The Inquiry Project
How can I empower my students to see themselves as resilient mathematicians?
Throughout this website, you have read about how resilience manifests itself in different stages of my life, as well as how it plays a crucial role in my students' math learning experiences. On this page, I highlight the more pointed work I have done on my inquiry project.
Identity Reflection
Resilience Building
Empowerment
Grounded in Literature
Below, you can see my literature synthesis map, where I connect many different areas of existing literature that support the three stages of building resilience as I have outlined throughout the website!
*Click image to magnify!
Data Collection
This is my data collection design, where I outlined all the different methods I wanted to collect data from students, what I hoped to learn, and how I could incorporate those data into my own teaching. You may have already seen a lot of the data presented elsewhere on this website. Here are a few quick links if you are having trouble finding them!
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Research Findings
In each stage of the resilience building work I've done with my students, I have observed and gathered much fascinating data, and have compiled them into specific research findings. Therefore, there are three research findings below, each corresponding to one of the stages:
1. identity reflection
2. building resilience in the classroom
3. finding purpose in the real world
Finding 1:
Students come into the class with a lot of toxic preconceptions about math that they have internalized from pop culture and media, but they are able to challenge their mindsets and redefine what it means to be a mathematician through reflective writing and storytelling.
The first goal in my inquiry project was to probe existing student understandings, prejudices, and general thoughts surrounding what it means to study math. Epstein et al. (2010) note that mathematics is represented in popular culture as a secret code that’s difficult to crack, and mathematicians are eccentric, obsessional, and even mad (p.49). I found this to be very true with both the high achieving seniors in Multivariable Calculus or Linear Algebra, as well as the novice 9th grade students in Algebra 2. For the younger students, they reflected on how their math learning comes from a place of fear (of bad grades), or that they have to get through the class even though they don’t know how math is useful in the future. This aligns with how Nelson (2021) describes common perception of mathematics by students as unapproachable and inapplicable (p.2). Students were asked to write “Dear Math” letters, where they were able to safely share their previous experiences with math, which oftentimes include traumatic experiences with particular classes/tests/teachers.
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Older students who have self-selected to take the most difficult elective classes wrote letters that show that they have gotten past the stage of finding math as impractical, but still struggle with imposter syndrome and have just gotten better at getting good grades while still learning from a place of fear (of bad grades). They also start exhibiting signs of resilience – at least they have accepted that math is difficult, and that they will get over it.
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Through a lot of discussions over time, and after watching a documentary featuring Andrew Wiles, who proved Fermat’s Last Theorem, as well as clips of Good Will Hunting. As Epstein et al. states, develop pedagogy of mathematics that “embrace popular culture, using it both as a jumping off point for exploring what mathematics is and as a way of identifying and unpicking the images and discourses that young people meet in their everyday lives” (Epstein et al., 2010, pp.58-59). Students then had evolved their understandings of what it means to be a mathematician, and this time offered revision to their previous ideas regarding necessary attributes.
One student’s argument against objective attributes for mathematicians:
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One student did her project on how bees are mathematicians. She reflected afterwards on her broadening perspectives.
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Finding 2
Students start talking about resilience, yet they continue to engage in negative self-talk out of habit, which will take a lot more time to dismantle.
Over time, students start reflecting more on their own resilience, and are more mindful of moments in and outside of the classroom when they show signs of resilience. In my observations, they are also a lot more likely to directly reference the word "resilience" when working in small groups. Students also are more likely to be resilient in their learning, if I physically leave the classroom and leave them to do the work. They are more willing to admit that they don’t know how to do a particular problem. ​
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Out of habits, students detest having to be uncomfortable in their learning and be "stuck". Even when they grow in their resilience and problem-solving skills, students would still habitually complain, mostly for fun, hoping I would feel bad and help them. The habitual negative self-talk also proceeds, and I believe will take much longer to dismantle -- this is a powerful habit that is the result of years of studying and working under constant high-pressure environments, especially at elite boarding schools like NMH. A few students of color, in particular, have talked to me about never getting positive feedback from their parents or other family members, so I must further offer those positive words of affirmation as much as I can in and outside of classes.
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Click the image below to watch the video and see an instance where students had to grapple with being stuck on a particular math task when I established myself as not-available for questions!
Finding 3
Through the process of resilience-building and doing mathematics for social justice, students feel more empowered to create real world impact, and actively seek out ways to engage with the community.
Ultimately, my goal as the teacher is to empower my students to find their purposes in the world, and use what they have learned in the math classroom to help them tackle these complex, relevant, ever-changing social issues. To me, mathematical modeling is the direction that I have chosen for my teaching. “Mathematical modeling, in contrast to modeling mathematics, links mathematics and authentic real-world questions… to understand, evaluate, or predict something relative to the world outside of mathematics” (NCTM, 2016, p.5). Students are given much more open-ended questions at the end of a particular chapter of math, and they are asked to use what they have learned to help them make better informed decisions. This way, there is no "objectively correct" answers in math, and “students will have to think about making decisions in the face of uncertainty. Their opinions matter and influence their answer to this question. They still have to do the same mathematics to answer the question, but they are forced to reconcile their answer with reality, making the mathematics more relevant and interesting” (SIAM, 2019, p. 10).
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Berry et al.(2020)’s book, High School Mathematics Lessons To Explore, Understand, and Respond to Social Injustice has provided me with a lot of lessons and resources that I can immediately use in the classroom. One lesson that I have particularly enjoyed asks “what’s a fair living wage?… Students use personal experiences to make decisions about fair living wages. Thus, students who have limited experience with renting or earning hourly wages can familiarize themselves with current debates about minimum and livable wages…” (p.148).
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For example, here are some student reflections after doing the minimum wage lesson.
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