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Parabolic mirror: focusing on science, technology, engineering, and math.


"It is the union of science, mathematics, and technology that forms the scientific endeavor that makes it so successful. Although each of these human enterprises has a character of its own, each is dependent on and reinforces the others" (AAAS, 1990). Operating from this premise, teachers at State College Area School District's Park Forest Middle School (PFMS) formed an interactive science, technology, engineering, and math (STEM) education team. Integrative STEM Education is defined as the "the application of technology/engineering design-based pedagogical approaches to intentionally teach content and practices of science and mathematics education concurrently with the practices of technology/engineering education" (Sanders, 2008, 2008, 2012).

In the fall of 2011, PFMS students approached the STEM faculty with numerous questions regarding the popular television show Myth Busters, which detailed Greek mathematician, physicist, engineer, and inventor, Archimedes. Two episodes featured attempts to test historical accounts that Archimedes developed a death ray based on mirror/ mirrors concentrating the sun's radiant energy into a tactical weapon. The device was then deployed to defend the island of Syracuse from Roman naval attack in 214-212 BC. The faculty instantly recognized the potential of the students' fascination and redirected it into a motivational STEM project. The PFMS Integrative STEM staff was not alone in acknowledging the aptitude of the idea, as First Energy Corporation,, and McDonalds Inc. generously provided financial support for what would become a cutting-edge STEM endeavor.


"Few educators would argue with the premise that student motivation is an important influence on learning. Motivation is of particular importance for those who work with young adolescents. Considerable research has shown a decline in motivation and performance for many children as they move from elementary school into middle school" (Eccles & Midgley, 1989). Student motivation in fields of study plays a key role in success, comprehension, retention, and application (Alexander, Jetton & Kulikowich, 1995). Studies have shown that making science and engineering interesting can demonstrate positive results in achievement (Baird, 1986; Wigfield, 2002). Additionally, research has revealed that integrating science and math can have a positive impact on students' interest and motivation in academic achievement (Furner & Kuman, 2007; Stinson, Harkness, Meyer, & Stallworth, 2009). Of greater importance is that students' interest can be connected to deeper levels of learning as compared to surface learning (Eccles & Wigfield, 2002). At PFMS, science, technology, engineering, and math are not force-fed through memorization, but rather applied in hands-on manipulation of the concepts. Student-centered STEM projects have proven to spark motivation and scientific/mathematical curiosity on our campus. More than a century ago, Dewey asserted that children must connect with the curricula if effective learning were to take place (Dewey, 1902). Putting it in straightforward terms "Long before the rules were codified in textbooks, people engaged with these disciplines to exercise one of the defining characteristics of our species: our ability to construct things we need to understand and function in our lives." (Honey & Siegel, 2011).


"The supply of secure, clean, sustainable energy is arguably the most important scientific challenge facing humanity in the 21st century. Among renewable energy resources, solar energy is by far the largest exploitable resource, providing more energy in one hour to the earth than all the energy consumed by humans in an entire year" (Lewis & Norcera 2006). There are numerous methods to directly harness the sun's energy. The most common ways are solar voltaic and hot-water-circulating panels. Gaining increased attention by scientists, engineers, and governments is a method that involves concentrating and storing the sun's radiant energy via parabolic mirrors (New York Times, 2008).

With rapid advances in electronics, large antiquated satellite dishes have become readily available for experimentation and research. Recycling parabolic reflectors or dishes for use in parabolic mirror research/experimentation has been gaining popularity both in the scientific community and among STEM-education-savvy teachers.


A parabolic reflector is a device used to collect or project energy such as light, sound, or radio waves. In this case, radiant heat is collected from the sun. The surface is roughly that of a parabola revolving around its axis. The parabolic reflector transforms an incoming plane wave traveling along the axis into a spherical wave converging toward the focus. The spherical wave generated by a point source, or focus, is then transformed into a plane wave propagating as a collimated beam along the axis. Parabolic reflectors are quite common, since the principles of reflection are reversible; some examples include spotlights and car headlights (Fitzpatrick, 2007).

A large satellite dish with a diameter of 120 cm was converted into a parabolic mirror with the idea that it could collect light to test the story of Archimedes as well other uses such as a solar cooker. The process was a student-led, inquiry-based integrative STEM education project that began with research and culminated in testing the parabolic mirror. First, the fiberglass satellite dish was cleaned, sanded, and painted black to prepare it for the transformation to a parabolic mirror. Then, a two-layer reflective tape obtained from Green Power Science was added to the satellite dish in overlapping two-inch wide strips. Once the dish was completed, students found the focus of the parabolic mirror both mathematically and in practice. Mathematically, students wrote the equations of a parabola to find the relationship between the diameter, D, the depth, d, and the focal distance, F, of the dish and found that:

F = D2 / 16d

The students found the focus of the mirror both mathematically and through gathering empirical data. Because of the large size of the mirror and the potential danger to the students, the focus of the parabolic mirror was tested indoors. The method used was to take chalk dust and fill the space over the parabolic mirror while sending the light from three laser pointers through the dust to reflect off the mirror--where those lasers converged was the focus of the mirror. Both mathematically and in practice, the focus of the mirror was at 73 cm.


As students became mathematically/scientifically conscious with parabolic mirrors, instructors steered them toward locating historical inquires concerning the Roman siege of Syracuse and searching out literature outlining others who might have tested the story of Archimedes' heat ray. Working backwards, they reviewed the Myth Busters programming conclusions that such a device would not have worked. Disappointed but undaunted, they dug deeper and discovered an article in the November 26, 1973 issue of Time Magazine entitled: "Archimedes' Weapon." A Greek scientist named Ioannis Sakkas had conducted an experiment near Athens with (70) 1.5 by 1m copper-coated mirrors. The mirrors were focused on a wooden mock-up of a Roman ship at a distance of 50 meters. After just a few seconds, the ship burst into flames!

More recent literature revealed that in October 2005 a group of students and professors from MIT had conducted a similar experiment with (127) 30cm square mirrors. Focused on a wooden ship model at a range of 30 meters, it instantly started smoking and burst into flames after 10 minutes of exposure (Archimedes Death Ray: Idea Feasibility Testing. October, 2005).

Other students explored the type of ships the Romans would have been sailing in 214-212 BC and, more specifically, what types of materials would have been used in their construction. An interesting anomaly arose. The scientist in the 1973 experiment utilized plywood for his target model. Both Myth Busters and MIT had used oak. Student research indicated that Roman ships of that era would have been made from cedar, pine, and larch. In addition, the hulls would have been coated in pine tar and the decks preserved with beeswax. One student commented, "The entire thing seems very flammable." Students with historically correct building materials constructed a three-dimensional scale model of a period-correct Roman Trireme. It would serve as a target to conduct a feasibility test of Archimedes' "Death Ray"-type weapon.

Owing to the winter months' cold temperatures and a low solar angle, students and teachers utilized the parabolic mirror inside to experiment with low-powered lasers and solar voltaic panels. Weather, and particularly the changing angle of the sun, became daily focal points of student interest, as they desired to test the device they had created. April was incessantly cloudy, and finally in mid-May we could hold back the students' enthusiasm no longer. Under a high degree of faculty supervision, the parabolic mirror was set up in clear view of the sun. The optimal spring seasonal angle of the sun was determined mathematically by taking the latitude of State College, Pennsylvania (40 degrees, 47' 35"N) and subtracting 2.5 degrees. Owing to the experiments and mathematical calculations done over the winter months, the focal point was well identified. As an overture to the big event, a pine board was placed in the convergence point. It instantly started billowing smoke. In a few moments, a hole was torched entirely through the .75-inch thick board. Students cheered. Next, the students' scale model was hoisted into the mirror's focal point. Instantly smoke and flames erupted from the side of the ship's hull. I am certain when parents asked their children what they did at school today not a single one responded: "nothing."

Presently, a new group of students are exploring heat transfer of copper, steel, aluminum, and brass as materials for modifying the mirror into a solar oven. Clearly the long-term use of the interactive STEM project is proving as bright and powerful as the sun itself. We believe one day our students will capitalize on their experiments to help develop clean, sustainable energy for society.


The following technological literacy standards (ITEA/ITEEA, 2000/2002/2007) are obtainable as a result of the concepts offered in this article.

STL 3: The relationships among technologies and the connections between technology and other fields

STL 8: The attributes of design

STL 10: The role of troubleshooting, research and development, invention and innovation, and experimentation in problem solving


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Sanders, M. E. (2008). Integrative STEM education: A primer. The Technology Teacher, 68(4), 20-26.

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Stinson, K., Harkness, S., Meyer, H., & Stallworth, J. (2009). Mathematics and science intergration: Models and characterizations. School Science and Mathematics. (109)153-161.

William Hughes is a technology and engineering teacher at State College Area Schools' Park Forest Middle School where he also serves as the Integrative STEM Chairman. He can be reached at whh11@scasd. org.

Karianne Smith is an eighth grade science teacher at Park Forest Middle School She is a Penn State graduate in Meteorology (B.S. 1998) and the Earth Sciences (M.Ed. 2005). Prior to teaching, she was a forecast and broadcast meteorologist for AccuWeather.
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Author:Smith, Karianne; Hughes, William
Publication:Technology and Engineering Teacher
Geographic Code:1USA
Date:Nov 1, 2013
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