Rationale
Geometry is a very important aspect of many of the standardized tests that have become so important to school districts throughout the United States. On standardized tests, the concepts are often not so straightforward, but are hidden within other concepts. Some students will automatically give up when they see such questions. Others that know the concept have a difficult time trying to relate it to other concepts and hence are not able answer the questions. By developing the confidence and the skills to tackle geometry and measurements, students will not only improve their math skills with the four basic operations, but will also hopefully transfer their knowledge to other mathematical areas. A key feature of this unit is that students will be required to spend considerable amount of time looking at various isometries. Through this exposure to isometries, not only are the students going to be more knowledgeable about these transformations and understand the main facts about them, but will also hopefully transfer their knowledge to other mathematical areas.
There are several articles in mathematical journals, written by professionals in the field, which expresses the need for teaching symmetry and its properties as a part of the math curriculum. Several articles focus on the different ways of teaching the same concepts and others concentrate more on the tools we have available that link us to technology. All of the articles that I have come across support, at a superficial level, the understanding that symmetry is all around us, and although it doesn't seem to be in mathematics, in fact, it involves very serious mathematics. According to Pumfrey & Beardon (2002), art and math go hand in hand. The connection has been there for a long time as we can trace the inspirations of mathematicians as a "product of the Islamic civilization brought to Europe by the Arab conquests in Spain in the thirteenth century". This relates specifically to tessellations that are a result of rotating, reflecting, and sliding objects in a plane so that there are no gaps or overlaps. Pumfrey & Beardon (2002) sum it up when they state "tessellations are a common feature of decorative art and occur in the natural world all around us."
Comments: