Math, Critical Thinking, and Supporting Tomorrow’s Changemakers

When Cara LaRoche reflects on what it means to be a changemaker, she doesn’t only think of the outspoken leader in her classroom, but also recognizes the quiet, reflective student who leads by example. To her, this alternative style of leadership also embodies what it means to be a changemaker.
In this question and answer session, hear from Ms. LaRoche, Ellis’ Mathematics Department Chair, about how both the math faculty and curriculum at Ellis are developing critical thinking skills in students to grow the changemakers of tomorrow.

How is the math curriculum at Ellis supporting the development of changemakers?
It starts early with our students and grows over time. The skills they develop over the years include things like learning from and being open to multiple perspectives, even if they don’t necessarily agree with those perspectives. Our students learn how to advocate for themselves. If they don’t understand something, we certainly expect them to let us know that.
What does this look like in your classes?
In a lot of math classes, whether it’s in the Lower, Middle, or Upper School, students are always being asked to defend or justify their outcome, or to reason through something. Math at Ellis is not memorization and regurgitation. For example, just today in my grade 5 math class, we were talking about divisibility and looking at multiples of 4 and 9 to try to identify patterns. I was working along with my students to see if we could come to a conclusion based upon a pattern. Some of the girls were saying, “oh, for divisibility by 4, it’s just every other even number,” and so then I asked them, “if we’re trying to test if 4,396 is divisible by 4, how would we know if we’ve landed on the right even number in that every other even number sequence?” So, collectively as a group, we were brainstorming and trying to see if we could figure out a rule that would apply.
Do you change the way you approach your students in order to support them as they develop the skills and characteristics needed to impact change?
In the math department, many of us don’t like to come right out and answer “yes” or “no” when students ask questions. If someone asks a question, I then try to pose another question that helps them reason their way through the question they just asked. I think the entire department encourages students not to expect correct answers immediately or to expect perfection in their work every single time. We spend a lot of time talking about the process and the reasoning behind it, not just the answer. How a student got to their solution is just as important, if not more important, than the actual answer. Being able to work collaboratively, and being able to build on other people’s ideas and appreciate a different solution path than what you thought of, helps develop that skill set of working with people who have different ideas than you even though you’re all working towards the same goal.
How do the faculty in the math department model change-making for students?
I think within our department we model working together collaboratively as a team. We do this with our students, too; we don’t teach them that only the teachers have all the answer. Solutions can come from anywhere, and anyone. As we’re doing this, we’re also giving students the language to use as they are describing findings and the patterns that they’re seeing. We’re constantly asking them “does your answer make sense?” Once they have an answer, we ask them to go back and try to make sense of the steps that they’ve taken, or the computation they’ve just done, to get to an answer. Thinking critically about their process is really important.
How do you think the rest of the community models change-making for Ellis students?
Within the community, I think the adults model being changemakers in the sense that we ourselves will speak up if we see something that we think needs to be addressed. I think modeling working together, and supporting each other in our work, even though it’s very subtle, is noticed by our students. In a girls’ school setting, there is no subtle or overt messaging that girls can’t do something because they’re a girl. Within our department we have both male and female teachers, so they have female role models that they can look to.
How do you think that “let’s try it” kind of support system is embodied in each division?
Within the math department, it happens in every classroom. We always ask them what they think or what they noticed. We ask questions such as, “What should have happened here?” or “What were you expecting to happen?” We’re constantly asking them for their input or ideas. These girls are also so used to being up in front of other people; whether it be in their classroom, onstage for a play or the candlelight recital, or at PJAS, they are regularly given the opportunity to put themselves out there. The more often they do that, the more comfortable it becomes for them. In the Upper School it’s the same, only now they can also be a part of Data Jam, where they get a project, conduct research, and then present it in Oakland with a big group of people. I think that when our girls have those opportunities, especially to work collaboratively in some competition, they typically do very well because they’re building off of each other’s strengths, they’ve got the poise, and they’re used to being up and speaking in front of their classmates or in a Middle School meeting. For so many of them it becomes a part of who they are.
Why is it important for girls in particular to develop and practice using their voices?
I think it’s important for us to model for girls not being afraid to take a stand. If there’s something that we believe in, it’s important for us to be able to use our voices if need be. I think it’s important in math specifically, for students who are interested in pursuing STEM fields. Even though women are making great strides in these fields, there are certainly pockets still dominated by men. I can still remember Jean YANG ’04 talking about how it was such a change when she entered the computer science field, especially in graduate school. She said she was the only female voice around the table and she had to work hard to prove herself. Having that voice, whether it’s an actual voice or that metaphor of strength, is something that is developed naturally over time in Ellis girls. It’s important because they may be the only one in a room that’s willing to speak up.  

Why is resilience an important characteristic for changemakers to have?
If our graduates want to impact change, it is important for them to have resilience, especially if they might be headed into a male-dominated field. They have to be okay with being a minority in the room. They need to know that they don’t have to be perfect 100 percent of the time and that it is ok for them to take a risk, to speak up, to try something new. If they don’t get it right the first time, they learn from what they tried previously and adjust what they’ve been doing if it doesn’t quite get them the result they wanted.
How do you cultivate resilience in girls?
A lot of us in the Math Department have embraced allowing kids to revise their work. Hopefully we’re sending that message that you don’t have to be perfect 100 percent of the time, especially as you’re learning something new. I sometimes see girls who have typically been very strong math students, but when the concepts get more abstract, they realize it’s a different kind of math. These girls have to adjust how they’re studying and how they’re preparing for assessments. That can be hard for a student who has typically been able to do very well by doing things a certain way. We let them focus more on the most important outcome being their understanding of the content, not necessarily a percentage or a grade. Knowing that the grade doesn’t define them as a learner and that there are lots of things that can go into the one grade helps students make sure they are taking advantage of all of the different components that can go into it.

Do you have a favorite example of an Ellis girl flexing her changemaker skills?
When I think of current Ellis students being changemakers, I think our girls just do it. They don’t even think about it anymore. When Francesca, my daughter, was in Lower School, she was an environmental ambassador. Environmental ambassadors met as a group to talk about ways that they could do things around the School to help the environment, whether it was putting signs above light switches reminding people to turn off the lights or helping others sort and recycle their trash during lunch. Any time there’s any sort of a local or national crisis, Ellis girls don’t even pause; they figure out what they’re going to do in order to support whichever group needs it. I know that there are students that do this kind of thing all over the place, but what I find particularly special about Ellis girls is that it seems to come so naturally to them.