Within most subjects, students are guided along a traditional progression of classes. For example, to succeed in AP Calculus, a student must have a solid grasp of Precalculus. This usually shifts the focus in Precalculus to bringing all students up to an acceptable level of performance. In this pursuit of universal proficiency, the richness of various concepts in Precalculus is glossed over. Beautiful ideas like roots of unity and rotated conics are ditched in favor of important, but often dull, topics such as trigonometric proofs and graph behavior.
At the same time, every class has a handful of students who “get” what is being taught. They don’t need the 10th worksheet or the 100th flashcard. They scoff at busywork and routinely balance incomplete homework assignments with perfect test scores. Simply put, they are bored. How do we engage them while not diverting attention from struggling students? If only there was some interesting material they could explore independently!
Halfway through my own Precalculus class, I found a textbook that explored the aforementioned skipped topics. I asked my teacher if I could replace classroom material with problems from this textbook and she agreed. Following this, I was no longer paying attention in class or doing regular homework assignments. Nor was I playing games on my cellphone. Instead, I was developing my problem-solving skills--without hurting anyone else’s learning! My interest in more advanced mathematics grew out of those experiences and three years later, I went on to win the Math League State Tournament.
From my own experiences, I have found it common for independent learning projects to foster newfound passions. However, I don’t believe this is a unique result. Because independent projects allow for rigorous exploration and hands-on engagement, these create meaningful academic experiences--the sort that can cascade into new interests.
I believe these independent projects break down into two categories: short-term projects and long-term projects.
Short-term projects are experiences that supplement classroom material. Suppose one of your students is genuinely excited by something being discussed in class. An alternative project, replacing traditional assignments, could help them further this interest. For example, in homework assignments for my AP Calculus class, I would often find interesting problems ripe for additional thought. Not only did my calculus teacher encourage this sort of academic excursion, but he routinely joined in this exploration as an equal; together, we would discover something new—no matter how trivial—that neither of us had seen before.
Long-term projects are broader and more extensive. These might take the form of an Independent Study at the high school level, which confers credit for a more formal course plan. These have been instrumental in my high school experience. I have studied material not offered in the district, including calculus-based physics and post-calculus mathematics. I have also taken on big projects, such as creating a new algorithmic ranking system and starting a podcast--Solving Systems—with a JM teacher (you should definitely check it out!). These Independent Studies were intellectually stimulating and extremely enjoyable. Projects like these require more forethought, but could easily become a student’s most rewarding high school experience.
How do you set up an independent project with a student? Regardless of the scope, there are a few essential steps:
Instead of prodding successful students into classes and assignments they find easy, we should encourage them to create their own opportunities. Whether it be breaking out of a prescribed curriculum or creating one’s own curriculum, there are numerous venues for worthwhile challenges. As Astrophysicist Neil deGrasse Tyson once said, “There is no greater education than one that is self-driven.” We can start by putting a few students in the driver’s seat, allowing them to steer their education toward what they desire.
This post brought to you by Nikhil Marda, Senior at John Marshall High School
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