to consider when choosing activities for math class: status and smartness. Horn defined status as the perception of academic capability or popularity, and stressed that students will make decisions about participating in math class based on their (often faulty) perceptions about how their standing might be affected. E_16_Reinventing-Math051Regarding smartness, she asked us to consider who students usually consider to be smart in math: those students who are the fastest and most efficient with calculating. Much like Conrad Wolfram, Horn insisted this is much too narrow a view of what constitutes smartness in math. To illustrate her point, we watched part of a TED talk from Pixar animator Tony DeRose, where he highlights the math involved in creating animation, hardly any of it involving the kind of calculation-based activities that normally dominate math instruction.

How do young children build conceptual understanding?

 Piaget teaches us that it is not the job of the teacher to correct a child from the outside, but to create the conditions in which the child corrects herself from the inside. – Dr. Constance Kamii

 According to Kamii, whose mentor was the father of constructivism, the Jean Piaget, the answer is simple: children build conceptual understanding on their own, independent of (and sometimes in spite of) the teacher’s instruction. “You can’t put numbers into children,” she insisted, claiming that a whole lot of useless instruction takes place in classrooms, trying in vain to get students to understand number concepts. What’s worse, she said, adults have invented standards that claim all students of certain ages should be able to do certain mathematical tasks, when decades of research contradicts this very notion. In her words, “You cannot teach the concept of multiplication to children who haven’t invented the concept of multiplication yet.”

During her workshop, Kamii led teachers through a variety of card games designed to build a stronger number sense in primary-aged students.E_16_Reinventing-Math062 True to her constructivist perspective, she was emphatic that these games be played independently of any formal math instruction – that is, teachers should not be pointing out to students that they are adding or subtracting before, during, or after playing the games. Students must construct their own meaning, and this is achieved only through repeatedly playing the games, revisiting the concepts over and over again.

What should we teach in math class?

 I summarized much of Conrad Wolfram’s position on reinventing math classrooms in my previous post and his keynote at the Symposium touched on many of the same key points covered in his TED talk. Briefly, Wolfram’s key assertion is that far too much time is devoted in math classes to teaching calculation by hand; math is first and foremost a powerful tool for solving problems, and we should be teaching students to develop the ability to solve complex, worthwhile problems and outsource the calculating to the computers. He also underscored the importance of programming, which is essentially a notation system used to express mathematical ideas. E_16_Reinventing-Math063

In his breakout session, Wolfram took us through a few computer-based math activities, demonstrating how the tools his company have developed could be used to help students work with large data sets to solve interesting problems like “Are Premier League Officials Biased?” He also took us through some activities from the Wolfram Programming Lab, a free service that allows users to develop programs using Wolfram Language, the same coding language used to power WolframAlpha, their powerful online tool used by research and development organizations all over the world.

One notable idea that Wolfram shared is that we should be noticing and investigating the presence of mathematics in all subjects. Understanding patterns and the underlying logic within systems amongst a wide range of disciplines is a valuable skill worth cultivating in all students; math, he argued, is needed in today’s world for “logical mind training,” essentially a system for being able to think about how best to solve problems.

One lingering question that I had even after hearing from Wolfram was if 50% of mathematics was invented after World War II (he actually estimated that it was probably closer to 90%), and we shouldn’t be spending so much time on teaching hand calculation, then what exactly does he believe we should be spending our time in math class teaching? This inquiry led me to his blog, where I found a list of 5 major areas he believes we should be focusing on (along with his own reasons for each):

  • Data Science (everything data, incorporating but expanding statistics and probability).
  • Geometry (an ancient subject, but highly relevant today)
  • Information Theory (everything signals–whether images or sound. Right name for area?).
  • Modeling (techniques for good application of maths for real world problems)
  • Architecture of Maths (understanding the coherence of maths that builds its power, closely related to coding).

 Now what?

 Looking at the list above, I know that some of these can be found in Willows classrooms. Ultimately, the true purpose of the Symposium was to give vital food for thought to our school community and beyond about what could be possible in today’s math classroom. Since the Symposium, we’ve had Learning Lunches for grades DK-5 plus middle school math and science teachers to give everyone a time and place to properly reflect on everything. Further, just this week we invited parents to attend a Learning Breakfast led by Gary Stager, where we discussed the key ideas from the Symposium with parents.

And the conversation continues…

 

 

 

 

 

Reinventing Math

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On December 18, 2015

In 21st century learning, academics, curriculum, innovation, K-12 Schools, Math

Most students when asked what they think their role is in math classrooms say: it is to answer correctly. They don’t think they are in math classrooms to appreciate the beauty of mathematics, to approach the rich set of connections that make up the subject, or even to learn about the applicability of the subject. They think they are in the math classroom to perform. – Jo Boaler, What’s Math Got to Do With It?

At our Learning Lunches this month, teachers and administrators at the Willows began our time together pondering two questions:

Why do so many students loathe math?

Why do many teachers feel uncomfortable teaching math?

The initial discussion that followed focused on a few recurrent themes:

  • Math is different from other more open-ended subjects – there is just one correct answer, and you’re either right or you’re wrong
  • When students struggle with math problems, teachers feel they only have a limited amount of strategies to help students get to the correct answer
  • Teachers feel less comfortable with teaching math in different ways than they learned it as students

One teacher even spoke about math as being its own language, separate from the usual language we use to engage with language arts, history or even science.

All of this set the stage for us to watch a provocative TED talk from renowned physicist, mathematician and technologist Conrad Wolfram, who will be one the keynote speakers at the upcoming Reinventing Mathematics Education Symposium being held here at the Willows on January 4th.wolfram ted

In a recent Financial Times article, “Stop teaching kids to add up – maths is more important,” he states:

At its core, maths is a problem-solving process. You specify a real-world problem, develop an abstract representation of it, calculate an answer for the abstraction and then translate back into the real-world language you started with. Before computers, almost all human energy was focused on the third stage: calculating. Now it is usually focused on the other steps instead.

Throughout the video we watched, Wolfram essentially sidesteps much of the traditional debate about how to teach mathematics, in favor of a discussion about why we teach math – and, more crucially, what math is actually taught in schools.

Wolfram’s idea for reinventing math education: use computers. Not just for calculation, but also to build conceptual understanding beyond mere calculation. He maintains that the primary way that people understand processes and procedures that drive most of our modern world is through programming; a great way to check if someone understands math, he claims, is have them write a program to do it!

Implications

Looking at our classrooms at the Willows, we can see some applications of Wolfram’s ideas, mainly in the programming that students have been doing at our school for many years now. Even our youngest students begin wrestling early on with the basics of programming as they work with Bee Bots, working later with more formal programming in Turtle Art, Scratch and Microworlds.

beebots

Beyond providing opportunities for programming (year round, not just for the Hour of Code), Willows teachers have also begun to take steps this year to reinvent math in other ways. Inspired by our school-wide theme of action, teachers in the P.E. department have started to incorporate the concepts of estimation and averages into the weekly activities happening in the gym. Utilizing pedometers for precise data collection, K-5 students were asked to estimate and then discover how many steps it took to complete a lap around the gym. Real-world results enabled rich discussions, as students saw that different student factors (pace, stride, height) influenced the findings. Further conceptual understanding of variance was explored as they worked to estimate and find the average number of steps per grade level.pe data

Further data collection and analysis has taken place in Middle School classrooms, centered around the question: What does a typical middle school student do for all four of his/her P.E. physical fitness tests?  Students estimated mean, median, mode and range for the tests, used Excel to work with the data collected by the P.E. teachers, and created graphs to make conclusions about the data. Best of all, student engagement in real-world math in action was clearly evident throughout both of these projects.

Next Steps

With our Math Symposium right around the corner, mathematics is on everyone’s mind at the Willows. Look for future posts on the subject after the Symposium in January!

Reinventing_Math_Flyer

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