It is important for students to grasp the concepts of geometry and symmetry as a means of exposing them to things they see everyday that aren't obviously related to mathematics but have a strong foundation in it. Examples of people whose careers that incorporate these ideas are artists, craftspeople, musicians, choreographers, not to mention, mathematicians. People use concepts of symmetry, including translations, rotations, reflections, and their geometric figures and patterns as part of their careers. We see symmetry everyday but often don't realize it. It creates patterns that help us organize our world conceptually. Symmetry is a fundamental part of geometry, nature, and shapes. If they master these skills, I will need to teach them how to approach geometry in an investigative manner using such techniques as collaborative learning exploration and problem solving to formulate, test, and locally prove or disprove conjectures and written and oral assignments to develop effective communication skills and such tools as physical manipulatives, models, and software. I will have to teach my students the fundamental parts of geometry, nature and shapes. Of course, I have to begin my instruction "where they are." This means that I will not have the advantage of merely working on the concepts and strategies. Most of the time, there is a great difference between what the students need to know to "get started" and what they actually know. One of the domains that my students have consistently performed poorly on is Geometry and Measurement.Įach year, students come into my classroom who are supposed to possess skills that are prerequisites for the math activities that I teach. Sometimes, students can pass the test while doing poorly on specific domains. If students meet standards according to state test, schools are viewed as successful and the stress in "passing the test" is put off for another year. Since NCLB has come into existence, for student outcomes, there is not much that matters except for their standardized test scores at the end of each school year. Some of these deficiencies can be positively affected in the classroom, some cannot. I have taught in under-resourced, urban areas and my students come with various academic deficiencies. They are 86% African American, and 75% are eligible for free or reduced lunch. I teach in a school district with approximately 23,000 students. It is my hope that implementing this curriculum unit will help teachers to teach geometry in a way that will excite students, assist their connection and application of "real world" scenarios to the concepts, aid their use of various strategies, and extend students' abilities to solve math problems in other contexts. I have tried to develop a series of lessons that will help teachers develop various strategies to teach geometry, with the help of symmetry, in their classrooms. Some people look at wallpaper and go "wow! That's an incredible pattern" but mathematicians see wallpapers and go "hmm! What's the fundamental domain? What type of symmetry can be found here?" among others. It is also one of the most important when it comes to the topic of geometry. Wallpaper is an example of a real world item that is seen everyday in most homes across the nation. I do not dispute these reasons for students' failure, but I propose that there is a way to ensure that geometric concepts, especially transformations and symmetry, permeate the mathematics classroom while, at the same time, maintaining student interest. These reasons include students' lack of exposure to life outside of their neighborhoods, minimal visual skills, and difficulty in understanding basic geometric concepts. Many reasons are suggested or put forward for the students' lack of success in this area. Many students have difficulties when attempting to solve geometry problems. Geometry and the Real World by Shamsu Abdul-Aziz Introduction
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