How does a high school math teacher make parabolas come to life?

By asking his students to make parabolic cookers!

June 12, 2015

Parabolic Cooker Title FrameHigh school students everywhere learn about quadratic equations and parabolas, but most will learn their lessons on white boards, or by solving problems with pencil and paper.

At Nueva, math students were challenged to take their theoretical knowledge of parabolas and design parabolic cookers that could boil water.

The inspiration for this project came from two sources. In true Nueva fashion, math teacher Mike Peller put two seemingly unconnected thoughts together to build curriculum that would move his Math II students from the classroom into the I-Lab and bring abstract math concepts to real-world problem-solving. After making observations during the 2014 ninth grade trip to Peru, Mike connected the country’s shortage of potable water with his own past vacation experience trekking in Nepal, where he saw many parabolic cookers in use. Why not have the students build cookers?

 

 

What does this mean? Simply stated, students were asked to take their understanding of the algebra and geometry behind parabolas — simple curves in 2D space —

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and develop a design for a functional paraboloid, a 3D structure that is, in its essence, a parabola rotated on its axis of symmetry (z in the diagram).

VIDEOS

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Math teacher Mike Peller describes the project

 

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Math teacher Mike Peller talks about teamwork

 

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I-Lab teacher George Jemmott describes one team’s design

 

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Student Jeremy T. describes how he made a cooker

 

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Of course, there are many types of paraboloids, but for the sake of this description, you get the picture.

A diagram or graph did not satisfy this project’s requirements. Students had to design a real structure that would use solar energy to boil 500 ml of water to the point that it was suitable for drinking. That means the parabola and its connected container of water must be appropriately positioned to reflect and absorb the sun’s heat. Mike also required students to make the cookers maneuverable, packable, producible, and aesthetically pleasing, all reasonable requirements before they could be useful.

Math class? Isn’t this topic more appropriate in science class, one might ask? Isn’t building full-scale models more suitable in a design engineering class? Isn’t the understanding of potable water concerns in remote places of the world more of a humanities concern?

Well, yes to all of those questions, but at Nueva, it was just another day in math class!

To put your mathematical minds at rest, this was the end of a longer unit of study covering foundational topics.

  • Operations of functions
  • Review of circles and binomials
  • Geometric understanding of parabolas
  • Volume of a paraboloid
  • Area, surface area, and volume of unknown shapes
  • Solving quadratic equations

And, scientifically speaking, one needs to understand that a properly designed paraboloid can harness the thermal energy of the sun by focusing its energy on one point. Depending upon the construction and materials used, it can create sufficient heat at that point to bring water to a boil. In some areas of the world, such units are currently used to generate energy for electricity or cooking.

Garnering heat and using it to boil water was the main objective of the project. The project required student teams to employ Design Thinking methodology to research requirements, focus their findings, and reach consensus in their team about the ideal design. From there they built prototypes; determined, measured, and purchased materials; and went to work constructing their cookers.

While students did some background research, originality in design was expected, and copying models available on the Internet was prohibited. In addition, teams were required to use equations to explain their shapes, and had to also program mathematical models and create contour maps using computational software, thereby keeping the academic underpinnings of the project always present.

According to Mike, all of the students were faced with a fundamental challenge: how to take their current two-dimensional understanding of quadratics and solve a three-dimensional problem. At various points each team struggled to account for the curved 3D shapes they designed with their current level of mathematical knowledge. By thinking through the challenge, they were skirting the conceptual edges of calculus.

And this is where Nueva’s constructivist model shines the brightest. Students actively applied their knowledge and constructed new knowledge based on their designs, their collaboration with teammates, their questioning skills, and their actual results. Mike’s work during the build phase in the I-Lab was to help students test their ideas and to guide them to practice inquiry, observation, modeling, testing, and feedback when they hit roadblocks.

As an anchor, frequent classroom assessments of the fundamental math principles ensured that each student had a solid grasp, and in Mike’s observations, the math theory became ingrained through the project, even easy, because students were stretching the boundaries of their knowledge through application.

The creativity demonstrated in design and building was impressive. Some teams’ paraboloids showed vertical orientations, looking like upside-down umbrellas to observers. Others used a horizontal approach using strips of reflective material within a shell to capture the sun’s energy, and one team created a parabolic trough that heated the water held within a stretch of pipe. In the end, heating 500 ml of water to the boiling point of 212° Fahrenheit proved too difficult, but teams successfully achieved temperatures ranging from 75° to 154° — after just 10 minutes in the sun!

As is usual at Nueva, students cemented their learning through reflections on the project, including their thoughts about the effectiveness of their creations for use in Peru based upon their recent trip there. Students shared their surprise at how much their understanding of 3D geometry improved, the fun they had using mathematical modeling, and the challenges of applying modeling to actual designs. Many commented on improvements they would make if asked to build another cooker, and everyone found personal growth in collaborative teamwork.

Please view our videos on the right side of this page to share the excitement!

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