Sunday, August 26, 2018

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.

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