At Mountain School, we approach math instruction as we do everything else, with an eye to love of learning and a work hard, play hard attitude. We realize a math problem can be as intimidating as sending a narrow chute during ski PE or trusting oneself to step out onto the Via Ferrata’s Main Event.
To do the former well and teach math well, we strive to engage and support every student. We embrace who we are, who our students are, and what our values are. To do this, the math team has identified four common goals that are consistent from Montessori to 12th grade. We strive to support students to
- Build confidence in problem-solving
- Develop skills and fluency through building conceptual understanding
- Stoke curiosity and a love of learning
- Strengthen our sense of community by working together
If you visit school, you’ll see our youngest students developing their math skills in a Montessori classroom, touching and moving tactile manipulatives to build their foundational knowledge. You’ll see our oldest students engaging in the International Baccalaureate curriculum, blending trigonometry, geometry, calculus, and algebra to solve complex problems. And, you’ll see our teachers continuing to reflect, collaborate, and build their skill sets to consistently and effectively engage students in innovative ways.
Our math teachers are challenging themselves as much as they challenge their students. Currently, they are working with an outside consultant to intentionally build “student agency” in the math classrooms across all grades.
In Mountain School terms, think of “student agency” this way. When students get tired while biking the White Rim, they find ways to keep going. They help each other, they shift, and they problem-solve. The SAG wagon may come by to encourage, but we don’t really offer to give them a ride. We want them to overcome their struggle, get support, and keep going. Metaphorically, this is also what we want them to do when they hit a hurdle in math.
Academians such as Glenn Whitman, co-author of Neuroteach, call student agency a “yet” sensibility. When students struggle and insist they can’t do something, we train them to add the word “yet”. Angela Duckworth, the author of Mindset, calls student agency a “growth mindset” — the belief with hard work, practice, and the right approach, a student’s ability can grow. Ability is not fixed. Others might use the word “independence”. We think of it as students having both a belief that they can use strategies to approach a challenging problem and a growing set of skills and strategies to be successful.
So, what does this look like in the math classroom?
Students first engage in an opening problem that activates prior knowledge, reminding them of skills they developed in a prior lesson or even prior year. It’s like a practice lap before a technical bike ride or skiing a quick groomer before heading to the upper mountain in ski PE. Next, we give students a problem or set of problems that is just challenging enough to engage them. We know these problems will be difficult, but we also know with the right support at the right time, students can work through these problems and develop as mathematicians. Think of the first time you skied North Chute or tried to clear Mill Creek. It was hard, you stumbled a few times, but you had the foundation and support to muscle through.
To muscle through a hard problem, students are given time to think and try the problem independently. Then they have opportunities to work with a small group of peers or a partner. Sometimes they remain stuck together, and other times a group member teaches a solution to their peers. When needed, they receive feedback or nudges from their teacher. Think SAG wagon. And, students always have an opportunity to share results and ask questions.
Class ends with an exit ticket that allows the teacher to gather data about each student’s understanding to better design the next session’s class. As students continue to practice, they gain confidence and strategies. Before they know it, they’ve mastered what once was hard and progress to the next challenge. They’ve cleared Mill Creek without a glitch and are moving on to Eider.
One of our goals is to build community in the classroom among students by facilitating them doing math together. We are building community among our teachers by engaging them in professional development and planning together. We’ve seen firsthand that, just like summiting a 14er, this work is important and hard, but also fun. And, in true Mountain School fashion, we approach these challenges — not only in the mountains but in the math classroom– with a sense of gratitude and shared success.