The Three Most Important Math Questions for EC and LS Classrooms

By Leah Silver, Math Specialist (JK-4)

While so much has changed in our teaching in the last few months, the essence of the math classroom has remained the same. Planning, teaching and visiting math classes JK through Grade 5 in recent weeks has helped me sharpen my answers to the following questions: What can our digital tools do really well? And what can our teachers do that our digital tools never can? Our digital tools like DreamBox give our students immediate and targeted feedback on their operational and problem-solving work, and we’re learning how to let these tools help us make the best use of our teaching time. 

Our teachers do incredible work every day that our digital tools cannot—and will not—ever be able to do. Our teachers work masterfully to guide our students to better articulate their mathematical thinking, learn to ask excellent questions, make keen observations and get comfortable in solving complex problems, even when the answer isn’t immediately clear. We know that the ability to work collaboratively on complex problems and express ideas clearly will be two of the most valued qualities as this group of students continues to grow up. We also know that our students’ ability to make sense of data presented to them and reach logical conclusions is essential in a world where we receive information from an infinite number of sources. Our teachers prioritize these and many other concepts in their work with students each day — no matter the distance. 

While there are so many different strategies teachers use to help students come to new understandings, one is asking the right question at the right time. Whether in a kindergarten Number Corner session or a fourth grade multiplication strategy talk, these three key questions help our students build their computational fluency: solve problems accurately, use efficient strategies and show flexibility.

Students in Mrs. Patton and Ms. Ferdinand’s Kindergarten class (the Blue Room) proudly show their completed work after an exciting math game.

Question 1: What do you notice?

Teachers methodically ask this throughout their math classes. Asking younger students what they notice helps them to make connections and to sort and categorize — an essential early childhood skill. We ask our youngest students what they notice about a group of objects, about how many days we’ve been in school, about a graph or a chart that collects student answers to the daily question. And we ask our oldest students what they notice about a set of numbers or a particular strategy to help them formulate and articulate math strategies. Asking students what they notice encourages them to put together all the math and logic learning that is in their heads to try to put some order and sense into what’s in front of them. 

Mr. Haltom based his (beautiful!) calendar creation on the one from the Bridges curriculum, adding in important days for the Grace community. He asked our youngest learners in Junior Kindergarten what they notice about the emerging pattern, and what they thought might come next. What do you notice?

Question 2: What do you wonder?

Encouraging curiosity is one of the highest priorities in our math classes. Curiosity breeds hunger for more learning and also breeds an eagerness to make sense of what’s around us. Our second grade teachers recently led an activity which gave students the opportunity to come up with questions usually left to curriculum writers. With a given amount of information, what questions could you ask? For example, if you know that there are 124 red legos and half as many blue, what questions could you come up with? 

Our students might ask:

  • How many blue legos are there?
  • How many legos are there in total?
  • How many more red legos are there than blue legos?

When we ask students to generate questions, we dismantle the notion that questions only come from those who are ‘in charge’ or older. Giving children the opportunity to come up with their own questions is one way we can show that we value their thinking encourage their developing curiosity.

Question 3: How do you know?

Verbalizing thinking is useful both in and out of the math classroom, and our students spend a lot of time writing and thinking not only about the numbers of math but about the words, too. Teachers are often encouraging students to move beyond a common initial student response, “I just know,” and instead give a reason or strategy. “I know that is ten because I started with five and added two more, which got me to seven. And I know that seven and three more equals ten.” We want to teach students that intuition does have a place in the math classroom, and that there is value to articulating what and how you are thinking.

Mr. Wanyoike guides fourth graders through a problem set from Bridges. These problems lend themselves to certain strategies that the class has been focusing on, encouraging them to flexibly solve problems and justify their thinking along the way.
In a recent first grade class, associate teacher Ms. Alonso poses a task for students. There are 18 dots all together, and some are covered up. How many are under the ‘Splat’? How do you know?

I am really proud of all of the math learning and teaching at Grace in the last few months, and I can’t wait for the day we get to safely be together, hearing our students excitedly call out everything they notice and wonder.

Dances for Very Small Spaces

By Jenny Pommiss, Dance

When Grace was forced to shut its doors, the advanced, senior-only Dance Repertory Class began a project I called, “Dances for Very Small Spaces.” The project was born out of quarantine and the desire, in fact, the need, to keep moving. It was inspired by “52 Portraits” (2016), which was a digital collaboration between British choreographer Jonathan Burrows, composer Matteo Fargion, and video maker Hugo Glendinning. In class, students were asked to look at their homes, the places where they may have lived all their lives, in a completely new way. They scouted locations for a dance that would not only use their bedroom or living room as a backdrop, but as a dance partner. Students were encouraged to have the location drive their choreographic explorations. They were then asked to film themselves from a variety of different perspectives, add music, and edit that footage together. At the same time, the students were asked to take time to reflect on what Dance has meant to them at Grace, how the pandemic has affected them, and how it may continue to affect Dance as a discipline moving forward. At the end, I whittled their final projects down to a minute each and layered their interviews over their chosen sound so that they could be strung together. The result was a collection of deeply personal movement portraits that represented four years of growth in the Dance Program at Grace. 

Check our Website in the coming days to see the students’ full final projects. In the meantime, please hear their voices and watch their dancing in a beautiful compilation. You can watch Dancing With Big Hearts in Small Spaces: Senior Edition, using the password: Seniors.

This project then became a component of a larger, full Ensemble piece called “Dancing with Big Hearts in Small Spaces.” This was a digital reimagining of the Ensemble’s canceled live performance, which was set to go up on April 17 and 18 in Tuttle Hall. As Devon M. ‘20 says in the piece, “Honestly, when I first heard that schools were going to be shut down, I did not think that Dance was going to continue”. To his surprise, the Ensemble continued to meet twice weekly to move together and explore what it means to dance alone and in place. Visiting teacher Simon Thomas-Train and I collaborated on the concept and direction. Josie M. ‘22 offers, “We have kept going….we are finding other ways to keep moving…and to keep the spirit of dance and the amazing gift of dance alive.” Each week, after a physical warm-up, students were given prompts, such as “make a dance in a doorway” or “use today’s headlines as an inspiration for a dance”. They were then asked to film themselves using a variety of different camera angles. The dancers also interviewed themselves, which gave their virtual audience the opportunity to delve deeper into the dancers’ creative process. You can view the full performance here, using the password: Bighearts.

For the virtual finale, I was inspired by the choreography and editing techniques used in a music video by Thao & The Get Down Stay Down that was produced in the early days of the quarantine and choreographed specifically for Zoom. I loved how it utilized the video medium to make dancers appear connected in new and exciting ways. You can view the Finale here, using the password: Finale.

Senior Directors Compelled to Take Films in New Direction

Film and Media Majors spent this year preparing to shoot their final film over spring break. After months of planning, and with spring break about to begin, Seniors Sasha Q., Otto L., Lucinda L. and Charlotte G. found their planned shoot and production completely shut down. Recognizing the less-than-favorable hand his students had been dealt, photography and film teacher Mr. Todd gave them the option of adapting their existing scripts or creating new films. Without exception, the students accepted the challenge of crafting entirely new films before graduation, even though they had already been working on their final projects for months. 

As the students began writing their new scripts, Mr. Todd shifted the focus of his class to delve deeper into the study of the avant-garde films and the pioneers of alternative cinema. The curriculum clearly inspired his pupils, whose films, either by design or necessity (or, more likely, a bit of both), began moving in a more surrealist direction, exploring the streets of New York City; a lofty apartment; even a kitchen sink. 

The uncharted territory lent itself to a somewhat surprising result. Said Mr. Todd, “While the students did not have the chance to experience building a production crew and filming with all the resources Grace has to offer, they were given the conceptual freedom to explore improvisation and a taste of auteurship on a level they probably wouldn’t have had prior to this crisis.”

View all films here using password “films2020.”

Bon Appétit! French Baking Inspires French Students

By Sylvie Larue, Middle School French Teacher

 I knew long before Spring Break that I would teach 6th grade French and replace Ms. Antonio who had a beautiful baby girl in March. Before she left to take care of her family, she told me that I had to teach two units about food and the city of Paris. In front of my computer during the vacations, I wrote a curriculum about how to order food at a restaurant and eventually found a dialogue online. The students learned the vocabulary, listened to pronunciations and intonations, and practiced reading the dialogue in our Zoom class. I prepared a slideshow with all the delicious food that the “customer” in the dialogue was ordering: Salade au chèvre chaud (goat cheese salad), boeuf bourguignon and tarte Tatin

Tarte Tatin is a specialty from the Center-Val de Loire region of France. It was accidentally created by two sisters, Stephanie and Caroline Tatin. Students were challenged to find out what had happened. We laughed a lot imagining what could have happened in that kitchen in the 1880s. Finally, students got it: the pie became an upside down tart because the chef had placed the tart in the oven the wrong way! To finish the class, we watched a cooking video to learn how to make this fabulous desert. Nothing else was expected. It was about sharing a good time together on Zoom. I posted the video on Gracenet and to my surprise the next day, Charlie had baked. On the weekend, I received photos and emails from Chloe, Bo, Olivia, Thea, Felix, Lulu…it was truly a treat. The video and  the lesson had inspired them. They took charge of their learning experience, they were curious about the French gastronomy, some used their French writing skills to write a critic about the tart: They made a French teacher’s dream come true!

Check out this recipe from PBS to make your very own tarte tatin, and check out the slideshow below to see all of the students’ tasty tarts!

Dancing Across the Globe

By Pam Vlach, Dance Specialist, Lower & Middle School; Director, Middle School Dance Ensemble

The past few weeks, the middle school dance ensemble has been working with Aphiwe Mpahleni, who’s zooming in from Cape Town, South Africa to share the history and technique of Gumboot. The first week of her residency, the students learned about the emergence of Gumboot in the gold mines of South Africa as a tool for communication and protest in poor working conditions. The racial inequities in South Africa as related to the origins of Gumboot were particularly poignant for students. The second week, the seventh and eighth graders practiced the technique of Gumboot and learned a combination that we’ll likely incorporate into the middle school dance concert next spring.

In planning this unit, Aphiwe and I met several times to discuss content and strategy for online teaching because it was important to address both the possibility of unreliable technology and specifics of pedagogy that are culturally informed. We wanted to create a process where the middle schoolers could learn successfully while experiencing the cultural intricacies of Gumboot in an authentic way. Although there are certainly challenges in teaching dance remotely, it’s also an excellent opportunity to think outside the box and make the world a little smaller for the kids. 

Technologically, nothing is perfect. During one class, my speaker stopped working and I didn’t realize it. There were a few minutes of Aphiwe communicating with the kids and I couldn’t hear any of them (but thought the problem was on their end). When I realized what had happened, I was incredibly embarrassed and apologized, and the kids laughed, then we continued on with class. I share this because in teaching remotely, connecting with the students has sometimes meant showing some vulnerability in learning these new online tools and platforms. We’re all in it together, and we’re learning as we go.