Expert Corner: Piecewise Functions A Great Year for GizmosWe stepped back to look at what we had accomplished in 2010, and we found it was a banner year for Gizmos! Last year our dedicated Professional Development staff trained almost 14,000 teachers. These teachers either took part in one of our recommended initial training sessions or helped build their ability to integrate Gizmos into their curriculum. Our customized programs of support now include onsite consultations, curriculum alignment assistance, and project management services. Visit our Training page for more information. Gizmos are now helping to improve instruction in classrooms all over the world. We are in all 50 U.S. states and more than thirty other countries. We hope 2011 will be even better! Expert Corner: Piecewise FunctionsBetty Korte is a Regional Professional Development Manager for ExploreLearning. Her credentials include 17 years teaching mathematics, with 14 years as the department chairperson, and a M.S. in Education with an emphasis in teaching mathematics. One of the most exciting aspects of Gizmos is their versatility. I recently watched a colleague demonstrate the Rainfall and Bird Beaks Gizmo and participated in an excellent discussion on natural selection. I thought that a statistics teacher could use the very same Gizmo to study distribution and variance. I worked with the Fraction Artist Gizmo at the elementary math level recently as well, visualizing a high school teacher using the simulation to introduce infinite geometric series (with |r| < 1) in Algebra II. The Distance-Time Graphs Gizmo has a seemingly endless array of pre-Algebra and Algebra applications, from graph sense to linear theory. Its strength lies in its simplicity. Students discuss (or model) the actions of the runner relative to the graph. Through these discussions, they construct meaningful definitions for such abstract concepts as rate of change, y-intercept, and parallel lines. Because the runner can change speeds and direction during the simulation, higher-level concepts can also be introduced. For instance, an Algebra II topic that challenges many students is piecewise functions. A piecewise function is simply a function whose definition changes depending on the input value. In theory, this is not difficult for students, but the notation can be overwhelming, especially if it is presented too early in the learning process. A better way to structure the learning is to allow the students to develop a concrete understanding of the function and then move to the abstract formulation. Students first create a scenario where the runner changes speed or direction during the simulation. They describe what they see in words then translate these descriptions into algebraic sentences with increasing precision. Once this step is complete, they are ready to use the complex notation that defines the function. Because they construct the notation themselves, it no longer seems difficult. Students should also be able to come full circle and create a graph or scenario from the notation. Watch the video "Using Distance Time Graphs to Study Piecewise Functions" for further details. Apart from the stated lesson objectives and the curriculum correlations, there are many more "outside the box" uses for Gizmos. Gizmo Educator of the MonthJeffrey Rich teaches several levels of Environmental Science and Biology at Edward H. White High School in Jacksonville, Florida. He has been teaching high school science for five years and is also on the adjunct faculty at nearby Fortis College. Jeffrey is also a track and cross country coach. He recently started using Gizmos and has become an avid fan. “I have only been involved for a short time, but the way my students are engaged in them and the way they help me explain a topic is priceless.” Jeffrey used the Diffusion Gizmo to help his students understand why diffusion takes place. After a hands-on experiment, he turned to the Gizmo to enable his students to visualize what was happening at the molecular level. Immediately, his students could see that the molecules' constant motion enabled them to move from one area to another without the help of an external force. Mr. Rich has already contributed several shared class Gizmo lists and Lesson Materials to the ExploreLearning community. Two of his lists are on cell structure topics and include the Diffusion Gizmo. Subscribers and free trial users can check out his contributions for ideas on how to incorporate this Gizmo and other Gizmos into their teaching. Gizmo Lesson Materials, recommendations, and Shared Class Gizmo Lists are available to ExploreLearning subscribers and free trial users, based on "What I Teach" settings. They are customized just for your teaching! Watch the Community Features Overview for more information. You can learn more about ExploreLearning and Teaching with Gizmos in our Video Library as well. Flip Camera WinnerCongratulations to high school science teacher Kimberly Samson from Michigan, who won our December Holiday Card Contest! We hope she'll use her new Flip camera to post a shot of her students using Gizmos. And if you have photos or video of Gizmos "in action," please share them on the ExploreLearning Facebook or YouTube pages. We always love to see students and teachers benefitting from Gizmos.
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