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Michele Jastrzembski H-Option Fall 2008 Technology in the Classroom Topology: Things Aren’t What They Seem Essential Questions: How does topology appear in the world around us? Why is a möbius strip special? Though rare that an elementary or middle school curriculum would include the topics of möbius strips and topology, it is a really fascinating mathematical phenomenon and can be used in conjunction with other subjects. Despite the study of topology having many higher level concepts, it is surprisingly easy for younger students to grasp. Since they haven’t been exposed to the strict rules of geometry to the extent that older students have, they are more open to the concept of distortions. I have found that because investigating möbius strips is not your typical arithmetic math activity, students, especially those that are kinesthetic or visual learners, are very adept at the topic and get excited by this hands-on activity. The movie is meant to be an interactive introduction to the concept of topology for upper elementary or middle school students. It uses questioning techniques to get students thinking on their own and then share with each other through active and cooperative learning. This encourages critical thinking. Furthermore, the movie incorporates activities for various learning styles: using playdough and models for the kinesthetic and tactile learner, close-ups for the visual learners, and the audio from the movie for the auditory learner. Lastly, the movie can be simply a starting point for group work, differentiated instruction, and assessment. When using this movie in a classroom setting, the teacher should use it to facilitate discussion. For example, when questions are asked or when the movie tells you to make a prediction, pause the movie and have the students discuss and write down their answers (see recommended worksheet). Have the students experiment with different distortions and as the movie tells you to make a möbius strip and then to cut it, do it as the movie does. To follow-up on the movie, the class should talk about how topology is used in life. For instance, the movie mentions kicking off the sheets in morning but doesn’t say how this is topological. Then, the discussion of topology can continue with more concrete topological concepts like Jordan Curves and what is significant about the MC Escher paintings used in the credits. The movie is intended to be adapted to best fit the needs of the classroom, the teacher, and the lesson.