My main goal when teaching is to show students that mathematics and humanity are inherently intertwined. To do so, I consider each perspective and design my class where the two converge.
I want my students to understand that math exists outside of equations, is grounded in the human experience, and that, as such, the steps we take in math are meaningful and rational. Students often have the preconceived notion that math is just an arbitrary set of rules that you follow in a certain order to get a certain result. I see this when working with students in office hours and even when helping workshop facilitators decide how to explain concepts to their students. To humanize mathematics, I frequently use analogies and stories to demonstrate that math is generalization and abstraction of things we experience in our daily lives. When teaching students about relative extrema, for example, I use the topography of Syracuse’s campus. After presenting the main idea for mathematically finding the relative extrema, I have them discuss in pairs: “How do you know you’re on top of the hill? ‘Being out of breath when you get there’ doesn’t count. Is this the tallest hill in the world? In the city? Is it still important that we ended up on top of a hill even if it isn’t the tallest one?” I walk around, encouraging discussion, listening to students’ answers, and helping students engage with one another. Returning to our lecture, students share their answers with the class and we discuss how the idea that “you aren’t going uphill anymore” is the same as “everywhere around you is down” and how this can be phrased in terms of increasing and decreasing functions. Using this type of investigative learning, which has been shaped by the theory of inquiry based learning, has been an effective way to help students internalize and actualize concepts. This is especially important when teaching a class such as Calculus for Life Sciences, as I have for the past two years. These students come from diverse math backgrounds and have a wide variety of career goals. These students will likely never need to locate relative extrema on a graph, apply the definition of continuity, or compute an integral in their future careers. They will, however, inhabit a world filled with patterns, use deductive reasoning to draw conclusions, and need to be mathematically literate to work with quantitative data. Using real world investigation, I aim to give students a way to relate the math they see in lecture to their experience and thus demonstrate that math is rooted in reality.
Mathematicians are firmly in the intersection of math and humanity. Consequently, it is imperative that students see themselves reflected in what they are learning and in how they feel learning it. To remind students that there is at least one human behind every theorem, I share stories about mathematicians like Pythagoras, Newton, and Pascal. Incorporating stories about a more diverse group of mathematicians in my teaching would be a huge advancement in the pursuit of showing my students that math has no age, race, or gender. More than just seeing their demographic represented in mathematicians, students need to see their feelings reflected in mathematicians. I speak openly with my students and workshop facilitators about my struggles in math, the fact that I make mistakes, and about my academic failures. I want students to understand that part of doing math is being wrong sometimes, that failing is part of learning, and that they are by no means alone in doing so. This effort to normalize being wrong is paramount in how I construct my classroom environment and how I help the workshop facilitators construct their workshops. From the first day of class I emphasize mutual respect, beginning with my Respect Policy included in my syllabus, as I have done since my time as a workshop leader at Cal Poly. This policy outlines how I respect my students’ time by being prepared for class, how they are to respect me by paying attention in class, and how they are to respect each other by allowing their classmates the freedom to make mistakes. I see evidence that my classroom is a supportive environment when, in a letter of endorsement, my former student Hannah Smith remarks:
“I am frequently nervous to speak up in class and ask questions about content, for fear of raising a ‘dumb question’ that would embarrass me in front of my of my instructor and my peers. However, with Erin, that fear washed away.”
I have also implemented this design into my weekly meetings with the workshop facilitators. It is crucial that these meetings embody this environment that I want the facilitators to create in their own workshops. While the facilitators are working in pairs to review their worksheets, I hear them talk openly about the questions they didn’t understand, graciously correct one another, and point out value in other responses. In either place, it is so crucial that my students, my facilitators, and their students feel that class/workshop is a place where they are allowed to be wrong. Once this environment is established, learning can happen.
The last component of connecting math and humanity in my classroom is recognizing who my students are as learners and as humans. These are students who feel awkward asking questions in class or may not know what questions to ask, but still know that they need someone to slow down. Knowing this, I frequently take “thumb polls” in addition to asking if my students have any questions. I pause my lecture or workshop meeting and ask the students or facilitators to show me on a scale of thumbs up to thumbs down how well they are understanding the material. Multiple students commented on this formative assessment in their letters of endorsement. One student, Brianna Lennehan, remarks that because of this “[she] and [her] peers felt like it was possible to succeed in the [my] classroom and leave the semester remembering the material.” Many of my student’s begin the semester apprehensive about doing math. To build students’ confidence, I help them take ownership of their learning and of the class as a whole. On exams, I offer them the option of getting hints/ next steps on problems for the cost of points on the problem. Doing this allows them to earn the remaining points on the problem and gives them a choice as to how much help they need. This offers me better insights into what the students actually know. More importantly, this choice gives them back some of the power on the exam, which boosts confidence, reduces nervousness, and improves performance. Furthermore, I want my students to be able to start to take ownership of learning outside of class. To accommodate my students’ diverse backgrounds, I incorporate parts of a universal classroom by providing a number of ways to learn the material by posting my notes, audio recordings of my lectures, quizzes, and helpful outside resources on our course blackboard page. Lastly, humans thrive in community. Specifically in a math class this gives students a group to study with outside of class and consistently provides them a reason to come to class. I often begin group work with introductions, encourage the students to discuss their lives while doing the assignment at hand, and end group work by suggesting students exchange contact info. Promoting the community between my students not only benefits their performance, but plays an essential role in building an accepting classroom where individuals can build confidence and do math together.
As an instructor, I of course want my students to understand the material. More than that, I want my students to realize that math is more than just rules. I want them to believe that they can do math. I want them to know that making mistakes is part of learning. I want them to feel empowered to take control of their learning. Most importantly, I want them to know that they are valuable and their contributions matter.