Dear Math

Dear Math, 

I’m sorry about the way I’ve treated you for the majority of my life. I can still remember the moment I turned on you, the moment I decided I wasn’t a “you-person”. It was in second grade when I didn’t pass the test on how to make change. Instead of attending my remedial math lesson, I hid in the classroom coat closet reading Ramona the Pest, swearing you off forever. I avoided you for the rest of my school experience. I even managed to get away with no math courses on my college transcript. It didn’t help that I spent ten years of my adult life as an English teacher, which sealed my fate as a “not a math person”. I called you names like boring and pointless for practically all of my childhood and most of my adulthood. It wasn’t until I took a statistics course just a few years ago when I realized that maybe…just maybe…I didn’t loathe you like I thought. 

I’ll never claim to be a non-math person again – and now I realize how foolish I was to accept the dichotomy of math and English. Two things can be true: I can be good at math and love to read and write. I can struggle to learn math, and I can enjoy the process. So, I’m sorry that it took me so long to come to this realization.Thanks for your patience, math. Please accept my apology.

Sincerely, 

Me

One of the first math challenges of the year in Adventure studio was to write a letter to math. The above is an excerpt from my own letter. What if you were tasked with the challenge – what would you write, what story would your letter tell? Would your letter sound similar to mine? If you had to graph your relationship with math over the course of your life, how would it look? Has your relationship with math changed since you were in school? Do you consider yourself a “math person” or not?  

Our goal at The Village School is to cultivate a culture of learning around math that focuses on curiosity, appreciation, and deep understanding. We design our curriculum in hopes that our learner’s letters to math sound much different from mine.

Research suggests that learning math is most meaningful when mistakes are valued as much as a correct answer, and when focused on authentic tasks rather than rote memorization. We can confirm these ideas through our experience as educators in many school settings, and especially through our observations of our own learners over the past four years. We keep this research at the forefront of our curriculum design as we strive to support our learners in developing mathematical mindsets. 

Khan Academy supports our learners in developing their own understanding through mastery-based online courses. The adaptive online programing allows learners to move through the curriculum at their own pace, focusing on mastery of specific math skills. Mistakes made in Khan are met with more learning opportunities instead of the traditional punitive consequences. Completing a course in Khan Academy requires a learner to fully engage with the learning process – they are the active participants determining the content and the pace of their learning. 

Great Problems are an opportunity for learners to collaborate on open-ended mathematical tasks. Learners engage in these In Discovery studio great problems take the shape of collaborative morning warm-up challenges. Adventure learners complete at least three great problems each session, spending sometimes up to one hour working on the solution to a single problem. 

Quests are a chance for our learners to engage with real-world, authentic math tasks. Science curriculum in Discovery and Adventure studio is delivered primarily through project-based learning Quests and often requires learners to engage in specific math skills that are in addition to their set curriculum on Khan Academy. Recent quests in Adventure studio include: The Physics quest, which required velocity and motion calculations using advanced math formulas, and the Money & Me quest required monthly budget, annual percentage rate, loan, and tax calculations. Recent quests in Discovery include: The Game Design quest where learners developed understanding around probability and statistics, and the Community Meal quest where learners are working on calculations that go into preparing a meal as well as the logistics of an event.

Math Coaching is an additional support we offer for our learners. Our Math Lab is open for learners for set times each week during both studio’s morning work sessions where they have access to a math educator to support them in their work on Khan Academy, Great Problems, and even Quest related math tasks. The dedicated time and space for math has been helpful in providing learners with the right level of structure and support in a self-directed learning environment.  

The learning opportunities focused on math go far beyond mastery on Khan Academy, and place learners in situations where mathematical reasoning and understanding is authentically relevant. The four elements of our math curriculum: Khan, Great Problems, Quests, and Math Coaching, are intentionally designed to instill an understanding, appreciation, and curiosity around math that hopefully results in a letter that sounds something like this…

Dear Math, 

Wow! Everywhere I look I see you. I see you in the design of the natural world, and in the architecture of the city where I live. You play such an important role in my life and in the world around me. Thank you for being patient with me, especially when I’m learning something new. Sometimes you can be really tricky, but I know if I’m patient with myself, I will figure you out. I’m so glad I’m a “you person!” 

Beyond Good

Since becoming a parent, the number of times I’ve uttered the words “Good job!”, “Great try”, or something similar has increased exponentially. I don’t even think about it, the words just roll off my tongue. I’ve said “good job” so many times the phrase falls into the same meaningless category as “hurry up” and “be careful”. If the words were so automatic, and I didn’t even have to think to say them, how much meaning could they hold for whoever was on the receiving end? The same holds true for the type of feedback that passes between learners and guides in our studios; our learning design relies on quality feedback. Instead of lots of “good jobs”, our goal is that feedback in our studios is meaningful, motivating, and kind. 

According to research, feedback in the form of cliches like “good job” are actually not feedback at all, and certainly don’t align with our definition of feedback at TVS. Carol Dweck, well known for her research on growth mindset, reminds us that the praise we get, especially from parents, educators, and coaches can shape the way we see ourselves, our abilities, and our intelligence. Instead Dweck suggests using phrases that are focused on effort and detail. Our Spark Guides give ongoing growth mindset praise and feedback, and their ideas about what to say instead of good job are a continued source of inspiration. 

Spark Studio’s Helpful Reminders during Session 1 Exhibition

Beyond praise, feedback is an integral part of the learning design at TVS. We rely on learners to provide meaningful feedback to each other and we prioritize feedback as a way for learners and their families to see growth. We like to think of feedback as an ongoing conversation that follows our learners in their studios with each other, with guides, and at home with their families. 

Guides spent time this summer thinking about how to strengthen the feedback systems to support learners as they step into their role as receiver and provider. In our planning, we used criteria identified by research across educational and workplace settings that point to three conditions that result in meaningful feedback. 

Feedback should be face to face: There are many systems within the studio that position learners beside one another to provide feedback. 

  • Community Meeting is something that happens almost every day, providing a venue for learners to present their work and ideas for group feedback dialogue. 
  • Guide meetings position guides and learners side by side for a feedback conversation. These conversations are documented by both learners and guides, allowing for transparency and accountability.  
  • Community Partners are often invited to provide feedback to learners both at the midway point and end of learning experiences like Quest, Writer’s Workshop, and Communications. 

Feedback should compare performance to a standard: Ron Berger is well known in the education community for his work surrounding experiential learning and what he calls, the “ethic of excellence.” His research shows how powerful models of excellence can be when inspiring young people to reconsider, rework, and revise. Berger’s work has informed our use of learner-created rubrics to help define excellent work. In session 1 learners in Discovery and Adventure created their own rubrics for their writing challenges based on close examination of model work from the real world. These rubrics were a helpful jumping off point for feedback conversations. 

Our new learning platform, Headrush, also highlights the learning goals and competencies that Discovery and Adventure learners are working towards in each of their badges. The competencies are all tied to the TVS Portrait of a Graduate, which informs our learning design. These competencies are a helpful frame for both feedback and documentation of each learner’s journey towards mastery. 

Feedback should include suggestions: Guides and learners in Discovery and Adventure studio started the year providing feedback using The Ladder of Feedback, a research based feedback protocol from Project Zero, Harvard Graduate School of Education’s research group. The Ladder provides a framework for a feedback discussion guiding participants through four steps on a ladder: clarifying questions, value statements, concerns, and finally suggestions. Learners have used this protocol with each other and with guides to discuss their writing and project ideas. 

Learners engaged in a feedback conversation using The Ladder of Feedback

Providing and accepting meaningful feedback is a skill that takes practice. The systems we’ve designed are meant to provide learners with many opportunities for just that. We invite you to join us – the next time you are in search of some feedback, as your learner. And, if you’re like me, “good job” will roll off your tongue at least once today (if it hasn’t already) and when it does, maybe you’ll take a minute to think beyond good. 

Exhibitions of Learning: Take a seat!

What is an Exhibition of Learning? Exhibitions at The Village School are one of our primary modes of assessment – but most importantly they are an opportunity for learners to share and celebrate their learning with their “village”. 

In the education world, an Exhibition of Learning is described as a performance-based summative assessment – another way of describing anything that is not a multiple choice, standardized test. As a student, my culminating assessment experience was almost always such a test, and my guess is that your experience was similar. 

There are decades of research that reveal the inadequacies of standardized, multiple choice tests. Most damaging are the studies that show that success on a standardized test predicts little to nothing about a person’s success in their life. Research and our own experience also reminds us that we can ace a test one week and forget all of the information we once “knew” the next. Education and brain science researchers will remind us that this is because these tests are good at measuring recall and surface level understanding, not deep learning. 

On a larger scale, many colleges and universities have gone test-optional and companies like Google stopped requiring transcripts and test scores years ago. If colleges and companies are moving beyond these tests and the research proves their inadequacies, we should all be wondering why more schools aren’t changing their assessment practices. The fact that this assessment experience remains the status quo for the current generation should be appalling. 

The word assessment is derived from the Latin root assidere, which means “to sit beside”. At the Village School our goal is to design assessments that are true to this definition. We believe in assessments for learning, not of learning. We believe in assessments that require learners to be “active protagonists” in their own experiences, not passive consumers. We believe in assessments that literally require us to “sit beside” each learner. Exhibitions of learning fulfill all of these goals. 

A TVS Exhibition of Learning is an opportunity for our village of guides and families to sit beside learners and understand their experience in order to help them grow and help us design the kind of learning environment and experiences that will continue to help them thrive. 

There are organizations dedicated to spreading the practice of exhibition-like assessments to schools and students all over the country. We are not alone in the effort to redefine assessments in schools – but we are ahead of the curve.

So, it is with great anticipation and excitement that we invite you to take a seat at our first Exhibition of Learning next week. How will you practice “sitting beside” your learner as they share their Session 1 journey with you? What questions will you ask them to help them reflect on their accomplishments and their future goals? What will listening to them share their learning reveal about them and who they are becoming? What will listening to them teach you about yourself?  

Making Connections & Learning to Live Together

During the first few moments of the first day in Adventure Studio, learners spent time making connections with a ball of yarn. They shared one of their individual strengths and how it might contribute to their team over the course of the year, each learner connecting to the previous learner’s thoughts to create a web with the yarn. When the web was complete, they noticed what happens when one person pulled too tight or let go:  the whole team felt the impact. This was their first step in Learning to Live Together.

Adventure learners make a web of connections with one another sharing their hopes for the year and the individual strengths they will bring to their team.

If you were a fly on the wall in Adventure Studio over the past month you would have heard more connections being made that sounded like this:

“I think religion and science are both saying the same thing, just in different languages.” 

“I think if a team is working well together, there isn’t just one person who is the leader, there are many.”

“I am really grateful for everyone in the studio because we all helped each other and played important parts in our team challenge today.” 

“I believe that evidence comes before all else when it comes to believing something is true – or not.”

“Flow is something that can come naturally to me if I convince myself that whatever I’m doing is important – and if I have friends to share it with.”

“I am grateful for our studio’s ability to share different opinions in a respectful way.” 

The past four weeks have included many connections and many first attempts at Learning to Live Together, one of the outcomes in our school’s Portrait of a Graduate. We measure Learning to Live Together through documenting growth in a learner’s ability to collaborate, be compassionate and respectful, hold themselves accountable, and be a servant leader. The learning opportunities in Session 1 are designed to build a foundation for these important and lifeworthy skills to flourish throughout the year.

Civilizations is a learning experience that provides a rich space for learners to grow in all of the skills noted above. During Civilizations learners engage in quality research about a specific topic, create original arguments, think critically about historical events and figures, and listen to each other through socratic discussions. Each Civilization experience creates another web of connections for learners to consider their role as individual learners and as members of the team. Did I engage with everyone, with whom the most, and who engaged with me? How much or how little did I contribute? Whose perspective made me reconsider my own? How did my thinking change as a result of the discussion?

A map of Adventure Learner’s Civilization discussion, marking the time they spent on each discussion question, how many times they contributed to the conversation, and who they exchanged ideas with.

We all play essential roles in the web of connections that we make in our studio and out in the world. Learning to Live Together is as much about understanding ourselves as it is about understanding each other. Adventure learners will continue to build on the connections from Session 1 – what will they discover about themselves and each other this year? What will their webs of connections look like in a few months? What will they teach all of us about what it means to Live Together? As one Learner put it, “We are all more alike than we are different. We should focus more on what we all have in common.”