As a secondary subject, society often views mathematics as an essential subject that students must learn to succeed. Often, mathematics serves as a gatekeeper for access to higher education and certain specific careers. Since the time of Plato, “mathematics was virtually the first thing everyone had to learn… common to all the arts, sciences, and forms of thought” (Stinson, 2004). Plato held that all students should learn arithmetic; advanced mathematics was reserved for those who would serve as the city’s “guardian philosophers” (Stinson, 2004). In the 1900s in the United States, mathematics became a cornerstone of students' school curriculum. National reports throughout the 20th century solidified the importance of mathematics to the success of our country and its students (Stinson, 2004). As a mathematics teacher, my role in educating all students in mathematics is important. My personal philosophy of teaching mathematics – including the optimal learning environment and the best teaching strategies – motivates my teaching strategies in my personal classroom. Math teachers teach their students a wide range of content areas – geometry, algebra, statistics and trigonometry – while also teaching 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 instrumental understanding, students know how to follow sequential steps and procedures without a true understanding of the mathematical reasons for the process...... middle of article ......S. and Stepelman, J. (2010). Teaching secondary school mathematics: enrichment techniques and units. 8th ed. Merrill Prentice Hall. Upper Saddle River, NJ.Skemp, R.R. (1976). Relational understanding and instrumental understanding. Teaching Mathematics, 77, 20-26. Retrieved from: http://math.coe.uga.edu/olive/EMAT3500f08/instrumental-relational.pdfStinson, D.W. (2004). Mathematics as “guardians” (?): Three theoretical perspectives that aim to give all children a key to open the door. 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.