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Tiling with polyminoes
The objective of this graduate thesis is to introduce the idea of tiling rectangular boards made up of squares with polyominoes. It is intended to present the abstract idea and the complexities of polyominoes through a simple mathematical application that can be used in any mathematics high school classroom. Mathematics is probably one of many, if not the only, subject that is misunderstood by many people in the world. The misconception comes because people believe that mathematics is about computations and memorization of formulas, and because we as teachers present the subject as a series of complex problems. But the reality is that in the real world, mathematics plays a completely different role. Real world problems are part of a broader context and in the real world situations, individual problems are not that terribly difficult. Mathematicians currently find ways to relate mathematical ideas into real world and suggest real life applications on textbooks to teachers of all different levels. Hence, the idea of this thesis is to minimize the misconceptions of mathematics. As a mathematics teacher, I feel it is important to join the quest to help ease the frustration of many students and teachers when learning and teaching mathematics. Therefore, this thesis aims to stimulate the student's interest and abilities to learn mathematics and to become better thinkers in broader mathematical terms.