As a secondary subject, society often views mathematics as a core subject that students must learn to succeed. Often, mathematics serves as a gatekeeper to higher learning and some specific careers. Since the time of Plato, “mathematics has been virtually the first thing everyone had to learn… common to all arts, sciences, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; advanced mathematics was reserved for those who would serve as the city's “philosophical guardians” (Stinson, 2004). In the 1900s in the United States, mathematics found itself becoming a cornerstone of the student curriculum. National reports throughout the 20th century solidified the importance of mathematics to the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role in educating all students about mathematics is important. My personal mathematics teaching philosophy – including the optimal learning environment and best practice teaching strategies – motivates my teaching strategies in my personal classroom. Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics and trigonometry – and at the same time teach their students mathematical skills: logical thinking, formal process, numerical reasoning and problem solving. In teaching my students, I must aspire to Skemp's (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow sequential steps and procedures without any real understanding of the mathematical reasons for the process...... half of the paper ......S. and Stepelman, J. (2010). Teaching Secondary Mathematics: techniques and enrichment units. 8th edition. Merrill Prentice Hall. Upper Saddle River, NJ. Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26. Retrieved from: http://math.coe.uga.edu/olive/EMAT3500f08/instrumental-relational.pdfStinson, D. W. (2004). Mathematics as “guardian of the gate” (?): three theoretical perspectives that aim to give all children the key to the gate. The Mathematics Educator, 14(1), 8-18. Retrieved from http://files.eric.ed.gov/fulltext/EJ848490.pdfTowers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M. L. Fernandez (Ed.), Proceedings of the Annual Meetings of the North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.