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Taking Calculus II to Another Level: Birdie Project

Updated: Jun 29, 2022

Jesse D'Oliveira

The Calculus II course at Dalton Academy offers students an opportunity to learn very high-level math that has real-world applications. The instructor of this course, Mr. Jesse D’Oliveira, during his time here in Beijing took an interest in a very common pastime; Badminton! As a means of fusing badminton and calculus together, he created the Birdie Project. 

What is the Birdie Project? 

The Birdie Project is an interdisciplinary, application and project-based learning exercise, that tasks students with solving a problem given minimal instruction. The project involves math, art, and computer programming, and is collaborative (i.e. groups of 2 – 4 students). It gives the students the opportunity to apply prior knowledge creatively, without direct supervision, over the course of four weeks. 

How does this project relate to the course? 

During the first 2 months of the semester, the students learned the Fundamental Theorem of Calculus, which acts as foundational knowledge for more advanced operations. Formulas for volume and surface area of irregularly shaped objects were developed and implemented through homework and testing. However, without a direct application project, there was a disconnect between the material and the usefulness of it for the students. The Birdie Project bridges this gap by synthesizing basic mathematical knowledge with advanced calculus formulas and concepts. 

Project requirements 

The Birdie Project requires students to calculate the volume and surface area of a birdie, by applying key formulas from the course to the mathematical models they create. They are then tasked with coding these models in Matlab (a coding software), to render the two-dimensional image, and execute their formulas. The students then have to design two scale models; the first 1:1, and the second 10:1 or higher. Lastly, the students were required to document their entire process, and present their project and models to the class. As a bonus, students were invited to create a three-dimensional model in Matlab for extra credit. 

How is this project innovative? 

This project is innovative in its approach, by taking a simple object and demonstrating from a design perspective, the role mathematics plays in its creation. The implementation of computer programming adds a unique element to the project, which most students were unfamiliar with before the course began. Lastly, the integration of scale models, allows the students to incorporate math with art, where part of the score goes towards creativity in their design. 

How did the students innovate? 

The most impressive moments of innovation from students come through the interdisciplinary application of knowledge. The best example of this is how several groups calculate the volume of their birdies by using a method of water displacement; they submerge the birdie into a beaker full of water, and the amount displaced gives the volume of the birdie. Another area of innovation comes from the students’ birdie choice. By selecting different types of birdies, students are able to simplify their mathematical models by making stated assumptions. Lastly, students innovate by demonstrating a broad range of math skills in the creation of their models. Every team uses multiple equations to describe the shape of their birdies, but the types of equations come in many forms. 

Instructor commentary | Mr. Jesse D'Oliveira

In many traditional math classes, getting the answer via a prescribed method is what’s being tested, but this project allows the students to find their own path, by receiving minimal direction, but with detailed instruction related to the expected results. This freedom to explore produces a vast array of solution paths, which impresses not only myself but also those spectating. The students aren’t required to do unnecessary research to find new solutions but are enabled to draw upon all avenues of prior knowledge in a team setting to find unique solutions. This project allows students to further develop the core values of Dalton Academy, such as creativity in the design of their project, responsibility in the role each team member plays, and integrity in presenting authentic individual work. As the first run of this project, I am not only impressed by these students but privileged to have them in my course!

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