I was recently awarded a Math for America Master Teacher fellowship. The five-year program will connect me to a terrific network of professionals in the math education community and will offer me support in pursuing my professional development goals. Many of those goals are on the topics that I’ve been discussing and will continue to discuss on this blog. I’m hoping to keep this blog along for this five-year ride!
Here is the personal statement I wrote and submitted with my application:
Prompt: How are you continuing to grow into the mathematics teacher you want to be?
For many of the students who walk into my classroom on the first day of school, math is an arcane foreign language with complicated rules and procedures requiring mindless memorization. To these students, math classes over the years have felt like a grueling race in which they are always behind. Confidence, curiosity and satisfaction in the subject have rarely if ever been a part of math class for them. I strive to change that. My goal is to have a math classroom where students are fearless, demonstrating perseverance and patience, and they believe that math is fun, satisfying, and makes sense. This quest will last my lifetime.
Changing my students’ mindsets is a pivotal step in this quest. I expend great effort dispelling students’ notion that there are “math people” and “non-math people.” Inspired by Carol Dweck’s work on growth mindset, I make a case that math proficiency is much more a function of time and hard work than it is of innate ability. I make this overt- by debunking myths about achievement, by telling stories of famous people who achieved great things through virtue of hard work, and by preaching catch phrases like “Mistakes are expected, respected & inspected” and my favorite three-letter word, “YET.” I litter my classroom with posters that send similar messages and I refer to them frequently. One such poster reflects my conception of the stages of understanding: “1. No Understanding. 2. Some Understanding. 3. Confusion. 4. Deep Understanding.” Stage 4 is a really satisfying place to be, I tell my students, but there are no shortcuts to getting there; confusion is a necessary and productive step along the way, so when you get there don’t give up hope!
Though I witness success stories in my classroom when it comes to mindset, reversing students’ preconceived notions about their ability is a never-ending task. I recognize that influential books, posters, and well-polished pitches are just part of the equation. As a learner myself, I have found that the most powerful mindset shifts come from personal experience and realization. I am always on the lookout for opportunities to illuminate flashes of my students’ growth mindset whenever they appear. One student that comes to mind is Sam*, who was determined not to try in math due to his perceived near certainty of failure. Sam took up skateboarding early in the year and had a propensity for skating right outside my classroom, trying and frequently failing tricks over and over again. In a conversation that served as a major turning point, he said without hesitation that improving his skating would not be possible without risk- taking and failing repeatedly, which provided opportunities for learning and adjustment. I helped him see that understanding math was not all that different from learning new skateboarding tricks. Sam is a perfect example of how people can have different mindsets in different contexts. For Sam and others to truly transfer the right mindset to a math context, though, it is crucial for students to see success specifically in the subject.
Towards that goal, I work hard to make math more accessible to my students. One way I implement this is by tapping into students’ current knowledge, prompting a need for a new skill or tool, and scaffolding the process of using what they know to learn something new. For students who know the Pythagorean Theorem and are learning distance formula, I might ask them to calculate the distance between two points on the coordinate plane that are horizontally or vertically aligned, a task that simply involves counting. Then I would ask them to find the distance between points that require a short diagonal line, prompting a right triangle and the Pythagorean Theorem. Finally, I would have students find the distance between points like (5, 10) and (305, 210) that make the previous method impractical, followed by the points (a, b) and (c, d), resulting in their own derivation of the distance formula.
Another example of my growth in this respect is in teaching students to solve quadratic equations in Algebra 1. In my first year of teaching, I drilled students on converting equations to standard form and plugging into the terrific and mysterious quadratic formula. Now, I begin by posing questions that remind students of what they already know – that isolating a variable is achieved by using the properties of equality: adding on both sides, dividing on both sides, and so on. I then ask them whether this can be extended by taking the square root on both sides. My students know to examine this claim by creating a basic example or two and testing them. We will then see if the theory can extend to more complicated examples, like perfect square binomials. Ultimately, we will generalize, turning this process into the terrific but no-longer-mysterious quadratic formula. Sequences like these typify my quest to help math make sense to students.
Part of the challenge in doing this is that all classrooms are comprised of heterogeneous learners. A heterogeneous environment is present in my current (untracked) classroom, in which my classes have students who have mastered Algebra 1 and Geometry learning alongside students who have failed Pre-Algebra. Successful teaching in contexts like this requires broadening what it looks like to be “smart” in math class. To most people, being smart in math is about speed and procedural fluency. I make it clear that being smart takes many forms, such as asking an insightful question, or decontextualizing a situation into a helpful diagram. To stay true to this, I dedicate an increasing amount of time in my class to perplexing math problems that prompt discussion and require out-of-the-box thinking. This presents opportunities for students to be smart in different ways. I have found that when posing math problems that require flexible, creative thinking, a heterogeneous group can build trust and confidence because group work may result in solving problems that individually might be out of reach.
That said, procedural fluency is an integral part of math. I have learned that when teaching math skills, heterogeneous groupings can sometimes lead to an unhealthy divide between students who know the skill and students who are learning it for the first time. Designing groupings to expose specific students to the right experiences is among the hardest parts of my job, and it is a skill I continue to hone. In the past few years, I have been blessed to partner with a number of prominent education technology companies that are working to ease this challenge. The progress we are making together is incredible, but knowing exactly where and how technology can be inserted appropriately is among the many things I continue to work on in my teaching practice. I am beyond excited at the prospect of working with Math for America to continue to grow in my practice in these ways, and certainly some new and unexpected ways as well.
* Name changed