During my teaching and coaching career, I have been told by the students in my classroom and by those I prepare for competitive mathematics that they learn many more concepts from me than from their other teachers or coaches in the same amount of time. Since I self-analyze, I have concluded that there are several factors that can explain their observations. At the beginning of each school year, I develop an outline that states the concepts students need to master. When writing the outline, I prioritize the concepts that need to be tackled first to ensure that the foundation needed for success is firmly in place. When I teach these concepts, I make sure that each one is subdivided into subtopics, a technique that will give students the best opportunity for mastery.

In addition to developing an outline, I believe I am also creating a roadmap which my students can use to be successful in other courses as well. When preparing students for a mathematics contest, I set individual goals for each one. Every student is made aware of target scores they will pursue. They are told that these scores are achievable through hard work and practice. When teaching concepts, I provide students with step-by-step solutions to numerous examples. As appropriate, common errors are integrated into the lessons. I also make sure that I offer them different variations of the problems they need to master. Of all the factors that contribute to the successful teaching of so many concepts in such a short period of time, the most important is my commitment to continually attempting to find the best way to teach the material in a course or in an individual mathematics event (number sense, calculator applications and mathematics).

My desire to grow as a teacher was fueled by my decision to become a teacher when I was six years old. Since my involvement with number sense in 1965, I have developed thousands of shortcuts to solutions for mathematics problems from the basic level to calculus. This means that I have been actively engaged in searching for the easiest way to solve mathematics problems for more than 50 years. Few teachers possess this experience and knowledge. Integrating methods developed with my work in number sense has had a positive impact on my career as a classroom teacher, mathematics coach and current online tutor. Number sense knowledge allows me to teach more concepts in less time. It gives me the opportunity to present more examples, common errors and problems beyond the various applications taught by your average math teacher. Number Sense knowledge allows me to mesmerize students with the magic of mathematics.

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