Virginia Mathematics Teacher Fall 2016

for scientific inquiry and problem solving (e.g. Maeng, Mulvey, Smetana, & Bell, 2013; NRC, 2011; Windschitl, 2000).

refraction and wavelength. They summarized patterns in their data to explain their observations, which resulted in a formal statement of Snell’s Law (i.e. the Law of Refraction). PHET Simulations, developed by UC-Boulder, are a repository of free, downloadable simulations that address a variety of math and science concepts. In a parallel morning activity, teachers used a plastic block, a laser beam and a protractor to measure angles and verify Snell’s Law (Figure 1). This activity required some knowledge of sines and cosines, but could have also been completed just by making use of the Pythagorean Theorem. Knowledge of sines and cosines has the potential to help teachers in other mathematical applications of science (e.g. determining the work done when pulling a cart along a road with a handle inclined at a 45° angle from the road). Teachers discussed the affordances and limitations of simulations and generated resource

PD Context

Morning sessions during the summer institute involved teachers engaging in modeled hands-on activities to build their content knowledge and that they could easily modify to include in their own classroom instruction. Across the 10 days of the summer institute, teachers engaged in 43 different hands-on investigations of light and optics. Many of these investigations related to the reflection and refraction of light (e.g. VA SCIENCE SOL 5.3, 8.9, PH.8) and relied heavily on an understanding of angles (e.g. VA MATH SOL 3.15, 5.11, G.3, G.4). For example, teachers explored the ray model of light, in which light is represented as straight lines emanating from an object. Using a laser beam as a ray of light and a single plane mirror teachers investigated the Law of Reflection (the angle of incidence is equal to the angle of reflection). They also used multiple plane mirrors to track a ray of light over several reflections to locate the final image. Later, they used these same mirrors to understand how images are actually formed, which required additional math skills. Using protractors, they measured the angles of incidence and reflection and looked for patterns in how the angle of reflection varied with the angle of incidence (e.g. VA MATH SOL 3.19, 5.17, 7.13). Each activity teachers engaged in involved some combination of making measurements, performing calculations, creating and interpreting graphs, describing patterns, and made use of their knowledge of geometry and trigonometry. Afternoon sessions addressed practical aspects of classroom implementation of light and optics content using a technology-enhanced POE model. During this time, teachers learned strategies to effectively integrate simulations and animations to support students’ scientific investigations through modeled lessons designed to reinforce the content they explored during morning investigations. For example, in one afternoon activity, teachers used a PHET simulation ( https:// phet.colorado.edu/en/simulation/bending-light ) to explore the Law of Refraction. First, they predicted an answer to the question, “What happens to the speed of light as a light ray passes through different mediums (for example air into water)? Why? How might this affect what we see?” Teachers used the simulation to make observations by manipulating the media (i.e. water, air, glass) through which the light waves traveled and measured the angle of

banks of simulations and animations to support their teaching of light and optics content. They also developed and received feedback on lesson plans that incorporated these strategies that they could directly implement into their classroom science instruction. Finally, they discussed how they could integrate the POE inquiry model and educational technology in cross curricular ways. For example, because the PHET simulation included a protractor Figure 1. A laser beam is used to illustrate how a ray of light incident on a glass block is reflected from the block as a faint red ray and the main ray is refracted through the block. A protractor is used to measure the angles involved.

Virginia Mathematics Teacher vol. 43, no. 1

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