IPTS Standard 1 | Content Knowledge
The competent teacher understands the central concepts, methods of inquiry, and structures of the discipline(s) and creates learning experiences that make the content meaningful to all students.
Wyzant Tutoring Website -- Math Resource Section
During the summer of 2010, I worked for a tutoring website that connects students to tutors all over the nation. My job was to oversee the development of the math help section as a resource for both students and teachers. I personally created the Calculus section and made modifications to the Algebra and Pre-Calculus sections. The lessons are designed to be easy to follow, informative, and interactive. This section of the website is a great resource for learning both step by step procedural knowledge, but also understanding the big ideas behind each concept. In the Calculus section, I give a brief description of the history of calculus, how it relates to other big math topics, and how we use calculus in various applications. All of these lessons are detailed with constructed images and practice problems for the visitor to test their comprehension.
The development of this math resource section requires a deep understanding of mathematics content. To construct the lessons, I made sure to use multiple representations of the topics and explain the overall ideas behind the procedures. The lessons are designed so that students can easily see the connections between mathematical ideas and take away some new knowledge about the math that they may have not seen before from their math textbooks. For instance, in the Quadratic Equations Section of Algebra, I present the lesson so that the reader discovers how quadratic equations can be constructed from linear equations, a connection that is not usually taught in Algebra classes. Before starting each lesson, there is a brief description of what terms and ideas you should know before moving on. At the end of each section, there may be an interactive review to test for comprehension, and a summary of the main ideas covered. My lessons also have motivations for the material and address common misconceptions that students may have in their math classes. An important aspect of understanding the math content is the structures behind it, and in my lessons I explain not only the how, but the why behind each concept. This way, the content becomes more meaningful to the students.
A crucial aspect of being a competent teacher is having deep knowledge and understanding of your content area. As a math teacher, I have a passion for the mathematics and continue to explore these topics as I teach them to my students. Because of this, I plan to have my students engage in their learning, pose their own problems, make conjectures and discoveries, allow them to be wrong, to have inspiration, and to question. I will not use my knowledge of the mathematics to tell my students what is right and wrong, but rather to ponder and be comfortable with uncertainty. Out of this, the students can feel the satisfaction of discovering knowledge that is new to them, which can be a truly meaningful learning experience. I plan to build an honest intellectual relationship with my students. They will be given ample opportunities to become active and creative mathematical thinkers. Since I believe I have a deep level of knowledge and passion for mathematics, I will have the ability to be open, to talk and listen to my students, and to share excitement and a love of learning.