Exploring the Solar System? Let the Math Teachers Help!

By Charles, Karen; Canales, J. D. et al. | Science Scope, February 2012 | Go to article overview

Exploring the Solar System? Let the Math Teachers Help!


Charles, Karen, Canales, J. D., Smith, Angela, Zimmerman, Natalie, Science Scope


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Scale measurement and ratio and proportion are topics that fall clearly in the middle-grades mathematics curriculum in our state, Texas. So does the solar system. In addition, the National Science Education Standards include the solar system in Earth and space science in the 5-8 grade band and promote the coordination of the science and mathematics curricula in Program Standard C (NRC 1996). In its chapter on Earth and space sciences, the new Framework for K-12 Science Education (NRC 2011) references Earth's place in the solar system and notes that these sciences "involve phenomena that range in scale from the unimaginably large to the invisibly small" (p. 121). But, as middle school mathematics teachers, we had never considered the connection until we participated in a weeklong academy offered by NASA this past summer in our school district. The academy encouraged middle and high school math and science teachers to consider how using models and simulations, or ModSim, could expand their repertoire of classroom strategies and engage students more fully in their own context-rich learning.

Through our work at the academy, we designed a cross-curricular lesson that incorporates the math skills we need to teach and the science concepts our colleagues teach their students, and uses ModSim to engage and challenge our students. We discovered that NASA was more than willing to help teachers like us upgrade our lessons with web-accessible materials and resources, many of which we will introduce the reader to in this lesson.

Scale, proportion, and ModSim

In our experience, we have found that students have trouble manipulating, much less comprehending, very large numbers and very small numbers. These concepts can be brought into students' realm of understanding through scale--scaling down very large objects and scaling up very small objects to develop models that can be seen and manipulated. Research by Schwarz and White (2005) found that activities ? requiring the creation and testing of models facilitated the learning of science concepts for the middle school students in their study.

A state map, for example, is a tool that students readily understand as a scaled-down model of a state's geography. Toys, such as trucks, trains, dolls, and action figures, are common examples of scaled-down models of real-world objects. So we assume that students understand the concept of scale, but we also know that the mathematics of scale, especially with large numbers, is a challenge in the middle grades. We believe that a concrete demonstration of scale and the opportunity to manipulate scaled objects should precede learning the related mathematics if large numbers are involved.

Another obstacle in teaching scale and ratio and proportion is finding an exciting context for the mathematics. Realizing that our middle school science colleagues were teaching the solar system while we were teaching scale, we hit upon the idea of enhancing their content with our mathematics. After all, who hasn't seen a bad model of the solar system, with disproportionate planet sizes and distances? Let the math teachers help!

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Our goal was to develop a three-to-five-day unit that would refresh students' measurement skills, link those skills to the concepts of scale and proportion, and introduce the real-world applications of these concepts by using modeling and simulation to interest our students in our continued study of ratio and proportion. As part of the engineering design process, engineers use modeling and simulation after they define problems and generate and evaluate possible solutions. They assess their solutions by building models that can be tested repeatedly under a variety of simulated circumstances until the engineers can confirm the success or failure of the model. The benefit is that there is no cost or danger in running a simulation hundreds, thousands, even millions of times.

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