Essential Questions: the ingredient that flavors all of my math classes

This blog post is part of Sam Shah's "Virtual Conference of Mathematical Flavors", which asked "How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?

Above the board in my classroom, there are 4 questions posted. They are:

• What is math?

• What is the pattern, and how many ways can I represent it?

• How does math connect to the world around me?

• How am I a mathematician?

These questions are my Essential Questions, which I developed during the Project Zero Summer Institute in 2007. They are touched upon constantly in my 6th, 7th, and 8th grade math classes. They are hard to answer concisely, yet we are constantly asking them and our answers will evolve over time. 

Here I will share some reflections on each of these questions and how they have helped me "move the needle" for my students.

What is math?

I ask my students this question on the first day of school. They write their answers up on the giant whiteboard wall in my room. I start with 6th grade and then 7th and 8th contributes. I love seeing what the 6th graders come in with, but also the complexity (and poetry!) that 8th graders (who I've taught for 2 years at this point) use to talk about math: 



What is the pattern, and how many ways can I represent it?
In exploring this question, we drive home the key ideas that 1) math is about describing patterns, not just problem solving or calculations and 2) there are multiple ways to make sense of a problem, and by taking time to look at these, we come away with a deeper understanding. While we look at patterns constantly in my classes, one of my favorite routines for doing this is using Fawn's Visual Patterns website. After staring at a pattern for a bit, my 7th graders come up and circle how they see the image growing, taking turns using different colored whiteboard markers. I love watching them have an aha moment as they realize how to use the growth to create an explicit formula for the number of objects based on the figure. After doing one pattern per week for the first half of the year, students create and analyze their own visual pattern. 


How does math connect to the world around me?
We do a lot of projects in my classes, and I always try to have the students use the math in a real-world way as a professional would (this was another big takeaway from Project Zero - see David Perkins Whole-Game Learning). My students are architects, cartographers, financial advisors, artists, engineers, and amusement park owners. They use the math in ways that are fun and practical (though I think there should also be room for appreciating the beauty and elegance of math for math's sake - see below). They learn how to use the tools of math and how to apply what they know to solve open-ended, creative problems. They look at math in the news once a week and learn to view statistics with a scrutinizing eye.

6th graders attending to precision as they build giant candy boxes.

8th graders use slope to find the steepest staircase in the school

How am I a mathematician?
This is perhaps the most important question of all. It is crucial to me that each student sees themselves reflected in the curriculum and feels empowered to not just do math, but feels like they are a mathematician. I do this by making frequent opportunities for creativity, collaboration, and connection. I want my students to see math as a dynamic, human subject that they have the power to influence and inform. Through the mathematician project, students research (and later present as) a mathematician, examining not only their person's math contributions but how their identity shaped their experiences with math. In collaborative groups, students work together to articulate their understanding and to move collectively towards the fulfilling aha moment. Students have opportunities to connect math to what they find relevant and interesting, be it music, baseball, feminism, food, or cars. Finally, I allow space for students to find beauty in math, honoring and displaying their creations. My hope is that when they go to high school, they will have a bank of positive math moments to come back to when they face a new challenge, as well as a deep appreciation for this nuanced and varied subject.

Reflections on my first Twitter Math Camp (better late than never)

Good morning, Cleveland.

Twitter Math Camp exceeded my expectations. It was undoubtedly the most welcoming group of educators I have ever seen (which is saying a lot - teachers are pretty nice on the whole). The conference is capped at 200 people, which keeps it small enough to facilitate a bunch of social meetups in addition to workshops and keynote speeches. I arrived on Wednesday for the Desmos pre-conference. I had signed up for this before I knew I was chosen for the Desmos fellowship (which was the weekend before!), and wasn’t sure if it would be redundant, but it wasn’t at all. I got a chance to  learn about the Desmos geometry tool and how to get the graph to do statistics calculations. These are two things I will definitely use next year in my quest to Desmos more in my 6th and 7th grade classes. The Desmos precon ended with a happy hour at a great local brewery, and then a bunch of us ended up playing games at a local game bar/restaurant (they had the biggest collection of games I have ever seen!).

Not a math game.

The next morning, I had my first of 3 consecutive mornings learning the math and art behind Islamic geometry design. This workshop was taught by Annie (@anniep_k), Megan (@veganmathbeagle), and Stephen (@sweimar). It was so relaxing and fun to create these 6-fold and 8-fold symmetric shapes!

6-fold symmetry with an extra point (oops)

8-fold symmetry with (sloppy) weaving

After lunch, we settled in for Marian Dingle's keynote called "Measures of Center." She spoke poetically and powerfully about her and her children's experience as black teachers, learners, and people. It was a call to action to all of us in the room and beyond, questioning who we truly serve when we teach, and begging us to consider the experiences of those who are not in the "center". By end, many of us were in tears. When she left the stage, Marian saw me crying and stopped to give me a hug!



The following day, there was a fun and empowering keynote from Julie Reulbach. She came bursting through a banner with pom-poms, as if we were in a pep rally!  She proceeded to be our cheerleader as she encouraged teachers with the following mantra (complete with stickers for each of us):

After Julie's keynote, it was time for my presentation on Social Justice Projects for Middle School. After Marian's call to action the day before, I was disappointed that only 6 people came to my talk! This left me wondering what I can do differently to get the message out to a broader audience about ways to incorporate social justice into our math curricula. I am still wondering about this.

Overall, the conference was extremely well-run. It really did feel like camp, what with all of the ways to connect with other MTBoS folks - speed dating, newbie dinner, and trivia night. I left on Saturday before game night and the writing of the annual TMC song! I definitely hope to go back next year when TMC is in Berkeley, CA.

Goodbye, Cleveland.