Rationale
Symmetry is everywhere. That may seem like a broad generalization, but it is true. People see reflections in the mirror every morning, wallpaper patterns as they sit and eat their morning cereal, traffic signs like the regular octagonal stop sign and the equilateral triangle yield, and frieze patterns on the buildings on their way to work. The students in my class are seeing the same things, and are probably paying more attention to how these kinds of patterns make them feel about what they are looking at than I do. Tapping into the child's natural curiosity about the world around them, and creating a deep connection with their life and what they are learning in school is a powerful teaching opportunity that I feel shouldn't be overlooked. This unit is designed to help make these kinds of connections with the real world, as well as make the subject matter more cohesive.
Symmetry, as a main idea, seemed very basic to me as an elementary school teacher. Before I participated in this seminar, my knowledge was limited to "line and rotational" symmetry. However, I feel that it is disadvantageous for me to approach symmetry in only these ways with my students. After learning how integrated symmetry is, not only to the understanding of the everyday world, but as it connects to science, art, and different aspects of geometry, I realized that I needed to increase my background understanding of this subject area to better serve my students. I also realized that it is imperative that I have an understanding of geometry as it relates to points and figures within a plane.
Before the unit begins, the students will have worked with geometry for several weeks. During this time I think it is important for them to build a working knowledge of the language of geometry. I have seen many instances in elementary school in which students learn mathematical concepts that are given more kid-friendly names for the sake of understanding. This allows them to work with an idea without having to understand the complicated language that may be attached to it. I believe that this works for awhile, but when the students are expected to become more sophisticated in their level of comprehension, sometimes this difference in language actually impedes their understanding. For my students, fifth grade is the appropriate year for them to start using more formal mathematical terms.
Therefore, I find that it is appropriate to maintain a level of expectation in my classroom in which students are expected to use the standard mathematical terms consistently. At first some of my students are apprehensive to do this, but as time progresses I find that this vocabulary starts to come naturally to them, and that students actually begin to correct each other when their peers do not use the more sophisticated words. In my experience in the classroom, setting up this level of expectation not only helps them understand the concepts better, but also makes the language of math more than just a vocabulary lesson.
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